Enhancements to Deep Turbulent Entrainment

Abstract

Abstract At first glance, one-dimensional mixed layer dynamics do not appear to predict sufficiently deep mixing to explain the formation of the large volumes of deep water observed in the polar and Mediterranean seas. However, two processes have been neglected in the turbulent kinetic energy (TKE) budget that led to larger vertical turbulent velocities that may enable deep penetrative convection, possibly contributing to the formation of dedeper waters. The energetics of deep convection are examined for two asymptotic regimes: (i) free convection with pressure augmentation of buoyancy flux, and (ii) forced convection with vertical mixing assisted by planetary rotational conversion of wind-generated horizontal TKE into vertical TKE. In the case of free convection, the buoyant production of vertical turbulence may be increased considerably by the increase in the thermal expansion coefficient (α) with pressure. An entrainment model including this nonlinearity in the equation of state predicts greater vertical mixing and penetrative convection into the pycnocline than does a model with the linear equation of state used traditionally for mixed layer predictions. The increase in thermal expansion coefficient with pressure is temperature-dependent and is more significant for cold polar water convection than it is for Mediterranean Sea convection. The significance of pressure enhancement of the buoyancy flux may be expressed in terms of the ratio of depth of mixing (h) to a depth scale H α = that depends mostly on mixed layer temperature. If h/H α ~ 1 or larger, the TKE budget will be dominated by pressure-enhanced free convection. For the Mediterranean Sea, h/H α = 0.3 when convection penetrates to the bottom. However, for the coldest polar seas h/H α = 8 for penetrative convection to the bottom, and h/H α is significant for mixing deeper than about a hundred meters. In the case of forced convection, maximum entrainment rate may be achieved when the wind stress is toward the west. Then the northward component of planetary rotation may transfer horizontal wind-generated turbulence to vertical turbulence. This enhances vertical flux rates in general and entrainment deepening by the mixed layer in particular. Such augmented wind mixing may cause sufficiently deep mixing to “turn on” the pressure-enhancement of buoyancy flux, with substantially increased vertical convection.