The Relative Roles of Diapycnal and Isopycnal Mixing on Subsurface Water Mass Conversion

Abstract

Fluid motion in the sea is known to occur predominantly along quasi-horizontal neutral surfaces but the very small diapycnal (i.e., across isopycnal) velocities often make a significant contribution to the conversation equations of heat, salt and tracer. By eliminating the diapycnal advection term between the conservation equations for (i) heat and (ii) salt, an equation is derived for the rate of change (Lagrangian derivative) of potential temperature ? on a neutral surface which has terms caused by (a) turbulent mixing along isopycnal surfaces (i.e., isopycnal mixing), (b) diapycnal turbulent mixing and (c) double-diffusive convection. Bemuse of the nature of the isopycnal reference frame, the diapycnal mixing terms do not take their expected forms. For example, the diapycnal turbulent mixing term is proportional to the diapycnal eddy diffusivity D multiplied by the curvature of the ?-S curve, d2S/d?2, rather than the usual form (D?x)x. If the ??S curve is locally straight, small-scale turbulent mixing can have no effect on the temperature (or salinity) measured on an isopycnal surface. For values of the ??S curvature appropriate to the Central Waters of the World's Oceans, the rate at which diapycnal turbulent mixing changes potential temperature on isopycnals is a fraction of D?xx (say 0.15 D?xx). This surprising result is due to the ability of the isopycnal surface to migrate quasi-vertically through the water column (or equivalently, for water to move diapycnally through the isopycnal surface) in response to the divergence (?·) of the fluxes of both heat and salt. In the interpretation of oceanographic data sets, it is not yet possible to estimate the diapycnal advection velocity and so it is customarily omitted from the conservation equations. It is the main aim of this paper to show that by so neglecting the diapycnal advective terms, the diapycnal mixing processes enter the conservation equations in greatly altered forms. The conservation equations for scalers (both active and passive) on a neutral surface which we develop are then the appropriate equations to be used in future studies of subsurface water mass conversion.