Simulation of the Largest Coherent Vortices (Rolls) in the Ekman Boundary Layer

A Unifying Perspective on Transfer Function Solutions to the Unsteady Ekman Problem

“…Because the wind-driven response depends upon the details of momentum mixing within the surface mixed layer, an important line of research has been understanding the dependence of the near-surface currents on the assumptions regarding the profile of vertical eddy viscosity, denoted here K(z), together with the lower boundary conditions [5][6][7][8][9][10][11][12][13][14][15][16]. Recent work on the wind-driven currents has focused on the impacts of diverse phenomena, including Stokes drift and wave breaking [11,14,15,[17][18][19], realistically structured mixed layer turbulence [20][21][22], diurnal cycling [23,24], stratification and buoyancy gradient effects [25][26][27][28], instabilities of the Ekman solution itself [15,[29][30][31] arising from various mechanisms [32,33], and the impact of more general variations of the eddy viscosity with depth [10,13,14] and possibly also with time [9,15,22]. This goal of this paper is to contribute to obtaining the best possible estimate of the near-surface currents given the wind stress, by unifying and refining existing linear theories of the wind-driven response.…”

“…This profile, which vanishes both at the surface and at z = h, is of the form commonly used in the KPP model of Large et al [38], where the constant term in a cubic polynomial is set to zero as discussed in Appendix B1 of [39]. The solution of Song and Xu [14] is given in terms of the Gaussian hypergeometric function, see their Equations (29) and (47). While this transfer function is definitely worth investigating, a limitation with respect to the type of observational study we envision is that the cubic form is fixed.…”