Etudes et évaluation de processus océaniques par des hiérarchies ...
Etudes et évaluation de processus océaniques par des hiérarchies ...
Etudes et évaluation de processus océaniques par des hiérarchies ...
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4.8. ESTIMATION OF FRICTION LAWS AND PARAMETERS IN GRAVITY CURRENTS BY DATA<br />
Noname manuscript No.<br />
(will be inserted by the editor)<br />
Estimation of Friction Param<strong>et</strong>ers in Gravity Currents by<br />
Data Assimilation in a Mo<strong>de</strong>l Hierarchy<br />
A. Wirth<br />
Received: date / Accepted: date<br />
tel-00545911, version 1 - 13 Dec 2010<br />
Abstract This paper is the last in a series of three investigating the friction laws and<br />
their <strong>par</strong>am<strong>et</strong>risation in i<strong>de</strong>alised gravity currents in a rotating frame. Results on the<br />
dynamics of a gravity current (Wirth, Ocean Dyn. 59, 551, 2009) and on the estimation<br />
of friction laws by data assimilation (Wirth & Verron Ocean Dyn. 58, 247, 2008)<br />
are combined to estimate the friction <strong>par</strong>am<strong>et</strong>ers and discriminate b<strong>et</strong>ween friction<br />
laws in non-hydrostatic numerical simulations of gravity current dynamics, using data<br />
assimilation and a reduced gravity shallow water mo<strong>de</strong>l.<br />
I <strong>de</strong>monstrate, that friction <strong>par</strong>am<strong>et</strong>ers and laws in gravity currents can be estimated<br />
using data assimilation. The results clearly show that friction follows a linear<br />
Rayleigh law for small Reynolds numbers and the estimated value agrees well with the<br />
analytical value obtained for non-accelerating Ekman layers. A significant and sud<strong>de</strong>n<br />
<strong>de</strong><strong>par</strong>ture towards a quadratic drag law at an Ekman layer based Reynolds number<br />
of around 800 is shown, in agreement with classical laboratory experiments. The drag<br />
coefficient obtained com<strong>par</strong>e well to friction values over smooth surfaces. I show that<br />
data assimilation can be used to d<strong>et</strong>ermine friction <strong>par</strong>am<strong>et</strong>ers and discriminate b<strong>et</strong>ween<br />
friction laws and that it is a powerful tool in systematically connection mo<strong>de</strong>ls<br />
within a mo<strong>de</strong>l hierarchy.<br />
Keywords ocean dynamics · gravity current · friction laws · <strong>par</strong>am<strong>et</strong>er estimation ·<br />
data assimilation<br />
PACS 65N35 · 76M22 · 86A05<br />
1 Introduction<br />
The realism todays and tomorrows numerical mo<strong>de</strong>ls of the ocean dynamics is and will<br />
be governed by the accuracy of the <strong>par</strong>am<strong>et</strong>risations of the processes not explicitly<br />
A. Wirth<br />
LEGI / MEOM<br />
CNRS<br />
BP 53, 38041 Grenoble Ce<strong>de</strong>x 9, France<br />
E-mail: achim.wirth@hmg.inpg.fr
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