Diapycnal diffusivities in Kelvin–Helmholtz engendered turbulent mixing: the diffusive–convection regime in the Arctic Ocean

Abstract

Recent progress in the direct measurement of turbulent dissipation in the Arctic Ocean has highlighted the need for an improved parametrization of the turbulent diapycnal diffusivities of heat and salt that is suitable for application in the turbulent environment characteristic of this polar region. In support of this goal we describe herein a series of direct numerical simulations of the turbulence generated in the process of growth and breaking of Kelvin–Helmholtz billows. These simulations provide the data sets needed to serve as basis for a study of the stratified turbulent mixing processes that are expected to exist in the Arctic Ocean environment. The mixing properties of the turbulence are studied using a previously formulated procedure in which the temperature and salinity fields are sorted separately in order to enable the separation of irreversible Arctic mixing from reversible stirring processes and thus the definition of turbulent diffusivities for both heat and salt that depend solely upon irreversible mixing. These analyses allow us to demonstrate that the irreversible diapycnal diffusivities for heat and salt are both solely dependent on the buoyancy Reynolds number in the Arctic Ocean environment. These are found to be in close agreement with the functional forms inferred for these turbulent diffusivities in the previous work of Bouffard & Boegman (Dyn. Atmos. Oceans, vol. 61, 2013, pp. 14–34). Based on a detailed comparison of our simulation data with this previous empirical work, we propose an algorithm that can be used for inferring the diapycnal diffusivities from turbulent dissipation measurements in the Arctic Ocean.