REGIMES AND SCALING LAWS FOR ROTATING DEEP CONVECTION IN THE OCEAN

Numerical experiments are presented which explore the dependence of th e scale and intensity of convective elements in a rotating fluid on va riations in external parameters in a regime relevant to open ocean dee p convection. Conditions inside a convection region are idealized by r emoving buoyancy at a uniform rate B from the surface of an initially homogeneous, motionless, incompressible ocean of depth H with a linear equation of state, at a latitude where the Coriolis parameter is f. T he key nondimensional parameters are the natural Rossby number Ro = ( B/f3H2)1/2 and the flux Rayleigh number Ra(f) = BH4/(k2v), where k and v are (eddy) diffusivities of heat and momentum. Ro is set to values appropriate to open ocean deep convection (0.01 < Ro <1), and modera tely high values of Ra(f) (10(4) < Ra(f) < 10(13)) were chosen to prod uce flows in which nonlinear effects are significant. The experiments are in the 'geostrophic turbulence' regime. As Ro and Ra(f) are reduc ed the convective elements become increasingly quasi-two-dimensional a nd can be described as a field of interacting 'hetons'. The behavior o f the flow statistics-plume horizontal length scale L, speed scale U a nd buoyancy scale G, and the magnitude of the mean adverse density gra dient measured by the stratification parameter H -are studied as a fun ction of Ro and Ra(f). Physically motivated scaling laws are introduc ed, which, when appropriate, employ geostrophic and hydrostatic constr aints. They are used to interpret the experiments. In the heton regime , in which the motion is predominantly geostrophic and hydrostatic, th e observed scales are sensitive to moderate variations in Ro and larg e variations in Ra(f). We demonstrate broad agreement between our nume rical experiments and previous laboratory studies. The lateral scale o f the convective elements and the (adverse) stratification in which th ey exist adjust to one another so that NH/fL almost-equal-to 1; the ho rizontal scale of the hetons is thus controlled by a pseudo Rossby rad ius based on the unstable stratification parameter N, the scale at whi ch the overturning forces associated with N are balanced by the counte r-overturning forces associated with rotation.