Consider the development of a simplified, convective, oceanic mixed layer in win
ID: 77134 • Letter: C
Question
Consider the development of a simplified, convective, oceanic mixed layer in winter. Initially at the start of winter, the temperature profile is given by
T(z) = Ts + G*z
where Ts is the temperature at the surface, z is depth (which is zero at the sea surface and increases upwards), and the gradient G > 0. During the winter, heat is lost from the surface at a rate Q W/m^2. As the surface cools, convection sets in and mixes the developing, cold, mixed layer of depth h(t), which has a uniform temperature Tm(t).
Assume that temperature is continuous across the base. By matching the heat lost through the surface to the heat content of the water column, determine how h(t) and Tm(t) evolve in time over the winter period.
Then solve for if Q = 25 W/m^2 and G = 10 degrees Celcius per kilometer, how long will it take the mixed layer to reach a depth of 100m?
Explanation / Answer
O-o