# Problem 59696. Solve an ODE: Ekman spiral on a solid surface

Problem
Write a function to solve for u and v as a function of z in this system of ordinary differential equations:
where f, U, V, and η are constants. The boundary conditions are that at and and as .
Background
This set of equations results from simplifying the Navier-Stokes equations (i.e., conservation of momentum for a fluid with a linear stress-rate of strain relation) for large-scale flow subjected to rotation. The horizontal velocity components are u and v. The Coriolis parameter f is related to Earth’s rotation rate and the latitude, and η is the kinematic viscosity, which can be interpreted as an eddy viscosity to account for the effects of turbulence.
The velocities far above the surface, U and V, result from the pressure gradient: and , where p is pressure and ρ is density. Notice that far above the surface, the flow is along the isobars, or lines of constant pressure. As the surface is approached, the velocity vector rotates—or spirals.

### Solution Stats

100.0% Correct | 0.0% Incorrect
Last Solution submitted on Mar 12, 2024

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!