<p>There are a number of causes, for a variety of scales.
Generally speaking, you can boil it down to convergence/divergence, as a continuity of mass problem, or buoyant motion.</p>

<p>You can refer to the vertical component of the Navier Stoke's equations.
$$
\frac{Dw}{Dt}=\frac{∂w}{∂t}+\vec{v}\cdot\nabla w + w\frac{∂w}{∂z} =-\frac{1}{ρ}\frac{∂P}{∂z}-g+\nu\nabla^2w
$$
Additionally, it must also be constrained by the conservation of mass.
$$
\frac{∂P}{∂t}=-\nabla\cdot(\rho\vec{v})
$$
The Quasigeostrophic Omega Equation may also provide you some insight. This equation is filtered down from the above Navier-Stokes equation, though it may not seem like it. Omega is vertical velocity in pressure coordinates.
$$
(\nabla^2+\frac{f_0^2∂^2}{\sigma∂\Phi^2})\omega=\frac{f∂}{\sigma∂p}(\vec{v}\cdot\nabla(\frac{1}{f_0}\nabla^2\Phi+f)) + \frac{1}{\sigma}\nabla^2[\vec{v_g}\cdot\nabla(-\frac{∂\Phi}{∂p})]
$$</p>

CC BY-SA 3.0
2016-04-14T03:31:40.783Z
2016-04-14T03:31:40.783Z
BarocliniCplusplus
<p>My question is about how vertical component of wind may change over time; in particular, as I am interested in simulating the effect of vertical wind on flight mechanics, I'd like to know whether I should consider vertical wind as a deterministic function of time or a stochastic one. Furthermore, should I consider vertical wind persistent over time or having a limited duration (e.g. few seconds)?
Note that I am not interested in horizontal wind.</p>

CC BY-SA 3.0
2016-04-11T18:46:35.353Z
There are lots of different causes.  Off the top of my head, there are thermals caused by differential heating of the ground, orographic effects when horizontal winds flow across mountain ridges (ridge lift, mountain waves), downslope winds where cool air at high elevations flows downwards...
jamesqf
CC BY-SA 3.0
2016-04-11T19:52:19.597Z
Please be more specific about what exactly you want to know about vertical wind and what is your current state of knowledge on it. Which resources did you use to get to know this topic already?
daniel.heydebreck
CC BY-SA 3.0
2016-04-11T20:48:59.353Z
I have to simulate the effect of vertical wind in flight mechanics. Therefore I need to know which kind of signal better describes the vertical wind.
sax631
CC BY-SA 3.0
2016-04-12T05:46:11.560Z
@sax631: All the kinds of vertical air movement I mentioned are of importance in flight.  I drew the examples mostly from my experience as a pilot.  I'm not sure what you mean by 'signal': do you mean rate of climb as indicated by instruments?
jamesqf
CC BY-SA 3.0
2016-04-12T17:59:38.127Z
@jamesqf By "signal" I mean a function of time; in other words, if I have to put wind in a flight mechanics model, I should know how it evolves over time. My question is to know how vertical component of wind may change over time; should I use a deterministic signal, a stochastic one ? Should I consider it persistent or having a limited duration (e.g. few seconds)? Hope it is a little bit more clear.
sax631
CC BY-SA 3.0
2016-04-14T09:00:29.600Z
@sax631 Could you modify your question accordingly?
daniel.heydebreck
CC BY-SA 3.0
2016-04-15T08:44:08.840Z
@daniel.neumann I've rephrased my question.
sax631
CC BY-SA 3.0
2016-04-15T18:11:28.057Z
@sax631: The duration still depends on the particular cause.  Thermals may last minutes to hours.  Wave lift and ridge lift will last as long as the horizontal wind blows appropriately.  Turbulence can change in seconds.  Then there's the fact that when flying, you aren't stationary in the air mass, but moving through it at speed, so you pass quickly from rising to descending air mass...
jamesqf
<wind>
How does vertical wind change over time?
sax631
# How does vertical wind change over time?

(Asked by: username_0 on 2016-04-11)

My question is about how vertical component of wind may change over time; in particular, as I am interested in simulating the effect of vertical wind on flight mechanics, I'd like to know whether I should consider vertical wind as a deterministic function of time or a stochastic one. Furthermore, should I consider vertical wind persistent over time or having a limited duration (e.g. few seconds)?
Note that I am not interested in horizontal wind.

**Tags:** wind

> **Comments:**
> **username_1**: There are lots of different causes.  Off the top of my head, there are thermals caused by differential heating of the ground, orographic effects when horizontal winds flow across mountain ridges (ridge lift, mountain waves), downslope winds where cool air at high elevations flows downwards...  
> **username_2**: Please be more specific about what exactly you want to know about vertical wind and what is your current state of knowledge on it. Which resources did you use to get to know this topic already?  
> **username_0**: I have to simulate the effect of vertical wind in flight mechanics. Therefore I need to know which kind of signal better describes the vertical wind.  
> **username_1**: @username_0: All the kinds of vertical air movement I mentioned are of importance in flight.  I drew the examples mostly from my experience as a pilot.  I'm not sure what you mean by 'signal': do you mean rate of climb as indicated by instruments?  
> **username_0**: @username_1 By "signal" I mean a function of time; in other words, if I have to put wind in a flight mechanics model, I should know how it evolves over time. My question is to know how vertical component of wind may change over time; should I use a deterministic signal, a stochastic one ? Should I consider it persistent or having a limited duration (e.g. few seconds)? Hope it is a little bit more clear.  
> **username_2**: @username_0 Could you modify your question accordingly?  
> **username_0**: @daniel.neumann I've rephrased my question.  
> **username_1**: @username_0: The duration still depends on the particular cause.  Thermals may last minutes to hours.  Wave lift and ridge lift will last as long as the horizontal wind blows appropriately.  Turbulence can change in seconds.  Then there's the fact that when flying, you aren't stationary in the air mass, but moving through it at speed, so you pass quickly from rising to descending air mass...  

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## 1 answers

### Answer by username_3 on 2016-04-14. Score: 1

There are a number of causes, for a variety of scales.
Generally speaking, you can boil it down to convergence/divergence, as a continuity of mass problem, or buoyant motion.

You can refer to the vertical component of the Navier Stoke's equations.
$$
\frac{Dw}{Dt}=\frac{∂w}{∂t}+\vec{v}\cdot\nabla w + w\frac{∂w}{∂z} =-\frac{1}{ρ}\frac{∂P}{∂z}-g+\nu\nabla^2w
$$
Additionally, it must also be constrained by the conservation of mass.
$$
\frac{∂P}{∂t}=-\nabla\cdot(\rho\vec{v})
$$
The Quasigeostrophic Omega Equation may also provide you some insight. This equation is filtered down from the above Navier-Stokes equation, though it may not seem like it. Omega is vertical velocity in pressure coordinates.
$$
(\nabla^2+\frac{f\_0^2∂^2}{\sigma∂\Phi^2})\omega=\frac{f∂}{\sigma∂p}(\vec{v}\cdot\nabla(\frac{1}{f\_0}\nabla^2\Phi+f)) + \frac{1}{\sigma}\nabla^2[\vec{v\_g}\cdot\nabla(-\frac{∂\Phi}{∂p})]
$$


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