Motion with wind stress, rotation and friction In the following, you may use these values if needed:
· density of air = 1 kg/m3
· density of ocean = 1000 kg/m3
· Coriolis parameter = 10-4 s-1
· gravity = g = 10 m/s2
· air temperature = 25 oC
· water temperature = 2 oC
Consider a slab of water on average 100 meters thick (i.e., the surface layer of the ocean) at mid-latitudes. It is forced by a surface wind of 15 m/s towards the northeast. The surface of the ocean is tilted upwards towards the east at 10 cm per 100 km.
Lastly, the wind has been blowing long enough that the motion in the slab is approximately steady (not changing in time).
a) Ignoring the transport terms (Rossby number ~ 0), write down the horizontal momentum equations that apply to this situation. Which of the forcings (wind, surface tilt) is the stronger in this case; i.e., which provides the stronger relative force?
b) Solve for the horizontal velocity components (u, v). Draw a vector diagram of the velocity.
c) Suppose now that the motion is resisted by a stress at the bottom of the layer. Suppose further that the stress provided by this drag force is given by
tbottom = cb (u, v)
where
cb = 2 kg / m2 s
What is the resulting steady flow now? How does the vector diagram change? Is it physically sensible (e.g., has friction reduced the speed of the flow)?