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• W2562300426 abstract "Nonlinear Interactions of Two Incident Internal Waves Tom E. Dobra 1 , Andrew G. W. Lawrie 1 and Stuart B. Dalziel 2 Department of Mechanical Engineering, University of Bristol Department of Applied Mathematics and Theoretical Physics, University of Cambridge tom.dobra@bristol.ac.uk Abstract We present experiments and analysis of the nonlinear interactions of two incident internal gravity wave beams of comparable amplitude. By using a wave maker consisting of a flexible boundary to a tank, driven by an array of independent actuators, incident beams of large amplitude several wavelengths in width are generated. Additional wave beams, produced via triadic interactions, are observed emanating from where incident beams of moderate amplitude cross. We decompose the fields, both temporally and spatially, in order to identify the transfer of energy between the modes. A perturbation approach is used to predict the the frequencies of the generated waves, which is in close agreement with observations. Finally, in the related configuration where the two incident frequencies are the same, wave breaking with the emission of other internal waves is observed when a large amplitude wave reflects off an interface. Introduction Internal waves in the ocean and atmosphere are generated by a variety of mechanisms, such as interaction with surface waves on the ocean produced by wind shear and flow over topography (lee waves). Due to their ubiquity in the oceans, it is inevitable that two such waves will intersect, which, if their amplitudes are sufficiently large, may lead to a nonlinear interaction. This is important for modelling the transport of energy within the oceans as well as for predicting where internal waves might break leading to the transfer of energy from larger scales to smaller scales (see e.g. Staquet and Sommeria (2002)). Many of the well-known interactions depend on the conditions of triadic interaction, k 1 + k 2 + k 3 = 0, for three waves with wavevectors k i and frequencies ω i of either sign, to produce an energy exchange which occurs at second order. In the case of Boussinesq, linear internal waves, this can only occur if all three disturbances also satisfy the dispersion relation, ω = N cos Θ, where Θ is the angle the wavevector makes with the horizontal and s g dρ h N = − ρ 0 dz is the buoyancy frequency with reference density ρ 0 and background density stratification ρ h (z). In the well-studied case of parametric subharmonic instability in a linear strat- ification (uniform buoyancy frequency), only one wave is specified a priori, from which VIII th Int. Symp. on Stratified Flows, San Diego, USA, Aug. 29 - Sept. 1, 2016" @default.
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• W2562300426 date "2016-08-29" @default.
• W2562300426 modified "2023-09-28" @default.
• W2562300426 title "Nonlinear Interactions of Two Incident Internal Waves" @default.
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