(a) At latitude , a steady geostrophic flow of water, with molecular viscosity ,…
PHYSICS · Subjective · Fermi University Physics · Fluids & Continuum Physics · Kinematics, conservation laws and ideal flow · Convection, rotation and geophysical flows
Fluid Dynamics, Ch Rotating fluids: geostrophy, Taylor columns and Ekman layers
Problem
(a) At latitude 35∘N, a steady geostrophic flow of water, with molecular viscosity ν=1.0×10−6m2s−1, produces a bottom Ekman layer of thickness δE=2ν/f. Set beside it, as a formal comparison, a plate oscillating in the same water in a tank that does not rotate, at an angular frequency ω chosen equal to that f; it produces a Stokes layer of thickness δs=2ν/ω. Compute the two thicknesses, and explain from the balance of terms in each layer's momentum equation why they come out equal. (b) In the rotating fluid at 35∘N, a column of water of height h1=2.0m with zero relative vorticity flows over a submerged ridge that reduces its height to h2=1.4m. Using conservation of the shallow-water potential vorticity (ωz+f)/h, find the relative vorticity ωz of the column after it crosses the ridge, state whether the resulting spin is cyclonic or anticyclonic, and relate the result to the stretching of frozen-in vortex lines.