Stably stratified air with buoyancy frequency and upstream speed approaches a ridge…

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

Stably stratified air with buoyancy frequency

N = 0.015\,\mathrm{s^{-1}}

and upstream speed

U = 3.0\,\mathrm{m\,s^{-1}}

approaches a ridge of height

H = 900\,\mathrm{m}

. The flow is steady, inviscid and Boussinesq, and the approach flow has no horizontal density variation before it meets the ridge. ((a)) Calculate the Froude number

Fr = U/(NH)

. ((b)) Calculate the dividing-streamline height

z_d

below which the air cannot cross the ridge and instead goes round it. ((c)) Calculate the wind speed that would be needed for all the air to pass over the ridge.

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