A current on a continental shelf has speed scale

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

Fluid Dynamics, Ch Stratified flow, double diffusion and geophysical scales

Problem

A current on a continental shelf has speed scale U=0.30 m s−1U = 0.30\,\mathrm{m\,s^{-1}}, horizontal length scale L=50 kmL = 50\,\mathrm{km}, depth H=100 mH = 100\,\mathrm{m}, Coriolis parameter f=1.0×10−4 s−1f = 1.0\times10^{-4}\,\mathrm{s^{-1}} and eddy viscosity νE=5.0×10−3 m2 s−1\nu_E = 5.0\times10^{-3}\,\mathrm{m^2\,s^{-1}}. Within a shallow shear layer the buoyancy frequency is N=8.0×10−3 s−1N = 8.0\times10^{-3}\,\mathrm{s^{-1}} and the vertical shear is dU/dz=0.010 s−1\mathrm{d}U/\mathrm{d}z = 0.010\,\mathrm{s^{-1}}. ((a)) Calculate the Rossby number Ro=U/(fL)Ro = U/(fL) and the Ekman number Ek=νE/(fH2)Ek = \nu_E/(fH^2). ((b)) Calculate the Rossby deformation radius LR=NH/fL_R = NH/f and the Burger number Bu=(LR/L)2Bu = (L_R/L)^2. ((c)) Calculate the gradient Richardson number Ri=N2/(dU/dz)2Ri = N^2/(\mathrm{d}U/\mathrm{d}z)^2 in the shear layer, and say what the Miles-Howard theorem can and cannot conclude from it.

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