On the rate of descent of overflows

The path taken by dense turbulent outflows usually requires the numerical s olution of along-flow equations for mass, tracers, and momentum and cannot easily be predicted. Instead, we consider the consequences of two simple as sumptions. First, there is a quadratic turbulent bottom drag. Second, the o utflow is assumed to be approximately in local equilibrium so that a best f it formula from atmospheric and ocean surface layer observations plus large -eddy simulations, used by Zilitinkevich and Mironov [1996], can be used to predict the local thickness. (No energy budget for turbulent bottom layers is known, which is a constant difficulty for numerical models of such laye rs.) The equilibrium solution is approximately equivalent, for most oceanic conditions, to a constant bulk Richardson or Froude number. It is shown th at dense turbulent overflows follow a simple trajectory, in which the rate of depth increase is a constant, until the level of turbulence drops suffic iently that the equilibrium solution becomes invalid. This result is indepe ndent of the detailed thermodynamics, entrainment or detrainment, and the q uadratic drag coefficient (but does depend on the assumption of quadratic d rag). Trajectories for the major overflow regions give reasonable results w hen compared with the limited available data. An argument is given as to wh y entrainment should only occur over limited regions, with detrainment else where.