Question 2 19 Marks Consider The Wind Stress Driven Oceanic Flow Generated By A Large Scale High Pressure System In The 1 (42.66 KiB) Viewed 24 times
Question 2 19 marks] Consider the wind-stress-driven oceanic flow generated by a large-scale high pressure system in the atmosphere. When the wind blows entirely in the x-direction (as in the figure below), there is a constant wind stress vector (Twind: 0). Twind (Plan view) L. WATER LAND For a positive upwards (= = 0 at the water surface), it has been proposed that the resulting steady-state fluid motion in the ocean is given by: (Varpins e=16 cos (á? - ) twind Z u(2) = V2Twind pfd V(2) = lez/d sin in pfd d where the length scale d = /2v/lf is known as the 'Ekman layer depth.
(a) Firstly, by considering the relative magnitudes of all the terms, simplify the Navier- Stokes equations in the horizontal directions down to two-term equations. [1 mark] (b) Verify that the solutions for flow velocities in the ocean (above) satisfy these Navier- Stokes equations and all relevant boundary conditions. 15 marks (c) Consider this phenomenon off the coast of San Francisco, California. A typical quantification of the wind stress on the ocean is 0.001pqUŽo, where Ule is the wind speed (at a height of 10 m) and Pa is the density of air. For a wind speed of 10 m/s, plot (not sketch!) the velocity vector in the ocean, and its variation over depth. Use this plot to explain why this flow is called the 'Ekman spiral'. [2.5 marks] (d) How would your plot in (c) change if the flow was turbulent? [0.5 marks]
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