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Laboratory experiments and a non-harmonic theory for topographic Rossby waves over a linearly sloping bottom on the f-plane

Published online by Cambridge University Press:  09 February 2010

YAIR COHEN ,
NATHAN PALDOR  and
JOËL SOMMERIA
YAIR COHEN
Affiliation:
The Fredy and Nadine Herrmann Institute of Earth Sciences, Edmond J. Safra Campus, Givat Ram, The Hebrew University Jerusalem, Jerusalem 91904, Israel
NATHAN PALDOR*
Affiliation:
The Fredy and Nadine Herrmann Institute of Earth Sciences, Edmond J. Safra Campus, Givat Ram, The Hebrew University Jerusalem, Jerusalem 91904, Israel
JOËL SOMMERIA
Affiliation:
Laboratoire des Ecoulements Géophysiques et Industriels (LEGI, CNRS-INPG-UJF) BP53 38041, Grenoble CEDEX 9, France
*
†Email address for correspondence: nathan.paldor@huji.ac.il
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Abstract

Low-frequency waves that develop in a shallow layer of fluid, contained in a channel with linearly slopping bottom and rotating with uniform angular speed are investigated theoretically and experimentally. Exact numerical solutions of the eigenvalue problem, obtained from the linearized shallow water equations on the f-plane, show that the waves are trapped near the channel's shallow wall and propagate along it with the shallow side on their right in the Northern hemisphere. The phase speed of the waves is slower compared with that of the harmonic theory in which bottom slope is treated inconsistently. A first-order approximation of the cross-channel dependence of the coefficient in the eigenvalue equation yields an approximation of the cross-channel velocity eigenfunction as an Airy function, which, for sufficiently wide channels, yields an explicit expression for the wave's dispersion relation. The analytic solutions of the eigenvalue problem agree with the numerical solutions in both the wave trapping and the reduced phase speed. For narrow channels, our theory yields an estimate of the channel width below which the harmonic theory provides a more accurate approximation. Laboratory experiments were conducted on a 13 m diameter turntable at LEGI-Coriolis (France) into which a linearly sloping bottom of 10 % incline was installed. A wavemaker generated waves of known frequency at one end of the turntable and the wavenumbers of these waves were measured at the opposite end using a particle imaging velocimetry technique. The experimental results regarding the phase speed and the radial structure of the amplitude are in very good agreement with our theoretical non-harmonic predictions, which support the present modification of the harmonic theory in wide channels.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 645 , 25 February 2010 , pp. 479 - 496
Copyright
Copyright © Cambridge University Press 2010

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