The Buoyancy Reynolds Number Instability and Thermohaline Staircase
Formation in the Polar Oceans
Abstract
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.