Fluxes of Properties through a Series of Double-Diffusive Interfaces with a Nonlinear Equation of State

View More View Less
  • 1 Research School of Earth Sciences, The Australian National University, Canberra 2600 A.C.T.
© Get Permissions
Full access

Abstract

Foster and Carmack (1976) and Middleton and Foster (1980) have observed a series of “diffusive” double-diffusive interfaces in the deep, central Weddell Sea which are very close to the conditions under which cabbeling is thought to be possible. Prompted by these observations, McDougall (1981b) has studied the fluxes and the entrainment across a single horizontal double-diffusive interface when the equation of state is significantly nonlinear. This work has shown how the nonlinearity of the equation of state affects the double-diffusive convection process by causing entrainment across the interface. For values of the density anomaly ratio Rρ < 2, it was concluded that this modified double-diffusive convection is much more important than the cabbeling mechanism. In this note we use these recent results to predict what signature these processes would have on a series of such interfaces in the Weddell Sea. We show that regular CTD profiles over a 48 h period would shed considerable light on the magnitude of the fluxes caused by entrainment across the interfaces as compared to the fluxes of ordinary (symmetrical) double-diffusive convection. By considering a regular series of migrating double-diffusive interfaces which are steady in the mean we show that the total flux of heat through a fixed depth is Fħ + ½ρ0eΔh, where FĦ is the double-diffusive heat flux across each interface, e the entrainment velocity across the interfaces (migration rate of the interfaces), Δh the difference in enthalpy between adjacent layers and ρ0 a reference density.

Abstract

Foster and Carmack (1976) and Middleton and Foster (1980) have observed a series of “diffusive” double-diffusive interfaces in the deep, central Weddell Sea which are very close to the conditions under which cabbeling is thought to be possible. Prompted by these observations, McDougall (1981b) has studied the fluxes and the entrainment across a single horizontal double-diffusive interface when the equation of state is significantly nonlinear. This work has shown how the nonlinearity of the equation of state affects the double-diffusive convection process by causing entrainment across the interface. For values of the density anomaly ratio Rρ < 2, it was concluded that this modified double-diffusive convection is much more important than the cabbeling mechanism. In this note we use these recent results to predict what signature these processes would have on a series of such interfaces in the Weddell Sea. We show that regular CTD profiles over a 48 h period would shed considerable light on the magnitude of the fluxes caused by entrainment across the interfaces as compared to the fluxes of ordinary (symmetrical) double-diffusive convection. By considering a regular series of migrating double-diffusive interfaces which are steady in the mean we show that the total flux of heat through a fixed depth is Fħ + ½ρ0eΔh, where FĦ is the double-diffusive heat flux across each interface, e the entrainment velocity across the interfaces (migration rate of the interfaces), Δh the difference in enthalpy between adjacent layers and ρ0 a reference density.

Save