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Simultaneous velocity and density measurements for an energy-based approach to internal waves generated over a ridge

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A Publisher's Erratum to this article was published on 23 August 2011

Abstract

We present experimental results of internal wave generation by the oscillation of a two-dimensional topography in a linearly stratified fluid. Simultaneous synthetic schlieren and particle image velocimetry high-resolution measurements are made in a series of experiments with different forcing frequencies, all other parameters being kept constant. This setup allows us to obtain the potential and kinetic components of the mechanical energy transported by the internal wave beam for different relative values of the maximum topographic slope to the slope of internal wave phase lines, in a quasi-linear regime. Measurements are carefully validated and a combined wavelet and principal component analysis are carried out to extract the most energetic physical processes associated with the internal waves. The duration of the transient regime is evaluated in order to consider only results during the steady regime. We discuss the evolution of the radiated mechanical energy with respect to the forcing frequency, and we show that it reaches a maximum in the near-critical regime, in good agreement with recent numerical and theoretical works. New insights are provided about the role played by the relative values of the maximum topographic slope and the internal wave beam slope in the efficiency of energy transfers from barotropic tide to radiated internal waves. This study is a step toward a better quantification of the energy transported away by internal waves and available for mixing the ocean.

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Acknowledgments

This work has been supported by LEFE-IDAO Program “ondes et marées interne dans l’océan” (LEFE-IDAO-07/29) and ANR “TOPOGI-3D” contract (ANR-05-BLAN-0176). We thank B. Beaudoin, A. Belleudy, J.-C. Boulay, B. Bourdelles, J.-C. Canonici, S. Lassus-Pigat, F. Murguet, M. Morera, and H. Schaffner of the CNRM-GAME (URA1357, METEO-FRANCE and CNRS) fluid mechanics laboratory, as well as J. Gil for their kind support during the experiments. We also wish to thank F. Pétrélis for helpful discussions as well as R. Montroty.

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Authors and Affiliations

  1. CNRM-GAME/GMEI/SPEA, 42 avenue Gaspard Coriolis, 31057, Toulouse cedex 01, France

    Yuan Dossmann & Alexandre Paci

  2. Laboratoire d’Aérologie, 14 avenue Edouard Belin, 31400, Toulouse, France

    Yuan Dossmann & Francis Auclair

  3. Maaskant 7, 5512 BA, Vessem, The Netherlands

    Jochem W. Floor

Authors
  1. Yuan Dossmann
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  2. Alexandre Paci
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  3. Francis Auclair
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  4. Jochem W. Floor
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Correspondence to Yuan Dossmann.

Additional information

An erratum to this article can be found at http://dx.doi.org/10.1007/s00348-011-1155-6

Appendix

Appendix

1.1 Internal wave amplitude modulation and potential relationship to the forcing spectrum

The principal internal wave temporal field evolution is extracted from the first TSV (Fig. 12a). In addition to this general behavior, an amplitude modulation of the internal wave beam appears in the second TSV (Fig. 12b). As described in the next section, this phenomenon may be related to the intrinsic width of the peak in the forcing spectrum.

In the series of experiments, this modulation pattern has an approximate period of T m  = 1/f m  = 16T. One hypothesis is that this amplitude variation results from the interferences of two waves of close frequency f 1 and f 2 = f 1 + Δf with \( \Updelta f/f_{ 1} \ll 1 \). These interferences lead to an oscillation centered at f c  = (f 1 + f 2)/2, whose amplitude is modulated at a frequency f m  = Δf/2.

Figure 3b displays the Fourier transform of an experiment of forcing period T = 61.2 s. The peak at the forcing frequency has a finite width of Δf pk  \( \simeq \) 0.0015 Hz (at the ordinate for which the amplitude equals 0.2) similar to Δf = 1/8T = 0.002 Hz. The good matching between these 2 values indicates that the width of the forcing spectrum may cause a modulation of the internal wave amplitude.

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Dossmann, Y., Paci, A., Auclair, F. et al. Simultaneous velocity and density measurements for an energy-based approach to internal waves generated over a ridge. Exp Fluids 51, 1013–1028 (2011). https://doi.org/10.1007/s00348-011-1121-3

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