Where does wind come from?

Question

Wind is (according to Wikipedia) 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?

Answer 1

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.