A western boundary current is bordered by a density front: the water is denser on its…

PHYSICS · Subjective · Fermi University Physics · Earth, Climate & Energy Physics · Atmosphere and ocean dynamics · Atmosphere and ocean dynamics

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

Problem

A western boundary current is bordered by a density front: the water is

1.5\,\mathrm{kg\,m^{-3}}

denser

40\,\mathrm{km}

on its offshore side than on its inshore side, with reference density

\rho_0 = 1025\,\mathrm{kg\,m^{-3}}

and Coriolis parameter

f = 9.0\times10^{-5}\,\mathrm{s^{-1}}

. The current is Boussinesq and in geostrophic and hydrostatic balance. Calculate the magnitude of the vertical shear of the geostrophic current,

\partial u_g/\partial z

, implied by this density gradient, using

f\frac{\partial u_g}{\partial z} = \frac{g}{\rho_0}\frac{\partial\rho}{\partial y}.