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
Problem Comments
-
2 Comments
Christian Schröder
on 10 Mar 2024
"where f, U, V, and v are constants" - do you mean f, U, V and nu?
ChrisR
on 11 Mar 2024
To reduce confusion, I changed nu (which Cody rendered closer to v) to eta.
Solution Comments
Show commentsProblem Recent Solvers2
Suggested Problems
-
2042 Solvers
-
Calculate the area of a triangle between three points
3060 Solvers
-
Remove from a 2-D matrix all the rows that contain at least one element less than or equal to 4
135 Solvers
-
47 Solvers
-
104 Solvers
More from this Author281
Problem Tags
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!