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Accueil > Actualités > Séminaires > Séminaires 2009

Mardi 20 oct à 11:00 - amphi Craya

Yair COHEN (Department of Atmospheric sciences of the Hebrew University in Jerusalem)

Titre/Title :
A non-harmonic theory and laboratory experiments for low frequency waves over a linearly slopping bottom on the f-plane

Contact :
Achim WIRTH

Résumé/Abstract :
Low frequency waves that evolve in a fluid over a linearly slopping bottom on the f–plane
are investigated in two cases : An infinitely wide channel, with two long shore boundaries and
a shelf of finite width, where the fluid surface intersects the slopping bottom at the shallow
side while a long-shore boundary is present on the shelf’s deep side. A Linear Shallow Water
Model is solved for each of the two cases and the theoretical results are compared to
experimental findings.
In both cases numerical solutions reveal the existence of waves that propagate with the
shallow boundary on the right in the northern hemisphere. In a channel the dispersion relation
shows vanishing frequencies for both large and small wavenumbers and a maximal frequency
at a finite wavenumber. The frequencies were found to differ from the classical harmonic
theory by more than an order of unity in wide channels or in steep slopes. In a shelf the
dispersion relation shows vanishing frequencies for small wavenumbers and a non-vanishing
frequency that approaches a constant value at large wavenumbers. These solutions are
consistent with existing asymptotic approximated solutions that were derived for an infinite
shelf.
Both cases were tested in laboratory experiments on a 13 m diameter turntable at LEGI-
Coriolis (France). The linear slope in the experiments was 10% and the wave’s period and
wavenumber were measured using a Particle Imaging Velocimetry (PIV) technique. The
experimental results regarding the dispersion relation (in both channel and shelf) and the
radial structure of the radial velocity (channel only) are in good agreement with the
(numerically derived) theoretical predictions. These results clearly showed that in wide
channels the amplitude is trapped near the shallow wall.
In a channel a simple formula for the dispersion relation is developed by approximating
the velocity eigenfunctions by Airy function, which agrees with the numerical solution for a
wide channels or a steeply sloping bottom. These solutions (that apply for infinitely wide
channels as well) mandate that the waves occupy a small part of the channel located close to
the shallow side and vanish throughout most of the channel width, so the channel width is
filtered out of the problem provided it is sufficiently large. A length scale for the channel’s
width is found that defines the harmonic regime and the Airy solution regime depending on
the channels slope, wave mode and wavenumber.