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- Title
Resonant and near-resonant internal wave triads for non-uniform stratifications. Part 2. Vertically bounded domain with mild-slope bathymetry.
- Authors
Gururaj, Saranraj; Guha, Anirban
- Abstract
Weakly nonlinear internal wave–wave interaction is a key mechanism that cascades energy from large to small scales, leading to ocean turbulence and mixing. Oceans typically have a non-uniform density stratification profile; moreover, submarine topography leads to a spatially varying bathymetry ($h$). Under these conditions and assuming mild-slope bathymetry, we employ multiple-scale analysis to derive the wave amplitude equations for weakly nonlinear wave–wave interactions. The waves are assumed to have a slowly (rapidly) varying amplitude (phase) in space and time. For uniform stratifications, the horizontal wavenumber ($k$) condition for waves (1, 2, 3), given by ${k}_{(1,a)}+{k}_{(2,b)}\!+\!{k}_{(3,c)}\!=\!0$ , is unaffected as $h$ is varied, where $(a,b,c)$ denote the mode number. Moreover, the nonlinear coupling coefficients (NLC) are proportional to $1/h^2$ , implying that triadic waves grow faster while travelling up a seamount. For non-uniform stratifications, triads that do not satisfy the condition $a=b=c$ may not satisfy the horizontal wavenumber condition as $h$ is varied, and unlike uniform stratification, the NLC may not decrease (increase) monotonically with increasing (decreasing) $h$. NLC, and hence wave growth rates for weakly nonlinear wave–wave interactions, can also vary rapidly with $h$. The most unstable daughter wave combination of a triad with a mode-1 parent wave can also change for relatively small changes in $h$. We also investigate higher-order self-interactions in the presence of a monochromatic, small-amplitude topography; here, the topography behaves as a zero-frequency wave. We derive the amplitude evolution equations and show that higher-order self-interactions might be a viable mechanism of energy cascade.
- Subjects
SUBMARINE topography; OCEAN turbulence; MULTIPLE scale method; OCEANIC mixing; BATHYMETRY; INTERNAL waves
- Publication
Journal of Fluid Mechanics, 2022, Vol 946, p1
- ISSN
0022-1120
- Publication type
Article
- DOI
10.1017/jfm.2022.431