PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Earth, Climate & Energy Physics · Atmosphere and ocean dynamics
Fluid Dynamics, Ch Rotating fluids: geostrophy, Taylor columns and Ekman layers
Problem
Following a storm, a drifting buoy in the North Sea at latitude 54∘N follows a current that, once the wind dies, rotates steadily with almost no change of speed: an inertial oscillation of peak speed U=0.15ms−1. Positions of the buoy, relative to its position x=y=0 at the moment the wind stress ceased, are logged every few hours (x eastward, y northward): Data: at t=0, 3.7, 7.4 and 11.1h the positions (x,y) in km are (0,0), (1.27,−1.27), (0,−2.54) and (−1.27,−1.27). Treat the water of the storm's mixed layer as unforced and frictionless once the wind has dropped, so the Coriolis force is the only horizontal force acting on the tracked parcel.
((a)) Predict the period and the radius of the inertial circle from theory, using Ω=7.292×10−5s−1 for the Earth's rotation.
((b)) Check the logged positions against this prediction and state the sense in which the current turns, viewed from above.
((c)) State two idealisations behind the inertial-circle model that a real storm-forced current might not fully satisfy.