arXiv subjects

Raunak Raj

Publications and source records attributed to Raunak Raj.

4 recordsLinked to original sources

arXiv2019

On Bragg resonances and wave triad interactions in two-layered shear flows

The standard resonance conditions for Bragg scattering as well as weakly nonlinear wave triads have been traditionally derived in the absence of any background velocity. In this paper, we have studied how these resonance conditions get modified when uniform, as well as various piecewise linear velocity profiles, are considered for two-layered shear flows. Background velocity can influence the resonance conditions in two ways (i) by causing Doppler shifts, and (ii) by changing the intrinsic frequencies of the waves. For Bragg resonance, even a uniform velocity field changes the resonance condition. Velocity shear strongly influences the resonance conditions since, in addition to changing the intrinsic frequencies, it can cause unequal Doppler shifts between the surface, pycnocline, and the bottom. Using multiple scale analysis and Fredholm alternative, we analytically obtain the equations governing both the Bragg resonance and the wave triads. We have also extended the Higher Order Spectral method, a highly efficient computational tool usually used to study triad and Bragg resonance problems, to incorporate the effect of piecewise linear velocity profile. A significant aspect, both in theoretical and numerical fronts, has been extending the potential flow approximation, which is the basis of studying these kinds of problems, to incorporate piecewise constant background shear.

physics.flu-dyn↗

arXiv2018

On the inertial effects of density variation in stratified shear flows

In this paper, we first revisit the celebrated Boussinesq approximation in stratified flows. Using scaling arguments we show that when the background shear is weak, the Boussinesq approximation yields either (i) $A_t\ll \mathcal{O}(1)$ or (ii) $Fr_c^2 \ll \mathcal{O}(1)$, where $A_t$ is the ratio of density variation to the mean density and $Fr_c$ is the ratio of the phase speed to the long wave speed. The second clause implies, contrary to the commonly accepted notion, that a flow with large density variations can also be Boussinesq. Indeed, we show that deepwater surface gravity waves are Boussinesq while shallow water surface gravity waves are not. However, in the presence of moderate/strong shear, Boussinesq approximation implies the conventionally accepted $A_t\ll \mathcal{O}(1)$. To understand the inertial effects of density variation, our second objective is to explore various non-Boussinesq shear flows and study different kinds of stably propagating waves that can be present at an interface between two fluids of different background densities and vorticities. Furthermore, three kinds of density interfaces - neutral, stable and unstable - embedded in a background shear layer, are investigated. Instabilities ensuing from these configurations, which includes Kelvin-Helmholtz, Holmboe, Rayleigh-Taylor and triangular-jet, are studied in terms of resonant wave interactions. The effects of density stratification and the shear on the stability of each of these flow configurations are explored. Some of the results, e.g. the destabilizing role of density stratification, stabilizing role of shear, etc. are apparently counter-intuitive, but physical explanations are possible if the instabilities are interpreted from wave interactions perspective.

physics.flu-dyn↗

arXiv2018

Explosive instability due to flow over a rippled bottom

In this paper, we study Bragg resonance, i.e. the triad interaction between surface and/or interfacial waves with bottom ripple, in presence of background velocity. We show that when one of the constituent waves of the triad has negative energy, the amplitudes of all the waves grow exponentially. This is very different from classic Bragg resonance in which one wave decays to cause growth of the other. The instabilities we observe are `explosive', and are different from normal mode shear instabilities since our velocity profiles are linearly stable. Our work may explain the existence of large amplitude internal waves over periodic bottom ripples in presence of tidal flow observed in oceans and estuaries.

physics.flu-dyn↗

arXiv2017

Large density stratification stabilizes Rayleigh-Taylor instability in presence of shear

This letter investigates the effect of shear on Rayleigh-Taylor instability (RTI). Even simple uniform shear strongly influences the instability; longer waves are completely stabilized when density stratification is large (higher Atwood numbers). This apparently counter-intuitive result is due to the presence of Atwood number in the shear term. When the unstable density interface is embedded in a shear layer, shear is again found to stabilize the RTI. However, this configuration introduces additional unstable shear instability modes in the lower wavenumber regime. A new type of shear instability, whose growth rate increases with Atwood number, plays a dominant role, while Kelvin-Helmholtz instability (KHI), which was previously understood to be the only possible shear instability in this context, has little significance. Hence the billows observed in the nonlinear stages of RTI, which are usually attributed to KHI, may actually be the nonlinear manifestation of this new instability.

physics.flu-dyn↗