Abstract
This paper focuses on the internal tide emitted from a continental slope in a uniformly stratified fluid. Results from numerical simulations using the MITgcm and from laboratory experiments performed on the Coriolis platform in Grenoble are compared. Due to their peculiar dispersion relation, internal gravity waves organize into localized beams of energy. We show that the beam structure is well-predicted by the viscous theory of (Hurley and Keady, 1997), assuming that the internal gravity wave field is emitted by a horizontally oscillating cylinder whose radius is the radius of curvature of the topography at the beam emission. The wave beam can bear a sub-harmonic parametric instability whose vertical scale is recovered from resonant interaction theory. Reflection of the wave beam on the bottom leads to the generation of harmonic beams, consisting of free and trapped waves.
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References
Baines, P.G., Fang, X.H.: Internal tide generation at a continental shelf/slope junction: A comparison between theory and a laboratory experiment. Dynamics of Atmospheres and Oceans 9, 297–314 (1985).
Ferrari, R., Wunsch, C: Ocean circulation kinetic energy: reservoirs, sources, and sinks. Ann. Rev. Fluid Mech. 41, 253–282 (2009).
Garrett, C, Kunze, E.: Internal tide generation in the deep ocean. Annu. Rev. Fluid Mech. 39, 57–87, 2007.
Gerkema T., Staquet C., Bouruet-Aubertot, P.: Nonlinear effects in internal tide beams and mixing. Geophysical Research Letters 33, L08604 (2006).
Gerkema T., Staquet C., Bouruet-Aubertot, P.: Nonlinear effects in internal tide beams and mixing. Ocean Modelling 12, 302–318 (2006).
Gostiaux, L, Dauxois, T. Laboratory experiments on the generation of internal tidal beams over steep slopes. Physics Fluids 19(1), 1–4 (2007).
Hasselmann, K: A criterion for nonlinear wave stability. J. Fluid Mech. 30, 737 (1967).
Hibiya, T., Nagasawa, M., Niwa, N.: Nonlinear energy transfer within the oceanic internal wave spectrum at mid and high latitudes. J. Geophys. Res. 107(C11), 3207 (2002).
Holloway, P.E., Merrifield, M.A.: Internal tide generation by seamounts, ridges, and islands. J. Geophys. Res. 104(C11), 25937–25951 (1999).
Hurley, D.G., Keady, K.: The generation of internal waves by vibrating elliptic cylinders. Part 2. Approximate viscous solutions. J. Fluid Mech. 351, 11 (1997).
Jachec, S.M., Fringer, O.B., Gerritsen, M.G., Street, R.L.: Numerical simulation of internal tides and the resulting energetics within Monterey Bay and the surrounding area. Geophys Res. Lett. 33, L12605 (2006).
Khatiwala, S.: Generation of internal tides in an ocean of finite depth: analytical and numerical calculations. Deep Sea Research, 50, 3–21 (2003).
Lamb, K.B.: Nonlinear interaction among internal wave beams generated by tidal flow over supercritical topography. Geophys. Res. Lett. 31, doi:10.1029/2003GL01939 (2004).
Legg, S., Huijts, K.M.H: Preliminary simulations of internal waves and mixing generated by finite amplitude tidal flow over isolated topography. Deep Sea Research-II, 53, 140-156, 2006.
Lighthill, J.: Waves in fluids. Cambridge University Press (1978).
Marshall, J., Adcroft A., Hill C., Perelman L., Heisey, C: A finite-volume, incompressible navier-stokes model for studies of the ocean on parallel computers. Journ. Geophys. Res. 102:5753–5766 (1997).
MacKinnon, J.A., Winters, K.B.: Subtropical Catastrophe: significant loss of low-mode tidal energy at 28.9 degrees. Geophys. Res. Lett. 32, L15605, doi:10.1029/2005GL023376 (2005).
Mowbray, D.E., Rarity, B.S.H.: The internal wave pattern produced by a sphere moving vertically in a density stratified liquid. J. Fluid Mech. 30, 489–495 (1967).
Peacock, T., Echeverri, P., Balmforth, N.J.: An experimental investigation of internal wave beam generation by two-dimensional topography. J. Phys. Ocean. 38, 235–242 (2008).
Phillips, O.M.: The dynamics of the upper ocean. Cambridge University Press (1966).
Staquet, C., Sommeria, J., Goswami, K., Mehdizadeh, M.: Propagation of the internal tide from a continental shelf: laboratory and numerical experiments. Proceedings of the Sixth International Symposium on Stratified Flows, Perth, Australia, 11-14 December (2006).
Tabaei, A., Akylas, T.R.: Nonlinear Internal Gravity Wave Beams. J. Fluid Mech. 482, 141–161 (2003).
Tabaei, A., Akylas, T.R., Lamb, K.G.: Nonlinear Effects in Reflecting and Colliding Internal Wave Beams. J. Fluid Mech. 526, 217–243 (2005).
Thomas, N.H., Stevenson, T.N.: A similarity solution for viscous internal waves. J. Fluid Mech. 54, 495–506 (1972).
Zhang, H.P., King, B., Swinney, H.L.: Experimental study of internal gravity wvaes genarated by supercritical topography. Physics Fluids 19, 096602 (2007).
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Pairaud, I., Staquet, C., Sommeria, J., Mahdizadeh, M.M. (2010). Generation of harmonics and sub-harmonics from an internal tide in a uniformly stratified fluid: numerical and laboratory experiments. In: Dritschel, D. (eds) IUTAM Symposium on Turbulence in the Atmosphere and Oceans. IUTAM Bookseries, vol 28. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0360-5_5
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DOI: https://doi.org/10.1007/978-94-007-0360-5_5
Publisher Name: Springer, Dordrecht
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