Thermobaricity, cabbeling, and water‐mass conversion

Abstract

The efficient mixing of heat and salt along neutral surfaces (by mesoscale eddies) is shown to lead to vertical advection through these neutral surfaces. This is due to the nonlinearities of the equation of state of seawater through terms like ∂2ρ/∂θ∂p (thermobaric effect) and ∂2ρ/∂ θ2 (cabbeling). Cabbeling always causes a sinking or downwelling of fluid through neutral surfaces, whereas thermobaricity can lead to a vertical velocity (relative to neutral surfaces) of either sign. In this paper it is shown that for reasonable values of the lateral scalar diffusivity (especially below a depth of 1000 m), these two processes cause vertical velocities of the order of 10−7 m s−1 through neutral surfaces (usually downward!) and cause water‐mass conversion of a magnitude equal to that caused by a vertical diffusivity of 10−4 m2 s−1 (often equivalent to a negative diffusivity). Both thermobaricity and cabbeling can occur in the presence of any nonzero amount of small‐scale turbulence and so will not be detected by microstructure measurements. The conservation equations for tracers are considered in a nonorthogonal coordinate frame that moves with neutral surfaces in the ocean. Since only mixing processes cause advection across neutral surfaces, it is useful to regard this vertical advection as a symptom of various mixing processes rather than as a separate physical process. It is possible to derive conservative equations for scalars that do not contain the vertical advective term explicity. In these conservation equations, the terms that represent mixing processes are substantially altered. It is argued that this form of the conservation equations is the most appropriate when considering water‐mass transformation, and some examples are given of its application in the North Atlantic. It is shown that the variation of the vertical diffusivity with height does not cause water‐mass transformation. Also, salt fingering is often 3–4 times more effective at changing the potential temperature of a water mass than would be implied by simply calculating the vertical derivative of the fingering heat flux.