Ekman currents caused by variable wind in models of upper ocean with depth and time dependent eddy viscosity

• Main Author: Almelah, Rema Bashir
• Published: Keele University 2018
• Subjects: QA Mathematics
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.762217

The work examines response of the upper ocean to time-varying winds. In the Ekman paradigm the effect of wind is considered as time-varying horizontally uniform tangential wind stress applied to the ocean surface and the turbulent diffusion of momentum is described employing the Boussinesq closure hypothesis via a single scalar eddy viscosity. In contrast to all previous studies we take into account both its depth and time dependence and examine effects of density strati�cation. We found exact general solution to the full Navier-Stokes equations which describes dynamics of the Ekman boundary layer in terms of the Green's function. Several cases of varying eddy viscosity have been examined: (a) According to the Zikanov et al. [2003] parameterization (justified by LES) the eddy viscosity in non-strati�ed fluid increases linearly with depth in the upper part of the fluid, reaching the maximum value at some depth specifi�ed by the wind speed, and then decreases linearly with depth in the lower layer. For this model the explicit analytic solution describing Ekman response to arbitrary wind has been obtained and thoroughly compared with the available models employing more simple eddy viscosity pro�les lacking the LES validation. The range of situations where much simpler models can be used with acceptable accuracy has been identi�fied. (b) We considered the simplest model of the upper ocean with mixed layer at the top and strati�fied fluid below, which in terms of the Ekman model reduces to a two-layer model: the top (turbulent) layer is characterized by a high constant value of eddy viscosity, while the bottom layer has a much smaller viscosity also assumed to be constant. Basic scenarios such as sharp increase of wind and switch o� of the wind have been analysed from the viewpoint of fi�nding how and when the vertical profi�le of strati�cation affects the surface current caused by wind varying in time. It has been found under what conditions the surface velocity vector is noticeably affected by the presence of strati�cation. The parameter controlling whether the presence of strati�cation will manifest itself on the surface is shown to be the non-dimensional depth of the pycnocline: the surface velocity �field is quite sensitive to the depth of the mixed layer, but is much less sensitive to the strength of strati�cation. From the perspective of remote sensing of the characteristics of strati�fication the using HF radars, it has been concluded that these fi�ndings open new possibilities. (c) When the eddy viscosity is assumed to be both time and depth dependent, three basic scenarios have been thoroughly examined: (i) An increase of wind ending up with a plateau; (ii) Switch-off of the wind; (iii) Periodic wind. Their analysis shows that accounting for time dependence of eddy viscosity substantially changes the response, compared to the predictions of the models with constant in time viscosity. We also report a severe limitation of the Ekman type models employed in modelling of the oceanic surface boundary layer. The Ekman current caused by a growing wind quickly becomes unstable with respect to inviscid inflectional instability. These instabilities are fast, which suggests spikes of dramatically enhanced mixing in the corresponding parts of the water column. The instabilities also break down a fundamental element of the Ekman-type models the assumed spatial uniformity. The results require a radical revision of the existing paradigm.