An ocean current of speed flows towards a broad seamount of horizontal width rising…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Convection, rotation and geophysical flows · Convection, rotation and geophysical flows

Fluid Dynamics, Ch Rotating fluids: geostrophy, Taylor columns and Ekman layers

Problem

An ocean current of speed

U = 0.05\,\mathrm{m\,s^{-1}}

flows towards a broad seamount of horizontal width

L = 20\,\mathrm{km}

rising from a sea floor at depth

H = 4000\,\mathrm{m}

, at latitude

30^\circ\mathrm{N}

. Take the ocean's turbulent eddy viscosity as

\nu = 1.0\times10^{-2}\,\mathrm{m^2\,s^{-1}}

and

\Omega = 7.292\times10^{-5}\,\mathrm{s^{-1}}

. The sea surface rises and falls so little that it may be treated as a rigid lid. ((a)) Compute the Rossby number

Ro = U/(fL)

and the Ekman number

Ek = \nu/(fH^2)

for this flow. ((b)) Predict, with a reason based on these two numbers, what the current does as it approaches the seamount: does the water near the sea surface flow straight over the top, or is it steered around it? Describe the pattern you expect at every depth.

Browse the problem library