A large swimming pool at latitude is stirred by a jet pump

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

Fluid Dynamics, Ch Rotating fluids: geostrophy, Taylor columns and Ekman layers

Problem

A large swimming pool at latitude 45∘45^\circ is stirred by a jet pump. The resulting circulation has a speed scale U=0.05 m s−1U = 0.05\,\mathrm{m\,s^{-1}}, a horizontal length scale L=5 mL = 5\,\mathrm{m}, and a depth H=1.5 mH = 1.5\,\mathrm{m}. Take the kinematic viscosity of water as ν=1.0×10−6 m2 s−1\nu = 1.0\times10^{-6}\,\mathrm{m^2\,s^{-1}}. ((a)) Compute the Rossby number of the flow. ((b)) Compute the Ekman number of the flow, and state whether the Earth's rotation could plausibly set the sense of the circulation.

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