Saranraj Gururaj | Searcharxiv

arXiv2025

5-wave interactions in inertia-gravity waves

In oceans, multiple energetic inertia-gravity waves often coexist in a region. In this paper, we study the stability of two coexisting plane inertia-gravity waves (hereafter, primary waves), with the same frequencies ($ω_1$) and wavevector norms, in a region of constant background stratification (denoted by $N$). Specifically, we explore the decay of two primary waves through triadic resonant instabilities (TRIs) in cases where the primary waves do not resonantly interact with each other. Two coexisting primary waves undergoing triadic resonant instability can force two secondary waves each, and this results in two 3-wave systems (3WS). In some cases, two primary waves can have a common secondary wave, and this results in a 5-wave system (5WS) composed of two different triads. We show that 5WSs are the dominant instabilities with higher growth rates than standard triads for a wide range of Coriolis frequency values ($f$). For 2D cases, 5WSs have higher growth rates than triads for $f/ω_1\gtrapprox0.3$ and for primary waves with the same horizontal (vertical) wavenumber but with opposite vertical (horizontal) wavenumber. Similar results are observed for 3D cases where the primary waves are not on the same vertical plane. Numerical simulations match the theoretical growth rates of 5WSs for a wide range of latitudes, except when $f/ω_1\approx0.5$ (critical latitude). Using theory and simulations, we show that the maximum growth rate near the critical latitude is approximately twice the maximum growth rate of all triads.

physics.flu-dyn↗

arXiv2022

Resonant and near-resonant internal wave triads for non-uniform stratifications. Part 2: Vertically bounded domain with mild-slope bathymetry

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 ocean depth ($h$). Under these conditions and assuming mild-slope bathymetry, we employ multiple-scale analysis to derive the wave amplitude equations for triadic- and self-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 modenumber. 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 both triads and self-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 bathymetry; here the bathymetry 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.

physics.flu-dyn↗