Arctic halocline response to changing surface stress forcing

Our study aims to develop a general framework for understanding the processes controlling key characteristics of the Arctic halocline and its response to transient surface stress forcing. There are three potential processes at play: i) Eulerian overturning cell due to wind-driven Ekman downwelling in the interior of the domain and corresponding upwelling at the lateral boundaries that lead to accumulation of fresh water and increased potential energy, ii) mesoscale eddy fluxes, generated at the boundaries as well as in the interior of the basin, that release the potential energy through isopycnal slumping, and iii) diabatic vertical mixing of buoyancy across the pycnocline.

To understand the complex interplay between these processes we use idealized eddy-resolving numerical simulation of the Arctic Ocean and explore solutions for a range of relevant non-dimensional parameters suggested by scaling arguments.

We find that, for external model parameters chosen to simulate present-day Arctic Ocean, it is a balance between the Ekman pumping and the mesoscale eddy fluxes that shapes the halocline properties. In the case of no buoyancy forcing at the surface or in the interior of the domain, the Eulerian overturning cell is almost entirely canceled by the eddy driven cell, with the residual circulation arising due to weak diabatic vertical mixing. Using a down-gradient eddy flux parameterization, we derive analytical solutions for the shape of the pycnocline and its asymptotic corrections due to weak vertical mixing which compares reasonably well with the numerical solutions.

At last, we present a theory for the time-dependent adjustment of the halocline and eddy field to changes in surface stress forcing. We derive an expression for the spin-up time scale t, that depends on the strength of surface-stress tau, eddy transfer coefficient k, size of the basin R, and a Coriolis parameter f such that t~=0.1 * R^2 * (k tau/f)^-0.5. For present-day Arctic conditions this time scale is of the order of a few years. Thus, on seasonal time scales the fresh water content is delayed in phase by pi/2 with respect to surface stress forcing, and it is only at decadal time-scales that one should expect the Arctic halocline to be in phase with surface stress forcing.