The Arctic Ocean main thermocline may be characterized by a series of fine-scale thermohaline staircase structures that are present in a wide range of regions, the formation mechanism of which remains unclear. Recent analysis has led to the proposal of a theoretical model which suggested that these staircase structures form spontaneously in the salinity and temperature-stratified ocean when the turbulent intensity determined by the buoyancy Reynolds number Reb is sufficiently weak (Ma and Peltier (2021)). In the current work, we have designed a series of Reb controlled direct numerical simulations of turbulence in the Arctic Ocean thermocline to test the effectiveness of this theory. In these simulations, the staircases form naturally when Reb falls in the range predicted by the instability criterion that is the basis of the proposed theory. In the DNS analyses described we show that the exponential growth-rate of the layering mode of instability matches well with the prediction of (Ma and Peltier (2021)). The staircases formed in our simulations are further compared with the classical diffusive interface model initially proposed by (Linden and Schirtcliff (1978)), which argued that stable staircase structures can only form when the density ratio Rρ is smaller than the critical value Rρ^{cr}=τ^(-1/2). . We show that the staircase structures can stably persist in the model regardless of whether or not Rρ is satisfied because of the involvement of stratified turbulence in the interfaces of the staircase.

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 obtain 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 (2013). 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.