Abstract
Abstract. This paper is the last in a series of three investigating the friction laws and their parametrisation in idealised gravity currents in a rotating frame. Results on the dynamics of a gravity current (Wirth, 2009) and on the estimation of friction laws by data assimilation (Wirth and Verron, 2008) are combined to estimate the friction parameters and discriminate between friction laws in non-hydrostatic numerical simulations of gravity current dynamics, using data assimilation and a reduced gravity shallow water model. I demonstrate, that friction parameters and laws in gravity currents can be estimated using data assimilation. The results clearly show that friction follows a linear Rayleigh law for small Reynolds numbers and the estimated value agrees well with the analytical value obtained for non-accelerating Ekman layers. A significant and sudden departure towards a quadratic drag law at an Ekman layer based Reynolds number of around 800 is shown, in agreement with classical laboratory experiments. The drag coefficient obtained compares well to friction values over smooth surfaces. I show that data assimilation can be used to determine friction parameters and discriminate between friction laws and that it is a powerful tool in systematically connecting models within a model hierarchy.
Highlights
The realism todays and tomorrows numerical models of the ocean dynamics is and will be governed by the accuracy of the parametrisations of the processes not explicitly resolved and resolvable in these models
I like to emphasise that without using data assimilation one might have thought that one just did not find the right minimum in parameter space, with data assimilation one can be more confident, so not certain, that the minimum was found but the model had major deficiencies so that it is not capable to represent well enough the dynamics
It is the effective drag coefficient that is usually represented in diagrams like Fig. 2 by the engineering community (Schlichting and Gertsen, 2000)
Summary
The realism todays and tomorrows numerical models of the ocean dynamics is and will be governed by the accuracy of the parametrisations of the processes not explicitly resolved and resolvable in these models. It is key to the climate dynamics of our planet and it is governed by small scale processes. When the dense water touches the ocean floor and/or passes through a strait, a gravity current is created, which is strongly influenced by the friction forces at the ocean floor (Wirth, 2009). Similar small scale processes are likely to determine the subsequent deep western boundary current and the upward transport and the mixing in the interior and coastal regions of the ocean. These small scale processes will not be explicitly resolved in ocean general circulation models (OGCMS) even in a far future. The understanding and parametrisation of these processes is of paramount importance to the progress in modelling the dynamics of the climate
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