The flow of the atmosphere generally moves in a west to east direction. This, however, can often become interrupted, creating a more north to south or south to north flow. These scenarios are often described in meteorology as zonal or meridional. These terms, however, tend to be used about localized areas of the atmosphere (at a synoptic scale). A fuller explanation of the flow of atmosphere around the Earth as a whole can be found in the three-cell model.
Atmospheric flow
Troposphere
Troposphere | Atmospheric flow
Sorry. I cannot find the answer based on the context. The flow of the atmosphere generally moves in a west to east direction. The flow of atmosphere in a west to east direction. The flow of the atmosphere generally moves in a west to east direction. This, however, can often become interrupted, creating a more north to south or south to north flow.
what are the alternating dark and light bands in jupiter’s atmosphere called
user
Lightly colored "zones" and relatively dark "belts."
assistant
what is the atmosphere like in jupiter?
user
It is mostly made of molecular hydrogen and helium in roughly solar proportions; other chemical compounds are present only in small amounts and include methane, ammonia, hydrogen sulfide, and water.
assistant
how can you describe its structure vertically?
user
The atmosphere of Jupiter is classified into four layers, by increasing altitude: the troposphere, stratosphere, thermosphere and exosphere
assistant
what is the definition of the first mentioned layer?
user
The troposphere is the lowest layer of Earth's atmosphere, and is also where nearly all weather conditions take place.
assistant
what is the flow here like?
user
The flow of the atmosphere generally moves in a west to east direction.
assistant
are there different types of flow?
user
Yes, Zonal flow, Meridional flow and Atmospheric flow
assistant
how do you explain the first type of flow?
user
A zonal flow regime is the meteorological term meaning that the general flow pattern is west to east along the Earth's latitude lines, with weak shortwaves embedded in the flow
assistant
how is the third type of flow?
user
A zonal flow regime is the meteorological term meaning that the general flow pattern is west to east along the Earth's latitude lines, with weak shortwaves embedded in the flow. The use of the word "zone" refers to the flow being along the Earth's latitudinal "zones". This pattern can buckle and thus become a meridional flow.
Troposphere | Zonal flow
The flow of the atmosphere generally moves in a west to east direction. This, however, can often become interrupted, creating a more north to south or south to north flow. These scenarios are often described in meteorology as zonal or meridional. These terms, however, tend to be used about localized areas of the atmosphere (at a synoptic scale). A fuller explanation of the flow of atmosphere around the Earth as a whole can be found in the three-cell model.
Troposphere | Atmospheric flow
When the zonal flow buckles, the atmosphere can flow in a more longitudinal (or meridional) direction, and thus the term "meridional flow" arises. Meridional flow patterns feature strong, amplified troughs of low pressure and ridges of high pressure, with more north–south flow in the general pattern than west-to-east flow.
Troposphere | Meridional flow
In meteorological term regarding atmospheric circulation, zonal flow brings a temperature contrast along the Earth's longitude. Extratropical cyclones in zonal flows tend to be weaker, moving faster and producing relatively little impact on local weather. Extratropical cyclones in meridional flows tend to be stronger and move slower. This pattern is responsible for most instances of extreme weather, as not only are storms stronger in this type of flow regime, but temperatures can reach extremes as well, producing heat waves and cold waves depending on the equator-ward or poleward direction of the flow.
Zonal and meridional flow | Introduction
Zonal and meridional flow are directions and regions of fluid flow on a globe. Zonal flow follows a pattern along latitudinal lines, latitudinal circles or in the west–east direction. Meridional flow follows a pattern from north to south, or from south to north, along the Earth's longitude lines, longitudinal circles (meridian) or in the north–south direction. These terms are often used in the atmospheric and earth sciences to describe global phenomena, such as "meridional wind", or "zonal average temperature". In the context of physics, zonal flow connotes a tendency of flux to conform to a pattern parallel to the equator of a sphere.
Zonal and meridional flow | Introduction
As the secondary flow is drawn upward the air cools and its pressure falls, causing extremely heavy rainfall over several days.
Secondary flow | Tropical cyclones
The flow in these regions is the secondary flow. These regions are usually in the vicinity of the boundary of the fluid adjacent to solid surfaces where viscous forces are at work, such as in the boundary layer. In engineering secondary flow also identifies an additional flow path.
Secondary flow | Introduction
HydroGeoSphere assumes that the subsurface flow equation in a porous medium is always solved during a simulation, either for fully saturated or variably saturated flow conditions. The subsurface flow equation can be expanded to incorporate discrete fractures, a second interacting porous continuum, wells, tile drains and surface flow. The following assumptions are made for subsurface flow: The Richards’ equation is used to describe three-dimensional transient subsurface flow in a variably saturated porous medium: The fluid flux, formula_2, is represented by the Darcy's law shown as:
HydroGeoSphere | Groundwater Flow
Then the continuity equation and the incompressible Navier–Stokes equations reduce to The boundary conditions are no-slip condition at both walls and the third condition is derived from the fact that the volume flux injected/sucked at the point of intersection is constant across a surface at any radius.
Jeffery–Hamel flow | Flow description
There is a pressure gradient toward the center of the vortex. This gradient, coupled with the slower speed of the air near the earth's surface, causes a "secondary flow" toward the center of the tornado or dust devil, rather than in a purely circular pattern. The slower speed of the air at the surface prevents the air pressure from falling as low as would normally be expected from the air pressure at greater heights. This is compatible with Bernoulli's principle. The secondary flow is toward the center of the tornado or dust devil, and is then drawn upward by the significantly lower pressure several thousands of feet above the surface in the case of a tornado, or several hundred feet in the case of a dust devil.
Secondary flow | Tornadoes and dust devils
The third case is referred to as three-dimensional mixed convection. This flow occurs when the buoyant motion acts perpendicular to the forced motion. An example of this case is a hot, vertical flate plate with a horizontal flow, e.g. the surface of a solar thermal central receiver. While the free stream continues its motion along the imposed direction, the boundary layer at the plate accelerates in the upward direction. In this flow case, buoyancy plays a major role in the laminar-turbulent transition, while the imposed velocity can suppress turbulence (laminarization)
Combined forced and natural convection | Three-dimensional mixed convection
constant) term of the expansion. This flow pattern is also both irrotational and incompressible flow.
Elementary flow | Two Dimensional line source
Even though the wind speed near the center of a tropical cyclone is very fast, at any point on the Earth's surface it is not as fast as it is above that point away from the retarding influence of the Earth's surface. The slower speed of the air at the earth's surface prevents the barometric pressure from falling as low as would be expected from the barometric pressure at mid altitudes. This is compatible with Bernoulli's principle. The secondary flow at the Earth's surface is toward the center of the cyclone but is then drawn upward by the significantly lower pressure at mid and high altitudes.
Secondary flow | Tropical cyclones
This flow of air across the isobars near ground level is a "secondary flow". It does not conform to the primary flow, which is parallel to the isobars. At heights well above ground level there is a balance between the Coriolis effect, the local pressure gradient, and the velocity of the wind. This is balanced flow. Closer to the ground the air is not able to accelerate to the speed necessary for balanced flow. Interference by the surface of the ground or water, and by obstructions such as terrain, waves, trees and buildings, cause drag on the atmosphere and prevent the air from accelerating to the speed necessary to achieve balanced flow.
Secondary flow | Wind near ground level
return to its initial position). So, such a process is a reversible process. According to the Second Law of Thermodynamics, whenever there is a reversible and adiabatic flow, constant value of entropy is maintained. Engineers classify this type of flow as an "isentropic" flow of fluids. Isentropic is the combination of the Greek word "iso" (which means - same) and entropy. When the change in flow variables is small and gradual, isentropic flows occur. The generation of sound waves is an isentropic process. A supersonic flow that is turned while there is an increase in flow area is also isentropic.
Isentropic nozzle flow | Overview
Three-dimensional flows have three degrees of freedom corresponding to the three coordinates, and usually result in chaotic advection, except when the flow has symmetries that reduce the number of degrees of freedom. In flows with less than 3 degrees of freedom, Lagrangian trajectories are confined to closed tubes, and shear-induced mixing can only proceed within these tubes.
Chaotic mixing | Conditions for chaotic advection
Taylor vortices (also named after Sir Geoffrey Ingram Taylor) are vortices formed in rotating Taylor–Couette flow when the Taylor number (formula_11) of the flow exceeds a critical value formula_12. For flow in which instabilities in the flow are not present, i.e. perturbations to the flow are damped out by viscous forces, and the flow is steady. But, as the formula_11 exceeds formula_12, axisymmetric instabilities appear. The nature of these instabilities is that of an exchange of stabilities (rather than an overstability), and the result is not turbulence but rather a stable secondary flow pattern that emerges in which large toroidal vortices form in flow, stacked one on top of the other.
Taylor–Couette flow | Taylor vortex
As a result, the wind direction near ground level is partly parallel to the isobars in the region, and partly across the isobars in the direction from higher pressure to lower pressure. As a result of the slower wind speed at the earth's surface, in a region of low pressure the barometric pressure is usually significantly higher at the surface than would be expected, given the barometric pressure at mid altitudes, due to Bernoulli's principle. Hence, the secondary flow toward the center of a region of low pressure is also drawn upward by the significantly lower pressure at mid altitudes.
Secondary flow | Wind near ground level
If we consider a line source and a line sink at a distance d we can reuse the results above and the stream function will be The last approximation is to the first order in d. Given It remains The velocity is then And the potential instead
Elementary flow | Two Dimensional doublet or dipole line source
Due to symmetry, pressure of the fluid can depend only on radial and axial coordinate formula_9. Then the continuity equation and the incompressible Navier–Stokes equations reduce to
Von Kármán swirling flow | Flow description
Given a uniform velocity of a fluid at any position in space: This flow is incompressible because the velocity is constant, the first derivatives of the velocity components are zero, and the total divergence is zero: formula_2 Given the circulation is always zero the flow is also irrotational, we can derive this from the Kelvin's circulation theorem and from the explicit computation of the Vorticity:
Elementary flow | Two Dimensional uniform flow
Vertical flows are found by applying one-dimensional flow equations in a vertical sense, or they can be derived from the water balance: excess of horizontal inflow over horizontal outflow (or vice versa) is translated into vertical flow, as demonstrated in the article Hydrology (agriculture).
Groundwater model | Semi three-dimensional
The case of a vertical line emitting at a fixed rate a constant quantity of fluid Q per unit length is a line source. The problem has a cylindrical simmetry and can be treated in two dimension on the orthogonal plane. Line sources and line sinks (below) are important elementary flows because they play the role of monopole(s) for incompressible fluids (which can also be considered examples of solenoidal fields i.e. divergence free fields). Generic flow patterns can be also de-composed in terms of multipole expansions, in the same manner as for electric and magnetic fields where the monopole is essentially the first non trivial (e.g.
Elementary flow | Two Dimensional line source
The three-cell model of the atmosphere attempts to describe the actual flow of the Earth's atmosphere as a whole. It divides the Earth into the tropical (Hadley cell), mid-latitude (Ferrel cell), and polar (polar cell) regions, to describe energy flow and global atmospheric circulation (mass flow). Its fundamental principle is that of balance – the energy that the Earth absorbs from the sun each year is equal to that which it loses to space by radiation. This overall Earth energy balance, however, does not apply in each latitude due to the varying strength of the sun in each "cell" as a result of the tilt of the Earth's axis concerning its orbit.
Troposphere | Three-cell model
There is another receiver pressure substantially below that of curve C that also results in isentropic flow throughout the nozzle, represented by curve D; after the throat the flow is supersonic. Pressures in the receiver in between those of curve C and curve D result in non-isentropic flow (a shock wave occurs in the flow) and will be considered in the next section. If pr is below that of curve D, the exit pressure pe is greater than pr. Once again, for receiver pressures below that of curve C, the mass flux remains constant since the conditions at the throat remain unchanged.
Isentropic nozzle flow | Converging nozzle
In the case of upstream air pressure at atmospheric pressure and vacuum conditions downstream of an orifice, both the air velocity and the mass flow rate becomes choked or limited when sonic velocity is reached through the orifice.
Choked flow | Vacuum conditions
The primary flow around the bend is vortex flow – fastest speed where the radius of curvature of the stream itself is smallest and slowest speed where the radius is largest. The higher pressure near the concave (outer) bank is accompanied by slower water speed, and the lower pressure near the convex bank is accompanied by faster water speed, and all this is consistent with Bernoulli's principle. A "secondary flow" results in the boundary layer along the floor of the river bed. The boundary layer is not moving fast enough to balance the pressure gradient and so its path is partly downstream and partly across the stream from the concave bank toward the convex bank, driven by the pressure gradient.
Secondary flow | River bends
The primary flow around a tropical cyclone is parallel to the isobars – and hence circular. The closer to the center of the cyclone, the faster is the wind speed. In accordance with Bernoulli's principle where the wind speed is fastest the barometric pressure is lowest. Consequently, near the center of the cyclone the barometric pressure is very low. There is a strong pressure gradient across the isobars toward the center of the cyclone. This pressure gradient provides the centripetal force necessary for the circular motion of each parcel of air. This strong gradient, coupled with the slower speed of the air near the Earth's surface, causes a secondary flow at surface level toward the center of the cyclone, rather than a wholly circular flow.
Secondary flow | Tropical cyclones
In advection-dominated flows, "μn" is greater than "αnh", and most of the incoming photons reach the ionization front and ionize fresh gas. In other flows, most photons fail to reach the ionization front, and instead balance recombinations in the flow.
Cometary knot | Relation to other photoevaporation flows
In toroidally confined fusion plasma experiments the term zonal flow means a plasma flow within a magnetic surface primarily in the poloidal direction. This usage is inspired by the analogy between the quasi-two-dimensional nature of large-scale atmospheric and oceanic flows, where zonal means latitudinal, and the similarly quasi-two-dimensional nature of low-frequency flows in a strongly magnetized plasma. Zonal flows in the toroidal plasma context are further characterized by
Zonal flow (plasma) | Introduction
The outflow from the first reservoir is divided into two separate flows (Q1 and Q2) where Q1 represents the fast flow which is triggered after a certain threshold L to be defined by the user and Q2 the intermediate flow. A constant K1 is used to find the outflows as a function of the storage in S1. To consider the percolation rate a constant Kd is used as along as the storage is S1. The outflow from the second reservoir is considered to be the groundwater flow (Q3) function of a constant K2 and the storage in S2. The total flow generated from a certain rain event is the sum of the 3 flows.
HBV hydrology model | Discharge modelling
Tornadoes and dust devils display localised vortex flow. Their fluid motion is similar to tropical cyclones but on a much smaller scale so that the Coriolis effect is not significant. The primary flow is circular around the vertical axis of the tornado or dust devil. As with all vortex flow, the speed of the flow is fastest at the core of the vortex. In accordance with Bernoulli's principle where the wind speed is fastest the air pressure is lowest; and where the wind speed is slowest the air pressure is highest. Consequently, near the center of the tornado or dust devil the air pressure is low.
Secondary flow | Tornadoes and dust devils
The secondary flow is then upward toward the surface where it mixes with the primary flow or moves slowly across the surface, back toward the concave bank. This motion is called helicoidal flow.
Secondary flow | River bends
In semi 3-dimensional models the horizontal flow is described by 2-dimensional flow equations (i. e. in horizontal x and y direction). Vertical flows (in z-direction) are described (a) with a 1-dimensional flow equation, or (b) derived from a water balance of horizontal flows converting the excess of horizontally incoming over the horizontally outgoing groundwater into vertical flow under the assumption that water is incompressible. There are two classes of semi 3-dimensional models: Continuous radial model Een example of a non-discretized radial model is the description of groundwater flow moving radially towards a deep well in a network of wells from which water is abstracted.
Groundwater model | Semi three-dimensional
A congestion pattern of synchronized flow (Synchronized Flow Pattern (SP)) with a fixed downstream and a not continuously propagating upstream front is called Localised Synchronized Flow Pattern (LSP). Frequently the upstream front of a SP propagates upstream. If only the upstream front propagates upstream, the related SP is called Widening Synchronised Flow Pattern (WSP). The downstream front remains at the bottleneck location and the width of the SP increases. It is possible that both upstream and downstream front propagate upstream. The downstream front is no longer located at the bottleneck. This pattern has been called Moving Synchronised Flow Pattern (MSP).
Three-phase traffic theory | Classification of synchronized flow traffic patterns (SP)
In fluid dynamics, a secondary circulation is a weak circulation that plays a key maintenance role in sustaining a stronger primary circulation that contains most of the kinetic energy and inertia of a flow. For example, a (horizontally swirling), but their evolution and maintenance against friction involves an in-up-out flow that is important to its clouds and rain. On a planetary scale, Earth's winds are mostly east-west or zonal, but that flow is maintained against friction by the Coriolis force acting on a small north-south or meridional secondary circulation.
Secondary circulation | Introduction
Different flow regimes have been categorized over the years including twisted Taylor vortices and wavy outflow boundaries. It has been a well researched and documented flow in fluid dynamics.
Taylor–Couette flow | Introduction
The flow in many fluids varies with density and depends upon the gravity. Due to which the fluid with lower density is always above the fluid with higher density. Stratified flows are very common such as the Earth's ocean and its atmosphere.
Stratified flows | Introduction
It thus permits visualization of this kind of flow in two dimensions.
Hele-Shaw flow | Introduction
The boundary layer spirals inward toward the axis of circulation of the water. On reaching the center the secondary flow is then upward toward the surface, progressively mixing with the primary flow. Near the surface there may also be a slow secondary flow outward toward the perimeter. The secondary flow along the floor of the bowl or cup can be seen by sprinkling heavy particles such as sugar, sand, rice or tea leaves into the water and then setting the water in circular motion by stirring with a hand or spoon. The boundary layer spirals inward and sweeps the heavier solids into a neat pile in the center of the bowl or cup.
Secondary flow | Circular flow in a bowl or cup
ZOOMQ3D applies a quasi-three-dimensional finite-difference approximation to the general three-dimensional governing partial differential groundwater flow equation: where: This equation is derived by considering a flow balance for an infinitesimally small volume element located anywhere within a body of saturated aquifer. A number of assumptions underlie this equation. First, the fluid is assumed to be of constant density; this allows the flow balance to be a consequence of mass conservation within the element. Next, the Cartesian coordinate system is aligned with the principal axes of the hydraulic conductivity tensor; this avoids the need for cross derivatives.
ZOOMQ3D | Groundwater flow equation
This is the case of a vortex filament rotating at constant speed, there is a cylindrical symmetry and the problem can be solved in the orthogonal plane. Dual to the case above of line sources, Vortex lines play the role of monopoles for irrotational flows. Also in this case the flow is also both irrotational and incompressible and therefore a case of Potential flow.
Elementary flow | Two Dimensional vortex line
With water circulating in a bowl or cup, the primary flow is purely circular and might be expected to fling heavy particles outward to the perimeter. Instead, heavy particles can be seen to congregate in the center as a result of the secondary flow along the floor.
Secondary flow | Circular flow in a bowl or cup
In fluid dynamics, a secondary flow is a relatively minor flow superimposed on the primary flow, where the primary flow usually matches very closely the flow pattern predicted using simple analytical techniques that assume the fluid is inviscid. (An inviscid fluid is a theoretical fluid having zero viscosity.) The primary flow of a fluid, particularly in the majority of the flow field remote from solid surfaces immersed in the fluid, is usually very similar to what would be predicted using the basic principles of physics, and assuming the fluid is inviscid. However, in real flow situations, there are regions in the flow field where the flow is significantly different in both speed and direction to what is predicted for an inviscid fluid using simple analytical techniques.
Secondary flow | Introduction
Flow volumes range from a few hundred cubic meters (yards) to more than 1,000 cubic kilometres (~240 cubic miles). Larger flows can travel for hundreds of kilometres (miles), although none on that scale has occurred for several hundred thousand years. Most pyroclastic flows are around 1 to 10 km (about ¼ to 2½ cubic miles) and travel for several kilometres. Flows usually consist of two parts: the "basal flow" hugs the ground and contains larger, coarse boulders and rock fragments, while an extremely hot ash plume lofts above it because of the turbulence between the flow and the overlying air, admixing and heating cold atmospheric air causing expansion and convection.
Pyroclastic flow | Size and effects
There are two kinds of flow structures: bidirectional (multiple directions, back-and-forth) and unidirectional. Flow regimes in single-direction (typically fluvial) flow, which at varying speeds and velocities produce different structures, are called bedforms. In the "lower flow regime", the natural progression is from a flat bed, to some sediment movement (saltation etc.), to ripples, to slightly larger dunes. Dunes have a vortex in the lee side of the dune. As the "upper flow regime" forms, the dunes become flattened out, and then produce antidunes. At higher still velocity, the antidunes are flattened and most sedimentation stops, as erosion takes over as the dominant process.
Sedimentary structures | Flow structures
Sink flow is the opposite of source flow. The streamlines are radial, directed inwards to the line source. As we get closer to the sink, area of flow decreases. In order to satisfy the continuity equation, the streamlines get bunched closer and the velocity increases as we get closer to the source. As with source flow, the velocity at all points equidistant from the sink is equal. The velocity of the flow around the sink can be given by – The stream function associated with sink flow is – The flow around a line sink is irrotational and can be derived from velocity potential.
Two-dimensional flow | Uniform sink flow
A radially symmetrical flow field directed outwards from a common point is called a source flow. The central common point is the line source described above. Fluid is supplied at a constant rate formula_15 from the source. As the fluid flows outward, the area of flow increases. As a result, to satisfy continuity equation, the velocity decreases and the streamlines spread out. The velocity at all points at a given distance from the source is the same. The velocity of fluid flow can be given as - We can derive the relation between flow rate and velocity of the flow.
Two-dimensional flow | Uniform source flow
This is because such flows can produce a net southward flow in the troughs and a net northward flow over the ridges without requiring any transformation of density. In practice both the thermohaline and the eddy/meander mechanisms are likely to be important.
Antarctic Circumpolar Current | Dynamics
Hence, the flow is referred to as quasi-viscous.
Taylor–Culick flow | Introduction
In hydrology, throughflow, a subtype of interflow (percolation), is the lateral unsaturated flow of water in the soil zone, typically through a highly permeable geologic unit overlying a less permeable one. Water thus returns to the surface, as return flow, before or on entering a stream or groundwater. Once water infiltrates into the soil, it is still affected by gravity and infiltrates to the water table or if permeabliity varies laterally travels downslope. Throughflow usually occurs during peak hydrologic events (such as high precipitation). Flow rates are dependent on the hydraulic conductivity of the geologic medium.
Throughflow | Introduction
Any fluid, including water in a stream, can only flow around a bend in vortex flow. In vortex flow the speed of the fluid is fastest where the radius of the flow is smallest, and slowest where the radius is greatest. (Tropical cyclones, tornadoes, and the spinning motion of water as it escapes down a drain are all visible examples of vortex flow.) In the case of water flowing around a bend in a stream the secondary flow in the boundary layer along the floor of the stream does not flow parallel to the banks of the stream but flows partly across the floor of the stream toward the inside of the stream (where the radius of curvature is smallest).
Point bar | Formation
The case of a converging-diverging nozzle allows a supersonic flow to occur, providing the receiver pressure is sufficiently low. This is shown in Fig. 9.6 assuming a constant reservoir pressure with a decreasing receiver pressure. If the receiver pressure is equal to the reservoir pressure, no flow occurs, represented by curve formula_30. If pr is slightly less than p_0, the flow is subsonic throughout, with a minimum pressure at the throat, represented by curve B. As the pressure is reduced still further, a pressure is reached that result in M =1 at the throat with subsonic flow throughout the remainder of the nozzle.
Isentropic nozzle flow | Converging nozzle
Another useful coordinate system is 3D cylindrical coordinates (typically where a pumping well is a line source located at the origin — parallel to the "z" axis — causing converging radial flow). Under these conditions the above equation becomes ("r" being radial distance and "θ" being angle),
Groundwater flow equation | Circular cylindrical coordinates
Inflow can originate from mid-levels of the atmosphere too. When thunderstorms are able to organize into squall lines, a feature known as a rear inflow jet develops to the south of the mid-level circulation associated with its northern bookend vortex. This leads to an erosion of rain within the broad rain shield behind the squall line, and may lead to acceleration of the squall line itself.
Inflow (meteorology) | Thunderstorms
The surface flow in the Brazil–Malvinas Confluence Zone is still not quite well understood, but more recently satellites have been able to give us a better idea of what this flow looks like. After the Brazil Current collides with the Malvinas Current at around 38 degrees South, it branches off into two different paths. The first path gets redirected back equatorward and actually creates a large anticyclonic eddy with the original Brazil Current. The second path of the Brazil Current, which is much stronger than the aforementioned redirected path, is deflected about 45 degrees east of its original tract poleward.
Brazil–Malvinas Confluence | Surface flow and thermohaline gradients in the confluence zone
Areal surface water flow is represented in HydroGeoSphere by a two-dimensional depth-averaged flow equation, which is the diffusion-wave approximation of the Saint Venant equation for surface water flow. HydroGeoSphere's surface water flow component is implemented with the following assumptions: The surface flow components are solved by the following three equations, which are given by the following mass balance equation: coupled with the momentum equations, neglecting inertia terms, for the x-direction: and for the y-direction: where formula_16 is the surface flow domain porosity, formula_17 is the water surface elevation, formula_18 and formula_19 are the vertically averaged flow velocities in the x and y directions, formula_20 is the depth of surface water flow, formula_21 is the internal fluid exchange, and formula_22 is the external fluid exchange.
HydroGeoSphere | Surface water flow
For the case of a sphere in a uniform far field flow, it is advantageous to use a cylindrical coordinate system ( "r" , φ , "z" ). The "z"–axis is through the centre of the sphere and aligned with the mean flow direction, while "r" is the radius as measured perpendicular to the "z"–axis. The origin is at the sphere centre. Because the flow is axisymmetric around the "z"–axis, it is independent of the azimuth "φ". In this cylindrical coordinate system, the incompressible flow can be described with a Stokes stream function "ψ", depending on "r" and "z": with "u" and "u" the flow velocity components in the "r" and "z" direction, respectively.
Stokes' law | Transversal Flow around a sphere
Since flows in opposite directions cancel out, "decreasing" the flow from to is the same as "increasing" the flow from to .
Flow network | Residuals
Given an incompressible two dimensional flow which is also irrotational we have: Which is in cylindrical coordinates We look for a solution with separated variables: which gives Given the left part depends only on r and the right parts depends only on :formula_40, the two parts must be equal to a constant independent from r and formula_40. The constant shall be positive. Therefore, The solution to the second equation is a linear combination of formula_44 and formula_45 In order to have a single valued velocity (and also a single valued stream function) m shall be a positive integer. therefore the most generic solution is given by The potential is instead given by
Elementary flow | Generic Two Dimensional potential flow
The seasonal pattern of flow is typical of rivers in high mountains of central Afghanistan taking into account seasonal snow melt. The average annual flow or module was calculated over a period of 6 years (from 1974 to 1979) and was more or less than 35 cubic meters per second. The curve oscillation observed daily flows in 1978 is quite similar to the average of these 6 years. The period of high water occurs in late winter and the beginning of spring. The maximum flow is observed in late February to early May when there is snowmelt. It reaches 200 to 300 cubic meters per second on average during the first half of April.
Kaj River | Hydrology
Gradient Flow is useful in studying atmospheric flow rotating around high and low pressures centers with small Rossby numbers. This is the case where the radius of curvature of the flow about the pressure centers is small, and geostrophic flow no longer applies with a useful degree of accuracy.
Balanced flow | Application
represents the case when the reservoir pressure is increased and the receiver pressure is held constant. When formula_24, the condition of choked flow also occurs; but Eq indicates that the mass flux will continue to increase as formula_25 is increased. This is the case when a gas line ruptures. It is interesting that the exit pressure formula_26 is able to be greater than the receiver pressure formula_27. Nature allows this by providing the streamlines of a gas the ability to make a sudden change of direction at the exit and expand to a much greater area resulting in a reduction of the pressure from formula_26 to formula_27.
Isentropic nozzle flow | Converging nozzle
This slow, widespread ascent of the air in a region of low pressure can cause widespread cloud and rain if the air is of sufficiently high relative humidity.
Secondary flow | Wind near ground level
The most common class of multiphase flows are two-phase flows, and these include Gas-Liquid Flow, Gas-Solid Flow, Liquid-Liquid Flow and Liquid-Solid Flow. These flows are the most studied, and are of most interest in the context of industry. Different patterns of multiphase flow are known as flow regimes.
Multiphase flow | Types
Inflow is the flow of a fluid into a large collection of that fluid. Within meteorology, inflow normally refers to the influx of warmth and moisture from air within the Earth's atmosphere into storm systems. Extratropical cyclones are fed by inflow focused along their cold front and warm fronts. Tropical cyclones require a large inflow of warmth and moisture from warm oceans in order to develop significantly, mainly within the lowest of the atmosphere. Once the flow of warm and moist air is cut off from thunderstorms and their associated tornadoes, normally by the thunderstorm's own rain-cooled outflow boundary, the storms begin to dissipate.
Inflow (meteorology) | Introduction
Here we have formula_50. Integration of formula_51 gives formula_52 and the three equations are The first equation is the Hicks equation. Marris and Aswani (1977) showed that the only possible solution is formula_30 and the remaining equations reduce to A simple set of solutions to the above equation is
Beltrami flow | Steady axisymmetric flows
In experimental fluid dynamics, flows are visualized by three methods: In scientific visualization flows are visualized with two main methods:
Flow visualization | Methods of visualization
A nozzle for a supersonic flow must increase in area in the flow direction, and a diffuser must decrease in area, opposite to a nozzle and diffuser for a subsonic flow. So, for a supersonic flow to develop from a reservoir where the velocity is zero, the subsonic flow must first accelerate through a converging area to a throat, followed by continued acceleration through an enlarging area. The nozzles on a rocket designed to place satellites in orbit are constructed using such converging-diverging geometry. The energy and continuity equations can take on particularly helpful forms for the steady, uniform, isentropic flow through the nozzle.
Isentropic nozzle flow | Supersonic flow
But then, by the first result, ξ must be fixed by "G".
Ergodic flow | Ergodicity of geodesic and horocycle flows
Below convergence zones narrow jets of downward flow form and the magnitude of the current will be comparable to the horizontal flow. The downward propagation will typically be in the order of meters or tenths of meters and will not penetrate the pycnocline. The upwelling is less intense and takes place over a wider band under the divergence zone. In wind speeds ranging from the maximum vertical velocity ranged from with a ratio of down-welling to wind velocities ranging from −0.0025 to −0.0085.
Langmuir circulation | Observations
The second and final major pyroclastic flow occurred when another pulse of gas-rich magma was erupted. This deposited of tephra on the earlier block and ash flow. In contrast to the first major pyroclastic flow, this pyroclastic flow was smaller and less energetic. Also, no burnt wood has been observed. Fine-grained volcanic ash, crystal and rock fragments comprise the matrix of the second major pyroclastic flow deposit. A second hot welded block and ash flow erupted off the face of an advancing lava dome into the Lillooet River valley, forming a pyroclastic dam at least high. This block and ash flow deposited irregularly welded, monolithologic and vitophyric breccia that ranges from thick at Keyhole Falls to thick between two creeks further downstream.
Bridge River Vent | Peléan phase
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Carton flow | References
The three main assumptions in the derivation of d'Alembert's paradox is that the steady flow is incompressible, inviscid and irrotational. An inviscid fluid is described by the Euler equations, which together with the other two conditions read where u denotes the flow velocity of the fluid, "p" the pressure, "ρ" the density, and ∇ is the gradient operator. We have the second term in the Euler equation as: where the first equality is a vector calculus identity and the second equality uses that the flow is irrotational. Furthermore, for every irrotational flow, there exists a velocity potential "φ" such that u = ∇"φ".
D'Alembert's paradox | Potential flow
Secondary flows occur throughout the impeller in a centrifugal compressor but are less marked in axial compressors due to shorter passage lengths. Flow turning is low in axial compressors but boundary layers are thick on the annulus walls which gives significant secondary flows. Flow turning in turbine blading and vanes is high and generates strong secondary flow.
Secondary flow | Turbomachinery
Flow velocity is used to classify flows according to speed regime. Subsonic flows are flow fields in which the air speed field is always below the local speed of sound. Transonic flows include both regions of subsonic flow and regions in which the local flow speed is greater than the local speed of sound. Supersonic flows are defined to be flows in which the flow speed is greater than the speed of sound everywhere. A fourth classification, hypersonic flow, refers to flows where the flow speed is much greater than the speed of sound. Aerodynamicists disagree on the precise definition of hypersonic flow.
Aerodynamics | Flow classification
In addition, if the particles are sufficiently light, they behave essentially like a second fluid. In this case, an Eulerian treatment of the dispersed phase is sensible.
Particle-laden flow | Coupling
These are the Taylor vortices. While the fluid mechanics of the original flow are unsteady when formula_16, the new flow, called "Taylor–Couette flow", with the Taylor vortices present, is actually steady until the flow reaches a large Reynolds number, at which point the flow transitions to unsteady "wavy vortex" flow, presumably indicating the presence of non-axisymmetric instabilities.
Taylor–Couette flow | Taylor vortex
To avoid this, vertical turbulent diffusion is treated using the second order Crank–Nicolson method.
MEMO model (wind-flow simulation) | Numerical solution of the equation system
Taylor showed that when the angular velocity of the inner cylinder is increased above a certain threshold, Couette flow becomes unstable and a secondary steady state characterized by axisymmetric toroidal vortices, known as Taylor vortex flow, emerges. Subsequently, upon increasing the angular speed of the cylinder the system undergoes a progression of instabilities which lead to states with greater spatio-temporal complexity, with the next state being called wavy vortex flow. If the two cylinders rotate in opposite sense then spiral vortex flow arises. Beyond a certain Reynolds number there is the onset of turbulence. Circular Couette flow has wide applications ranging from desalination to magnetohydrodynamics and also in viscosimetric analysis.
Taylor–Couette flow | Introduction
Relatively intermediate albedos and smooth, several hundred meter flows typify these materials. Contact with surrounding terrain not as sharp as observed with bright and dark flow material. Origin of flows is often hard to tell. It is difficult to distinguish individual flows in a group. It is believed to have origin in sulfur/silicate-rich effusive eruptions.
Chaac-Camaxtli region | Undivided flow
For interior flows, the terms with formula_38 are dropped, while for exterior flows the terms with formula_39 are dropped (often the convention formula_40 is assumed for exterior flows to avoid indexing by negative numbers).
Stokes flow | Spherical coordinates
In the original work of Taylor and Green, a particular flow is analyzed in three spatial dimensions, with the three velocity components formula_1 at time formula_2 specified by The continuity equation formula_6 determines that formula_7. The small time behavior of the flow is then found through simplification of the incompressible Navier–Stokes equations using the initial flow to give a step-by-step solution as time progresses. An exact solution in two spatial dimensions is known, and is presented below.
Taylor–Green vortex | Original work
MIKE 21C applies standard theory for the helical flow, which can be found in e.g. Rozowsky (1957). Standard helical flow theory provides a secondary flow velocity profile that is fully characterised by friction and the deviation angle between the main flow direction and the direction of the shear stress at the river bed.
MIKE 21C | Theory
Other geological flows that can be described as debris flows are typically given more specific names. These include:
Debris flow | Types
Sediment transport in rivers is subject to multiphase flow, in which the suspended particles are treated as a disperse second phase which interacts with the continuous fluid phase. An example of multiphase flow on a smaller scale would be within porous structures. Pore-structure modelling enables the use Darcy's law to calculate the volumetric flow rate through porous media such as groundwater flow through rock. Further examples occur within the bodies of living organisms, such as blood flow (with plasma being the liquid phase and red blood cells constituting the solid phase. Also flow within the intestinal tract of the human body, with solid food particles and water flowing simultaneously.
Multiphase flow | In nature
When a fluid is flowing through a closed channel such as a pipe or between two flat plates, either of two types of flow may occur depending on the velocity and viscosity of the fluid: laminar flow or turbulent flow. Laminar flow occurs at lower velocities, below a threshold at which the flow becomes turbulent. The velocity is determined by a dimensionless parameter characterizing the flow called the Reynolds number, which also depends on the viscosity and density of the fluid and dimensions of the channel. Turbulent flow is a less orderly flow regime that is characterized by eddies or small packets of fluid particles, which result in lateral mixing.
Laminar flow | Introduction
The second is a convection system, where the low density fluid on the bottom mixes with the high density fluid on the top until the density becomes evenly distributed. The second system arises when there is too much energy to be effectively dissipated by the first, and once both systems are in place, they will begin to interact. Self organization: The convection creates currents in the fluid that disrupt the pattern of heat diffusion from bottom to top. Heat begins to diffuse into the denser areas of current, irrespective of the vertical location of these denser portions of fluid. The areas of the fluid where diffusion is occurring most rapidly will be the most viscous because molecules are rubbing against each other in opposite directions.
Incomplete Nature | Morphodynamics
Energy equation for the steady flow:
Isentropic nozzle flow | Flow analysis
Extratropical cyclones are generally driven, or "steered", by deep westerly winds in a general west to east motion across both the Northern and Southern hemispheres of the Earth. This general motion of atmospheric flow is known as "zonal". Where this general trend is the main steering influence of an extratropical cyclone, it is known as a "zonal flow regime". When the general flow pattern buckles from a zonal pattern to the meridional pattern, a slower movement in a north or southward direction is more likely. Meridional flow patterns feature strong, amplified troughs and ridges, generally with more northerly and southerly flow.
Extratropical cyclone | Motion
In the application of the Strahler stream order to hydrology, each segment of a stream or river within a river network is treated as a node in a tree, with the next segment downstream as its parent. When two first-order streams come together, they form a second-order stream. When two second-order streams come together, they form a third-order stream. Streams of lower order joining a higher order stream do not change the order of the higher stream. Thus, if a first-order stream joins a second-order stream, it remains a second-order stream. It is not until a second-order stream combines with another second-order stream that it becomes a third-order stream.
Strahler number | River networks
Third calculation of the actual Evapotranspiration (ETPa), first by using an external model (ex: Penman) for finding the potential ETP and then fitting the result to the temperatures and the permanent wilting point(PWP) of the catchment in question. A parameter C which reflects the increase in the ETP with the differences in temperatures ( Actual Temperature and Monthly mean Temperature). The model consists of considering the catchment as 2 reservoirs (S1 and S2) connected together by a percolation flow, the inflow to the first reservoir is calculated as the surface runoff which is what remains from the initial precipitations after calculating the infiltration and the evapotranspiration.
HBV hydrology model | Discharge modelling
Jet streak dynamics through the imbalance of Coriolis and pressure gradient forces, causing subgeostrophic and supergeostrophic flows, can also create upward vertical velocities. There are numerous other atmospheric setups in which upward vertical velocities can be created.
Atmospheric convection | Boundaries and forcing
Mathematical equations and concepts Fields of study Types of fluid flow Fluid properties Fluid phenomena
Pipe flow | See also
In hydrology, interflow is the lateral movement of water in the unsaturated zone, or vadose zone, that first returns to the surface or enters a stream prior to becoming groundwater. Interflow is sometimes used interchangeably with throughflow; however, throughflow is specifically the subcomponent of interflow that returns to the surface, as overland flow, prior to entering a stream or becoming groundwater. Interflow occurs when water infiltrates (see infiltration (hydrology)) into the subsurface, hydraulic conductivity decreases with depth, and lateral flow proceeds downslope. As water accumulates in the subsurface, saturation may occur, and interflow may exfiltrate as return flows, becoming overland flow.
Interflow | Introduction
Von Kármán swirling flow is a flow created by a uniformly rotating infinitely long plane disk, named after Theodore von Kármán who solved the problem in 1921. This problem is used as a model for centrifugal fans or compressors. This flow is classified under the category of steady flows in which vorticity generated at a solid surface is prevented from diffusing far away by an opposing convection, the other examples being the Blasius boundary layer with suction, stagnation point flow etc.
Von Kármán swirling flow | Introduction
Different definitions have been put forward for secondary flow in turbomachinery, such as "Secondary flow in broad terms means flow at right angles to intended primary flow". Secondary flows occur in the main, or primary, flowpath in turbomachinery compressors and turbines (see also unrelated use of term for flow in the secondary air system of a gas turbine engine). They are always present when a wall boundary layer is turned through an angle by a curved surface. They are a source of total pressure loss and limit the efficiency that can be achieved for the compressor or turbine. Modelling the flow enables blade, vane and end-wall surfaces to be shaped to reduce the losses.
Secondary flow | Turbomachinery
This subsonic flow then decelerates through the remainder of the diverging section and exhausts as a subsonic jet. In this regime if you lower or raise the back pressure you move the shock wave away from (increase the length of supersonic flow in the diverging section before the shock wave) the throat.
Choked flow | The flow pattern
rotating), and bounded (influenced by wall effects) or unbounded (not influenced by wall effects). According to this classification the Taylor–Couette flow is an example of a flow pattern forming in a closed, bounded flow system.
Taylor–Couette flow | Gollub–Swinney circular Couette experiment
Whereas frequently the internal flow involves a single fluid phase (albeit often of a complex biological fluid such as blood), in many instances the presence of two or more distinct flowing phases is of primary importance (as is the case for air-liquid flows in peripheral lung airways, for example).
Collapsible flow | Introduction