<p>Wind is caused by pressure differences.  Think of a balloon full of air; poke a hole in it and the air comes out.  Why?  Because the pressure in the balloon is higher than outside, and so to regain equal pressure, mass moves and that is the wind.</p>

<p>There is a bit more to this in the atmosphere as the Earth rotates and near the surface friction also plays a role.  The equation of motion is the Navier-Stokes and in vector form in Cartesian space is:</p>

<p>$$\dfrac{\partial\mathbf u}{\partial t} = - \mathbf u \cdot \nabla \mathbf u  -\dfrac{1}{\rho}\nabla p-2 \mathbf \Omega \times \mathbf u + \mathbf g + \mathbf F$$</p>

<p>In this equation, $\mathbf u$ is the vector wind, $(\mathbf u \cdot \nabla)$ is the advection operator, $\rho$ is density, $\mathbf \Omega$ is the vector rotation of the Earth, $\mathbf g$ is effective gravity and $\mathbf F$ is friction.</p>

<p>The LHS is the time rate of change of the wind at a point in space (as opposed to following the parcel).  The RHS represent a number of factors that produce a change in the wind.  From left to right: </p>

<ul>
<li>Advection of momentum (non-linear)</li>
<li>Pressure gradient force (this is wind blowing from high to low pressure)</li>
<li>Coriolis force (this turns wind to the right in the NH and left in the SH and causes the wind to flow parallel to isobars)</li>
<li>gravity (provides hydrostatic balance with the PGF in the vertical)</li>
<li>Friction (in the boundary layer you may see this as $\nu\nabla^2\mathbf u$)</li>
</ul>

<p>For large scale synoptic flow above the surface, this is often simplified as a balanced flow called <em>geostrophic balance</em>.  This a steady flow with a balance between the PGF and Coriolis force in the horizontal and hydrostatic balance in the vertical.</p>

<p>$$ \dfrac{1}{\rho}\nabla p = 2 \mathbf \Omega \times \mathbf u $$</p>

<p>Which can also be written as </p>

<p>$$u_g = -\dfrac{1}{\rho f}\dfrac{\partial p}{\partial y}$$
$$v_g =  \dfrac{1}{\rho f}\dfrac{\partial p}{\partial x}$$
$$\dfrac{\partial p}{\partial z} = -\rho g$$</p>

<p>In these equations, $u_g$ is the geostrophic wind in the east/west direction and $v_g$ is the geostrophic wind in the north/south direction and $f$ is the Coriolis parameter ($f = 2\Omega\sin\phi$, where $\phi$ is lattitude).</p>

<p>For this idealized geostrophic and hydrostatic balance, there is no vertical motion and all horizontal flow is parallel to isobars, flowing clockwise (counter-clockwise) around high pressure in the NH (SH) and flowing counter-clockwise (clockwise) around low pressure in the NH (SH).</p>

<p>For curved flow, we can consider another balance, the <em>gradient wind balance</em> that allows acceleration of the flow though centrifugal forces.  This can be written as (where $n$ is in the cross-wind direction):</p>

<p>$$ \dfrac{V^2}{R_t} = -fV - \dfrac{1}{\rho}\dfrac{\partial p}{\partial n} $$</p>

<p>Where $R_t$ is the radius of curvature in the flow. In the limit of $R_t \rightarrow \infty$ the acceleration term vanishes and this becomes geostrophic flow.  The consequence of this balance is that wind will flow slower than geostrophic balance around a low pressure center, this is said to be <em>subgeostrophic</em>.  Around a high pressure center we have <em>supergeostrophic</em> flow, or faster than geostrophic.</p>

<hr>

<p>You may have noticed the wind balances above are non-divergent and lack vertical flow.  This makes for boring weather, and does not hold near the ground or where vertical motion is large.  </p>

<p>We term the deviation from geostrophic flow the <em>ageostrophic</em> wind and this accounts for friction.  This results in wind converging toward low pressure and diverging from high pressure. </p>

<hr>

<p>Another flow is the <em>isallobaric</em> wind, and this is wind that blows from pressure rises toward pressure falls.  A place you will normally see this wind is just as a cold front passes and the pressure rises behind the front and falls in front of it.  This enhances the cross frontal wind and helps produce the often strong, gusty winds after a cold front passes.</p>

CC BY-SA 3.0
2015-05-04T19:14:52.563Z
I feel like any "why does wind blow" explanation should at least mention solar heating, the primary cause of pressure differences.
f.thorpe
CC BY-SA 4.0
2023-07-17T12:56:47.483Z
I feel that most of this (otherwise excellent) answer is answering "how can the motion of the wind be described mathematically" rather than "Where does wind come from?".
Semidiurnal Simon
CC BY-SA 3.0
2014-04-24T20:25:24.663Z
2014-04-24T21:36:23.657Z
2014-04-24T21:36:23.657Z
casey
<p>Wind is (according to <a href="http://en.wikipedia.org/wiki/Wind">Wikipedia</a>) the flow of gases on a large scale.<br/>On the surface of the Earth, wind consists of the bulk movement of air.</p>

<p>What forces would cause such a mass movement of air?</p>

CC BY-SA 3.0
2014-04-24T20:58:37.520Z
A friend of mine once overheard a conversation between a father and his child on a public transit bus on a windy day. Child: "Why does the wind blow?". Father: "Some places are cold and some places are warm. That is not fair. Thus, the wind takes the cold air away and moves it to the warm place so that everybody's happy."
milancurcic
CC BY-SA 3.0
2014-04-24T22:33:08.253Z
Except it is the reverse : Second Law of Thermodynamics. You can't move heat from the colder to the hotter! :-)
winwaed
CC BY-SA 3.0
2014-04-24T23:34:58.363Z
@winwaed Not really! The air moves from a region of higher density (cold) to a region of lower density (warm) due to pressure gradient force, advecting lower temperature. What you are talking about is molecular diffusion, which is negligible on synoptic scales. :)
milancurcic
CC BY-SA 3.0
2014-04-25T10:40:50.173Z
A question with fun aspects... I was outside a few weeks ago as a good gust of air passed by. After it passed, I noticed the calm and suddenly thought "Well, what was pushing it from behind?" Took a few seconds to realize...
user2338816
CC BY-SA 3.0
2014-04-25T12:03:25.790Z
IRO: fair enough - good thing I'm not a meteorologist :-)
winwaed
<meteorology><atmosphere><wind><air-currents>
Where does wind come from?
Ben A. Noone
# Where does wind come from?

(Asked by: username_0 on 2014-04-24)

Wind is (according to [Wikipedia](http://en.wikipedia.org/wiki/Wind)) the flow of gases on a large scale.  
On the surface of the Earth, wind consists of the bulk movement of air.

What forces would cause such a mass movement of air?

**Tags:** meteorology, atmosphere, wind, air-currents

> **Comments:**
> **username_1**: A friend of mine once overheard a conversation between a father and his child on a public transit bus on a windy day. Child: "Why does the wind blow?". Father: "Some places are cold and some places are warm. That is not fair. Thus, the wind takes the cold air away and moves it to the warm place so that everybody's happy."  
> **username_2**: Except it is the reverse : Second Law of Thermodynamics. You can't move heat from the colder to the hotter! :-)  
> **username_1**: @username_2 Not really! The air moves from a region of higher density (cold) to a region of lower density (warm) due to pressure gradient force, advecting lower temperature. What you are talking about is molecular diffusion, which is negligible on synoptic scales. :)  
> **username_3**: A question with fun aspects... I was outside a few weeks ago as a good gust of air passed by. After it passed, I noticed the calm and suddenly thought "Well, what was pushing it from behind?" Took a few seconds to realize...  
> **username_2**: IRO: fair enough - good thing I'm not a meteorologist :-)  

---

## 1 answers

### Answer by username_4 on 2014-04-24. Score: 20 | Accepted answer

Wind is caused by pressure differences. Think of a balloon full of air; poke a hole in it and the air comes out. Why? Because the pressure in the balloon is higher than outside, and so to regain equal pressure, mass moves and that is the wind.

There is a bit more to this in the atmosphere as the Earth rotates and near the surface friction also plays a role. The equation of motion is the Navier-Stokes and in vector form in Cartesian space is:

$$\dfrac{\partial\mathbf u}{\partial t} = - \mathbf u \cdot \nabla \mathbf u -\dfrac{1}{\rho}\nabla p-2 \mathbf \Omega \times \mathbf u + \mathbf g + \mathbf F$$

In this equation, $\mathbf u$ is the vector wind, $(\mathbf u \cdot \nabla)$ is the advection operator, $\rho$ is density, $\mathbf \Omega$ is the vector rotation of the Earth, $\mathbf g$ is effective gravity and $\mathbf F$ is friction.

The LHS is the time rate of change of the wind at a point in space (as opposed to following the parcel). The RHS represent a number of factors that produce a change in the wind. From left to right:

* Advection of momentum (non-linear)
* Pressure gradient force (this is wind blowing from high to low pressure)
* Coriolis force (this turns wind to the right in the NH and left in the SH and causes the wind to flow parallel to isobars)
* gravity (provides hydrostatic balance with the PGF in the vertical)
* Friction (in the boundary layer you may see this as $\nu\nabla^2\mathbf u$)

For large scale synoptic flow above the surface, this is often simplified as a balanced flow called *geostrophic balance*. This a steady flow with a balance between the PGF and Coriolis force in the horizontal and hydrostatic balance in the vertical.

$$ \dfrac{1}{\rho}\nabla p = 2 \mathbf \Omega \times \mathbf u $$

Which can also be written as

$$u\_g = -\dfrac{1}{\rho f}\dfrac{\partial p}{\partial y}$$
$$v\_g = \dfrac{1}{\rho f}\dfrac{\partial p}{\partial x}$$
$$\dfrac{\partial p}{\partial z} = -\rho g$$

In these equations, $u\_g$ is the geostrophic wind in the east/west direction and $v\_g$ is the geostrophic wind in the north/south direction and $f$ is the Coriolis parameter ($f = 2\Omega\sin\phi$, where $\phi$ is lattitude).

For this idealized geostrophic and hydrostatic balance, there is no vertical motion and all horizontal flow is parallel to isobars, flowing clockwise (counter-clockwise) around high pressure in the NH (SH) and flowing counter-clockwise (clockwise) around low pressure in the NH (SH).

For curved flow, we can consider another balance, the *gradient wind balance* that allows acceleration of the flow though centrifugal forces. This can be written as (where $n$ is in the cross-wind direction):

$$ \dfrac{V^2}{R\_t} = -fV - \dfrac{1}{\rho}\dfrac{\partial p}{\partial n} $$

Where $R\_t$ is the radius of curvature in the flow. In the limit of $R\_t \rightarrow \infty$ the acceleration term vanishes and this becomes geostrophic flow. The consequence of this balance is that wind will flow slower than geostrophic balance around a low pressure center, this is said to be *subgeostrophic*. Around a high pressure center we have *supergeostrophic* flow, or faster than geostrophic.

---

You may have noticed the wind balances above are non-divergent and lack vertical flow. This makes for boring weather, and does not hold near the ground or where vertical motion is large.

We term the deviation from geostrophic flow the *ageostrophic* wind and this accounts for friction. This results in wind converging toward low pressure and diverging from high pressure.

---

Another flow is the *isallobaric* wind, and this is wind that blows from pressure rises toward pressure falls. A place you will normally see this wind is just as a cold front passes and the pressure rises behind the front and falls in front of it. This enhances the cross frontal wind and helps produce the often strong, gusty winds after a cold front passes.

> **Comments:**
> **username_5**: I feel like any "why does wind blow" explanation should at least mention solar heating, the primary cause of pressure differences.  
> **username_6**: I feel that most of this (otherwise excellent) answer is answering "how can the motion of the wind be described mathematically" rather than "Where does wind come from?".  

---

