Sensitivity of vortex pairing and mixing to initial perturbations in stratified shear flows

Abstract

The effects of different initial perturbations on the evolution of stratified shear flows that are subject to Kelvin-Helmholtz instability and vortex pairing have been investigated through Direct Numerical Simulation (DNS). The effects of purely random perturbations of the background flow are sensitive to the phase of the subharmonic component of the perturbation that has a wavelength double that of the Kelvin-Helmholtz instability. If the phase relationship between the Kelvin-Helmholtz mode and its subharmonic mode is optimal, or close to it, vortex pairing occurs. Vortex paring is delayed when there is a phase difference, and this delay increases with increasing phase difference. In three dimensional simulations vortex pairing is suppressed if the phase difference is sufficiently large, reducing the amount of mixing and mixing efficiency. For a given phase difference close enough to the optimal phase, the response of the flow to eigenvalues perturbations is very similar to the response to random perturbations. In addition to traditional diagnostics, we show quantitatively that a non-modal Fourier component in a random perturbation quickly evolves to be modal and describe the process of vortex pairing using Lagrangian trajectories.

Turbulent shear layers in a uniformly stratified background: DNS at high Reynolds number

“…Therefore, it is difficult to differentiate LCVI from SVBI without performing the stability analysis. Furthermore, the growth of secondary instabilities is highly sensitive to the initial broadband velocity fluctuations (Dong et al 2019). We have simulated the Ri = 0.16 case with two different choices for the initial velocity perturbations: one where the energy spectrum peaks at k 0 = 1.13 and another with a peak at k 0 = 1.24.…”

Predicting vortex merging and ensuing turbulence characteristics in shear layers from initial conditions

“…This shows that w β has the same phase as η β provided Ω β is purely imaginary (unstable flow with zero phase speed). The classic dispersion relation for KH instability under the Boussinesq approximation yields (Drazin & Reid 2004),…”

“…Experiments (Ho & Huang 1982; Husain & Hussain 1995), numerical simulations (Patnaik, Sherman & Corcos 1976; Corcos & Sherman 1984; Dong et al. 2019) and theoretical models (Kelly 1967; Nikitopoulos & Liu 1987) on vortex pairing have revealed that, depending on the phase difference (between the primary KH and the first subharmonic component), the outcome in the nonlinear stages can be radically different. An optimal phase difference leads to a ‘rolling interaction’ of vortices, while ‘shredding interaction’ occurs at a non-optimal value of phase difference.…”

“…This phase difference can be used as a parameter for controlling the transitional behaviour, turbulence structure and mixing in shear layers (Hajj, Miksad & Powers 1993; Dong et al. 2019) and round jets (Cho, Yoo & Choi 1998), and even in noise control applications (Bridges & Hussain 1987; Schram et al. 2005).…”

“…The sensitivity of vortex pairing to phase difference has also been established in laboratory experiments with round jets (Arbey & Williams 1984;Broze & Hussain 1994;Paschereit, Wygnanski & Fiedler 1995). This phase difference can be used as a parameter for controlling the transitional behaviour, turbulence structure and mixing in shear layers (Hajj, Miksad & Powers 1993;Dong et al 2019) and round jets (Cho, Yoo & Choi 1998), and even in noise control applications (Bridges & Hussain 1987;Schram et al 2005).…”