Diffusive convection contributes substantially to heat transport in the Arctic Ocean. Specifically, a region of active diffusive layering in the Arctic halocline separates the warm North Atlantic water from the colder waters of Pacific origin in the Canadian Basin and from the polar mixed layer above them.
The Arctic halocline is generally stable to the development of double-diffusive and dynamic instabilities – the two major sources of small-scale mixing in the mid-latitude oceans. Regardless, direct observations have shown the abundance of double-diffusive staircases in the Arctic Ocean, which suggests the presence of some destabilizing process facilitating the transition from smooth-gradient to layered stratification. In addition, recent publications have shown that an instability can develop in such circumstances if weak static shear is present even when the flow is dynamically and diffusively stable. However, the impact of oscillating shear, associated with the presence of internal gravity waves, has not yet been addressed for the diffusive case.
Recently, Dr. Justin Brown and Professor Timour Radko from the Department of Oceanography, Naval Postgraduate School in California, presented a study where they focused on investigating the impact of the magnitude and frequency of externally forced oscillatory shear on water with Arctic stratification by using two-dimensional simulations of diffusive convection. They hoped to confirm the relevance of the thermohaline-shear mechanism to the problem of layering in the context of oscillatory shear. Their work is currently published in the Journal of Fluid Mechanics.
The authors derived the equations responsible for governing their physical system. They then described the numerical considerations, including the numerical scheme, resolution tests and typical evolution of the simulations. Lastly, they engaged in simulations where they focused on capturing the early growth, quasi-equilibrium and late-time behavior, respectively, of the subject matter.
Simulations with stochastic shear – characterized by a continuous spectrum of frequencies from inertial to buoyancy – indicated that thermohaline layering occurred due to the presence of destabilizing modes (oscillations of near the buoyancy frequency). Furthermore, the simulations showed that such layers appeared as well-defined steps in the temperature and salinity profiles. In other words, the two researchers found out that the thermohaline-shear instability could be triggered by time-dependent shear.
In summary, the relevance of the thermohaline-shear mechanism to the problem of layering, the stability analysis that has to be reproduced for oscillatory shear, has been confirmed. Simulations of time-dependent shear in a fluid stable to the formation of double-diffusive instabilities showed that three major regimes are possible for shear flows with Richardson numbers greater than unity. However, one caveat of this work is that it considered only horizontal motion for simplicity, but very rapid oscillations tend to slope in the ocean . Nevertheless, they identified a plausible explanation for how staircases can develop for representative oceanographic parameters at high latitudes. Altogether, the thermohaline-shear instability, as presented by Brown and Radko is a plausible mechanism for staircase formation in the Arctic and merits substantial future study.
Justin M. Brown, Timour Radko. Initiation of diffusive layering by time-dependent shear. Journal of Fluid Mechanics (2019), volume 858, page 588–608.Go To Journal of Fluid Mechanics