Abstract
There has been a rich interplay between laboratory experimental studies of internal waves and advancing understanding of their role in the ocean and atmosphere. In this study, we present and demonstrate the concept for a new form of laboratory internal wave generator that can excite axisymmetric wave fields of arbitrary radial structure. The construction and operation of the generator are detailed, and its capabilities are demonstrated through a pair of experiments using a Bessel function and a bourrelet (i.e., ring-shaped) configuration. The results of the experiments are compared with the predictions of an accompanying analytical model.
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Notes
J. Sommeria, LEGI / CNRS-UJF-INPG, http://servforge.legi.grenoble-inp.fr/projects/soft-uvmat.
The mathematical expressions for the vector laplacian of X in the cylindrical coordinates are \(\Delta _h X =\frac{\partial ^2 X}{\partial z^2}+\frac{\partial ^2 X}{\partial r^2}+\frac{1}{r}\frac{\partial X}{\partial r} - \frac{X}{r^2} =\frac{\partial ^2 X}{\partial z^2} + \partial _r\left( \frac{1}{r}\partial _r(rX)\right)\) and \(\Delta _z X = \frac{\partial ^2 X}{\partial z^2}+\frac{\partial ^2 X}{\partial r^2}+\frac{1}{r}\frac{\partial X}{\partial r}\).
Note that, mathematically \(\partial _r\Delta _z=\Delta _h\partial _r\).
The choice of the first-order Bessel function, combined with expression (14) leads to \(\Delta _h\Psi =-k^2\Psi +\partial _{zz}\Psi\).
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Acknowledgements
We thank Neil Balmforth for insightful discussions. We thank M. Moulin and D. Le Tourneau for the design and production of the wave generator and the tank. This work has been achieved thanks to the resources of PSMN from ENS de Lyon. The team in Lyon also thanks CNRS and ENS de Lyon for providing the financial support to build the rotating platform PERPET. T. P. acknowledges the support of the NSF (OCE-1357434), as well as ENS de Lyon for providing funding for his visits in Lyon.
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Maurer, P., Ghaemsaidi, S.J., Joubaud, S. et al. An axisymmetric inertia-gravity wave generator. Exp Fluids 58, 143 (2017). https://doi.org/10.1007/s00348-017-2423-x
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DOI: https://doi.org/10.1007/s00348-017-2423-x