Advanced Ocean Modelling: Using Open-Source Software

3.16 Exercise 9: Convective Entrainment 65Given that the ambient water column is initially stably stratified, the penetrationdepth of the convective plumes gradually increases with time. The reader is encouragedto compare the simulated rate of mixed-layer deepening with that predicted bythe solution to Eq. (3.67). The spacing between plumes increases as the penetrationreaches greater depths. The predicted aspect ratio of convection cells of 1.5–2 is inagreement with theory. Convective plumes reach the sea floor at 100-m depth afterabout 3 hrs of applied surface heat loss. The final result of convection is an almostwell-mixed water column.3.15.6 Additional Exercise for the ReaderRepeat the convection exercise with a fluid of two superimposed layers of differentdensities. Do convective plumes induce internal waves at the density interface?The reader is also encouraged to repeat this exercise with a stronger initial densitystratification.3.16 Exercise 9: Convective Entrainment3.16.1 How It WorksConvection produces vigorous mixing in upper parts of an otherwise stratified watercolumn. As the convection layer deepens, convective plumes mix deeper water intothis layer – a process which is called entrainment. Convective entrainment of heatplays an important role in polar oceans, for it can delay or even prevent sea ice formation,which would occur if the surface water were cooled down to temperaturesbelow the freezing-point temperature.3.16.2 Entrainment VelocityFor an ocean of initially stable density stratification, Eq. (3.67) implies that thethickness of the convective mixed layer h increases at a rate of:dhdt= BN 2 hThis mixed-layer deepening can be directly taken as a vertical entrainment velocity.This velocity determines how much heat, salt and other water properties becomemixed into the convection layer.