Taking the curl of the Boussinesq momentum equation and using incompressibility gives the <vorticity equation>
$$
\boxed{
\partial_t\boldsymbol\omega+(\mathbf u\mathbin{\cdot}\nabla)\boldsymbol\omega
=(\boldsymbol\omega\mathbin{\cdot}\nabla)\mathbf u
+\nabla\left(\frac{\rho'}{\rho_0}\right)\times\mathbf g
+\nu\nabla^2\boldsymbol\omega}.
$$
The second term on the right is <baroclinic vorticity generation>. It is nonzero where a horizontal density gradient crosses the vertical gravitational acceleration.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 345 / 3 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-345/3/a/solution