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The evolution of superharmonics excited by internal tides in non-uniform stratification

Published online by Cambridge University Press:  20 March 2020

Lois E. Baker Open the ORCID record for Lois E. Baker [Opens in a new window]  and
Bruce R. Sutherland Open the ORCID record for Bruce R. Sutherland [Opens in a new window]
Lois E. Baker*
Affiliation:
Department of Civil and Environmental Engineering, Imperial College London, LondonSW7 2AZ, UK
Bruce R. Sutherland
Affiliation:
Departments of Physics and of Earth and Atmospheric Sciences, University of Alberta, Edmonton, AB T6G 2E1, Canada
*
† Email address for correspondence: [email protected]
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Abstract

A weakly nonlinear time-dependent theory for the evolution of superharmonics generated by the nonlinear self-interaction of a mode-1 internal tide in non-uniform stratification is developed and compared to numerical simulations. The forcing by the internal tide is found to excite near-pure mode-1 superharmonics whose natural frequency is moderately different from twice the internal tide frequency. Consequently, the superharmonics undergo a slow periodic growth and decay that is comparable to an acoustic ‘beat’. At low latitudes the beat frequency is smaller and the superharmonics can grow to larger amplitude, allowing for the possibility of a superharmonic cascade.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Waves in rotating fluids
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 891 , 25 May 2020 , R1
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

van den Bremer, T. S., Yassin, H. & Sutherland, B. R. 2019 Lagrangian transport by vertically confined internal gravity wavepackets. J. Fluid Mech. 864, 348–380.CrossRefGoogle Scholar
Craik, A. D. D. 1985 Wave Interactions and Fluid Flows. Cambridge University Press.Google Scholar
Diamessis, P. J., Wunsch, S., Delwiche, I. & Richeter, M. P. 2014 Nonlinear generation of harmonics through the interaction of an internal wave beam with a model oceanic pycnocline. Dyn. Atmos. Oceans 66, 110–137.CrossRefGoogle Scholar
MacKinnon, J. A., Zhao, Z., Whalen, C. B., Waterhouse, A. F., Trossman, D. S., Sun, O. M., St. Laurent, L. C., Simmons, H. L., Polzin, K., Pinkel, R. et al. 2017 Climate process team on internal wave-driven ocean mixing. Bull. Am. Meteorol. Soc. 98 (11), 2429–2454.CrossRefGoogle Scholar
Staquet, C. & Sommeria, J. 2002 Internal gravity waves: from instabilities to turbulence. Annu. Rev. Fluid Mech. 34, 559–593.CrossRefGoogle Scholar
Sutherland, B. R. 2016 Excitation of superharmonics by internal modes in non-uniformly stratified fluid. J. Fluid Mech. 793, 335–352.CrossRefGoogle Scholar
Sutherland, B. R. & Jefferson, R. 2020 Triadic resonant instability of horizontally periodic internal modes. Phys. Rev. Fluids (in press).Google Scholar
Varma, D. & Mathur, M. 2017 Internal wave resonant triads in finite-depth non-uniform stratifications. J. Fluid Mech. 824, 286–311.CrossRefGoogle Scholar
Wunsch, C. & Ferrari, R. 2004 Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech. 36, 281–314.CrossRefGoogle Scholar
Wunsch, S. 2015 Nonlinear harmonic generation by diurnal tides. Dyn. Atmos. Oceans 71, 91–97.CrossRefGoogle Scholar
Wunsch, S. 2017 Harmonic generation by nonlinear self-interaction of a single internal wave mode. J. Fluid Mech. 828, 630–647.CrossRefGoogle Scholar
Zhao, Z., Alford, M. H., MacKinnon, J. A. & Pinkel, R. 2010 Long-range propagation of the semidiurnal internal tide from the Hawaiian Ridge. J. Phys. Oceanogr. 40 (4), 713–736.CrossRefGoogle Scholar