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.
Zonal flow
Troposphere
Troposphere | Zonal flow
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 It 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. It means that the general flow pattern is west to east along the Earth's latitude lines, with weak shortwaves embedded in the flow. 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.
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. 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
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
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
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
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
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
constant) term of the expansion. This flow pattern is also both irrotational and incompressible flow.
Elementary flow | Two Dimensional line source
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
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
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Carton flow | References
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
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
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
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
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 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
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
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
It thus permits visualization of this kind of flow in two dimensions.
Hele-Shaw flow | Introduction
To start with, a zonal mean flow, "U", can be considered to be perturbed where "U" is constant in time and space. Let formula_1 be the total horizontal wind field, where "u" and "v" are the components of the wind in the "x"- and "y"- directions, respectively. The total wind field can be written as a mean flow, "U", with a small superimposed perturbation, "u′" and "v′". The perturbation is assumed to be much smaller than the mean zonal flow. Relative vorticity "η", "u and "v can be written in terms of the stream function formula_5 (assuming non-divergent flow, for which the stream function completely describes the flow):
Rossby wave | Free barotropic Rossby waves under a zonal flow with linearized vorticity 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
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
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
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
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
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
But then, by the first result, ξ must be fixed by "G".
Ergodic flow | Ergodicity of geodesic and horocycle flows
In magnetic confinement fusion the zonal direction primarily connotes the poloidal direction (i.e. the short way around the torus), the corresponding coordinate being denoted by "y" in the slab approximation or "θ" in magnetic coordinates. However, in the fusion context, usage is restricted to the context of zonal plasma flows and there will in general be a toroidal component in such flows as well. Thus, although the term zonal has come into use in plasma physics to emphasize an analogy with zonal flows in geophysics, it does not uniquely identify the direction of flow, unlike the case in geophysics.
Zonal and poloidal | Introduction
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
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
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
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
There are several mechanisms that can produce a pyroclastic flow:
Pyroclastic flow | Causes
From the eigenvalues and the eigenvectors of "A" it is possible to determine if an initial point will converge or diverge to the equilibrium point at the origin.
Dynamical system | Flows
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
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
Hence, the flow is referred to as quasi-viscous.
Taylor–Culick flow | Introduction
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
The mechanisms are as follows: The pressure flow mechanism depends upon:
Pressure flow hypothesis | Mechanisms
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
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
If a certain minimum flow is selected for the calculation it is possible that the largest pore in the sample was already open for a while before that particular flow was determined. With the step/stability method it is possible to measure the true FBP. When applying a constant gas flow, before the opening of the largest flow the pressure increases in a linear way. At the moment that the gas flow passes through the sample via the largest pore the pressure increase drops and it is this particular pressure the one that corresponds to the FBP of the sample.
Capillary flow porometry | Measured First Bubble Point (FBP)
For instance, the thermal wind associated with pole-to-equator temperature gradients is the primary physical explanation for the jet stream in the upper half of the troposphere, which is the atmospheric layer extending from the surface of the planet up to altitudes of about 12-15 km. Mathematically, the thermal wind relation defines a vertical wind shear – a variation in wind speed or direction with height. The wind shear in this case is a function of a horizontal temperature gradient, which is a variation in temperature over some horizontal distance. Also called baroclinic flow, the thermal wind varies with height in proportion to the horizontal temperature gradient.
Thermal wind | Introduction
Sir Francis Galton first discovered anticyclones in the 1860s. Preferred areas within a synoptic flow pattern in higher levels of the hydrosphere are beneath the western side of troughs, or dips in the Rossby wave pattern. High-pressure systems are alternatively referred to as anticyclones. Their circulation is sometimes referred to as cum sole. Subtropical high pressure zones form under the descending portion of the Hadley cell circulation. Upper-level high-pressure areas lie over tropical cyclones due to their warm core nature. Surface anticyclones form due to downward motion through the troposphere, the atmospheric layer where weather occurs. Preferred areas within a synoptic flow pattern in higher levels of the troposphere are beneath the western side of troughs.
Anticyclone | History
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
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
155–78).
Space of flows | Theoretic
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
Energy equation for the steady flow:
Isentropic nozzle flow | Flow analysis
Even if air columns are homogeneous with height, the density of each column can change from location to location, firstly since air masses have different temperatures and moisture content depending on their origin; and then since air masses modify their properties as they flow over Earth's surface. For example, in extra-tropical cyclones the air circulating around a pressure low typically comes with a sector of warmer temperature wedged within colder air. The gradient-flow model of cyclonic circulation does not allow for these features. Balanced-flow schematisations can be used to estimate the wind speed in air flows covering several degrees of latitude of Earth's surface.
Balanced flow | Horizontal differences of air properties
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
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
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
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
The group included Carl-Gustaf Rossby (who was the first to explain the large scale atmospheric flow in terms of fluid dynamics), Tor Bergeron (who first determined how rain forms) and Jacob Bjerknes.
Meteorology | Research into cyclones and air flow
Under these conditions, the first law of thermodynamics for a flow process states: "the increase in the internal energy of a system is equal to the amount of energy added to the system by matter flowing in and by heating, minus the amount lost by matter flowing out and in the form of work done by the system." Under these conditions, the first law for a flow process is written:
Flow process | Introduction
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
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
In particular, if is equipped with a topology, then is usually required to be continuous. If is equipped with a differentiable structure, then is usually required to be differentiable. In these cases the flow forms a one parameter subgroup of homeomorphisms and diffeomorphisms, respectively.
Flow (mathematics) | Formal definition
Some experiments indicate that bidirectional movement may occur in a single sieve tube, whereas others do not.
Pressure flow hypothesis | Criticisms
At an initial time a blocking-type circulation pattern establishes in the troposphere. This blocking pattern causes Rossby waves with zonal wavenumber 1 and/or 2 to grow to unusually large amplitudes. The growing wave propagates into the stratosphere and decelerates the westerly mean zonal winds. Thus the polar night jet weakens and simultaneously becomes distorted by the growing planetary waves. Because the wave amplitude increases with decreasing density this easterly acceleration process is not effective at fairly high levels. If the waves are sufficiently strong the mean zonal flow may decelerate sufficiently so that the winter westerlies turn easterly. At this point planetary waves may no longer penetrate into the stratosphere ).
Sudden stratospheric warming | Dynamics
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
Collapsible flow is a phenomenon that occurs in steady flow in tubes with significant distensibility, or the capability of swelling or stretching, under conditions of lower internal pressure relative to pressure outside the tube. Such conditions occur rarely in industrial applications but are very common in biological studies such as blood flow in veins and air flow in lungs. When a flow is driven through a deformable channel or tube, interactions between fluid-mechanical and elastic forces can lead to a variety of biologically significant phenomena, including nonlinear pressure-drop/flow-rate relations, wave propagation, and the generation of instabilities. Understanding the physical origin and nature of these phenomena remains a significant experimental, analytical, and computational challenge, involving unsteady flows at low or high Reynolds numbers, large-amplitude fluid-structure interactions, free-surface flows, and intrinsically 2D or 3D motion.
Collapsible flow | Introduction
For an isentropic flow, entropy density can vary between different streamlines. If the entropy density is the same everywhere, then the flow is said to be homentropic.
Isentropic process | Isentropic flow
The surface conductances, formula_23 and formula_24 are approximated by either the Manning or Chezy equation.
HydroGeoSphere | Surface water flow
Mathematical equations and concepts Fields of study Types of fluid flow Fluid properties Fluid phenomena
Pipe flow | See also
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
Other geological flows that can be described as debris flows are typically given more specific names. These include:
Debris flow | Types
a more zonally symmetric jet).
Thermal wind | Jet stream
Like any fluid, air may exhibit both laminar and turbulent flow patterns. Laminar flow occurs when air can flow smoothly, and exhibits a parabolic velocity profile; turbulent flow occurs when there is an irregularity (such as a disruption in the surface across which the fluid is flowing), which alters the direction of movement. Turbulent flow exhibits a flat velocity profile. The Reynolds number, a ratio indicating the relationship between viscous and inertial forces in a fluid, can be used to predict the transition from laminar to turbulent flow. This number and related concepts can be applied to studying flow in systems of all scales.
Airflow | Types of airflow
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
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
In this region the velocity profile develops and thus the flow is called the hydrodynamically developing flow. After this region, the velocity profile is fully developed and continues unchanged. This region is called the hydrodynamically fully developed region. But this is not the fully developed fluid flow until the normalized temperature profile also becomes constant. In case of laminar flow, the velocity profile in the fully developed region is parabolic but in the case of turbulent flow it gets a little flatter due to vigorous mixing in radial direction and eddy motion. The velocity profile remains unchanged in the fully developed region.
Entrance length | Boundary layer
In general, winds are strongest immediately under the tropopause (except locally, during tornadoes, tropical cyclones or other anomalous situations). If two air masses of different temperatures or densities meet, the resulting pressure difference caused by the density difference (which ultimately causes wind) is highest within the transition zone. The wind does not flow directly from the hot to the cold area, but is deflected by the Coriolis effect and flows along the boundary of the two air masses. All these facts are consequences of the thermal wind relation. The balance of forces acting on an atmospheric air parcel in the vertical direction is primarily between the gravitational force acting on the mass of the parcel and the buoyancy force, or the difference in pressure between the top and bottom surfaces of the parcel.
Jet stream | Cause
Elementary flow is a collection of basic flows from which is possible to construct more complex flows by superposition. Some of the flows reflect specific cases and constraints such as incompressible, irrotational or both as in the case of Potential flow.
Elementary flow | Introduction
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
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
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
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 waves propagate in the horizontal direction, with coordinate "x", and a fluid domain bound above by a free surface at "z" = "η"("x","t"), with "z" the vertical coordinate (positive in the upward direction) and "t" being time. The level "z" = 0 corresponds with the mean surface elevation. The impermeable bed underneath the fluid layer is at "z" = -"h". Further, the flow is assumed to be incompressible and irrotational – a good approximation of the flow in the fluid interior for waves on a liquid surface – and potential theory can be used to describe the flow. The velocity potential "Φ"("x","z","t") is related to the flow velocity components "u" and "u" in the horizontal ("x") and vertical ("z") directions by: Then, due to the continuity equation for an incompressible flow, the potential "Φ" has to satisfy the Laplace equation: Boundary conditions are needed at the bed and the free surface in order to close the system of equations.
Airy wave theory | Flow problem formulation
The Hydraulics of Open Channel Flow: An Introduction. Physical Modelling of Hydraulics Chanson, Hubert (1999)
Supercritical flow | References
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
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
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
The vertical coordinate "z" is positive in the upward direction, opposite to the direction of the gravitational acceleration, and the zero level of "z" is at the impermeable lower boundary of the fluid domain. While the free surface is at "z" = "ζ"("ξ"); note that "ζ" is the local water depth, related to the surface elevation "η"("ξ") as "ζ" = "h" + "η" with "h" the mean water depth. In this steady flow, the discharge "Q" through each vertical cross section is a constant independent of "ξ", and because of the horizontal bed also the horizontal momentum flux "S", divided by the density "ρ", through each vertical cross section is conserved.
Cnoidal wave | Direct derivation from the full inviscid-flow equations
This type of flow is named in honor of Maurice Couette, a Professor of Physics at the French University of Angers in the late 19th century.
Couette flow | Introduction
Part of this stemmed from the need to perform two different equations to deal with turbulent and low flows, depending on whether it was a windy or sunny day.
Assimitron | Introduction
The equation for shear flow in a particular web section of the cross-section of a semi-monocoque structure is: Shear stress may now be calculated using the following equation:
First moment of area | Shear stress in a semi-monocoque structure
The primary rotating flow in a tropical cyclone results from the conservation of angular momentum by the secondary circulation. Absolute angular momentum on a rotating planet formula_1 is given by where formula_3 is the Coriolis parameter, formula_4 is the azimuthal (i.e. rotating) wind speed, and formula_5 is the radius to the axis of rotation. The first term on the right hand side is the component of planetary angular momentum that projects onto the local vertical (i.e. the axis of rotation). The second term on the right hand side is the relative angular momentum of the circulation itself with respect to the axis of rotation.
Tropical cyclone | Primary circulation: rotating winds
In 1494, Christopher Columbus experienced a tropical cyclone, which led to the first written European account of a hurricane. In 1686, Edmund Halley presented a systematic study of the trade winds and monsoons and identified solar heating as the cause of atmospheric motions. In 1735, an "ideal" explanation of global circulation through study of the trade winds was written by George Hadley. In 1743, when Benjamin Franklin was prevented from seeing a lunar eclipse by a hurricane, he decided that cyclones move in a contrary manner to the winds at their periphery. Understanding the kinematics of how exactly the rotation of the Earth affects airflow was partial at first.
Meteorology | Research into cyclones and air flow
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
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
Consider a steady plane emerging into the same fluid, a type of submerged jets from a narrow slit, which is supposed to be very small (such that the fluid loses memory of the shape and size of the slit far away from the origin, it remembers only the net momentum flux). Let the velocity be formula_1 in Cartesian coordinate and the axis of the jet be formula_2 axis with origin at the orifice. The flow is self-similar for large Reynolds number (the jet is so thin that formula_3 varies much more rapidly in the transverse formula_4 direction than the streamwise formula_2 direction) and can be approximated with boundary layer equations.
Bickley jet | Flow description
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
Open-channel flow can be classified and described in various ways based on the change in flow depth with respect to time and space. The fundamental types of flow dealt with in open-channel hydraulics are:
Open-channel flow | Classifications of flow
A simple Taylor–Couette flow is a steady flow created between two rotating infinitely long coaxial cylinders. Since the cylinder lengths are infinitely long, the flow is essentially unidirectional in steady state. If the inner cylinder with radius formula_1 is rotating at constant angular velocity formula_2 and the outer cylinder with radius formula_3 is rotating at constant angular velocity formula_4 as shown in figure, then the azimuthal velocity component is given by where
Taylor–Couette flow | Flow description
Afterwards, collapses in the amphitheatre and within the vent enlarged both features and impeded further eruptive activity. A first pyroclastic flow was emplaced already during this time when the column became unstable. This stage was channelled by a fracture and had the characteristics of a fissure-fed eruption. Possibly, the second vent formed during this stage, but another interpretation is that the second vent is actually a collapse structure that formed late during the eruption. Much of the excavation of the conduit took place during this stage.
Huaynaputina | First Plinian stage
The Jovian bands are bounded by zonal atmospheric flows (winds), called "jets". The eastward (prograde) jets are found at the transition from zones to belts (going away from the equator), whereas westward (retrograde) jets mark the transition from belts to zones. Such flow velocity patterns mean that the zonal winds decrease in belts and increase in zones from the equator to the pole. Therefore, wind shear in belts is cyclonic, while in zones it is anticyclonic. The EZ is an exception to this rule, showing a strong eastward (prograde) jet and has a local minimum of the wind speed exactly at the equator.
Atmosphere of Jupiter | Zones, belts and jets
In fluid dynamics Jeffery–Hamel flow is a flow created by a converging or diverging channel with a source or sink of fluid volume at the point of intersection of the two plane walls. It is named after George Barker Jeffery(1915) and Georg Hamel(1917), but it has subsequently been studied by many major scientists such as von Kármán and Levi-Civita, Walter Tollmien, F. Noether, W.R. Dean, Rosenhead, Landau, G.K. Batchelor etc. A complete set of solutions was described by Edward Fraenkel in 1962.
Jeffery–Hamel flow | Introduction