A freshwater lake in late summer has a surface-mixed layer of density overlying a…

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 freshwater lake in late summer has a surface-mixed layer of density

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

overlying a thermocline

12\,\mathrm{m}

thick across which the density increases by

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

. Treat the lake as a Boussinesq fluid at rest with

\rho_0 = 998.0\,\mathrm{kg\,m^{-3}}

and

g = 9.8\,\mathrm{m\,s^{-2}}

, and take the density gradient across the thermocline as uniform. ((a)) Calculate the buoyancy frequency

N

of the thermocline. ((b)) Calculate the corresponding buoyancy period, in seconds and in minutes.

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