Etudes et évaluation de processus océaniques par des hiérarchies ...

126 CHAPITRE 4. ETUDES DE PROCESSUS OCÉANOGRAPHIQUES
Ocean Dynamics
the total friction is easily done whereas the distinction
between the nature of the friction, linear or quadratic, is
more complex, takes a longer amount time and requires
for smaller noise levels in the observed variable. The
dynamics in τ − c D parameter-space thus happen on
two time-scales, a fast convergence onto the manifold
of slow convergence followed by a slow convergence
within it.
It is, however, interesting to note that there is a
rather good convergence to the correct values with a
rather high noise level, which is actually larger than
the thickness of the gravity current itself. This feature
of fast convergence onto a manifold of slow convertel-00545911,
version 1 - 13 Dec 2010
Fig. 5 Distribution of the ensemble in τ (horizontal direction)
and c D (vertical direction) space for the three experiments:
G0221 (left column), G0021 (middle column) and G0121 (right
column), for different times: Initial distribution (upper line)
|u| ≈ 0.2 m s −1 . The space time mean absolute velocity
of the gravity current is defined by:
|u| = 1 ∫ T ∫
h|u|dxdt (10)
AT
0
L
where A = ∫ L
hdx is the cross-section of the gravity
current, L is the extension in the x-direction and T is
the duration of the experiment (7 days). Indeed, the
total friction is given by c D |u| + τ, which is constant
along a line of slope −|u| in τ-c D -space. The fast convergence
onto the line of slope −|u| (forthwith called
manifold of slow convergence) followed by a slow convergence
along the line means that the estimation of
(same in all experiments; some initial values lie outside the area
shown), after 7 days (middle line) and after seven iterations of
the 7-day dynamics (lower line). The values of τ and c D are
normalised by the true value used in the control run