Dynamics of unstably stratified free shear flows: an experimental investigation of coupled Kelvin–Helmholtz and Rayleigh–Taylor instability

Abstract

The dynamics of the coupled Kelvin–Helmholtz (KH) and Rayleigh–Taylor (RT) instability (referred to as KHRT instability or KHRTI) is studied using statistically steady experiments performed in a multi-layer gas tunnel. Experiments are performed at four density ratios ranging in Atwood number $A_{t}$ from 0.035 to 0.159, with varying amounts of shear and $\unicode[STIX]{x0394}U/U$ ranging from 0 to 0.48, where $\unicode[STIX]{x0394}U$ is the speed difference between the two flow streams being investigated and $U$ is the mean velocity of these two streams. Three types of diagnostics – back-lit visualization, hot-wire anemometry and particle image velocimetry (PIV) – are employed to obtain the mixing widths, velocity field and density field. The flow is found to be governed by KH dynamics at early times and RT dynamics at late times. This transition from KH-instability-like to RT-instability-like behaviour is quantified using the Richardson number. Transitional Richardson number magnitudes obtained for the present KHRT flows are found to be in the range 0.17–0.56 similar to the critical Richardson numbers for stably stratified free shear flows. Comparing the evolution of density and velocity mixing widths, the density mixing layer is found to be approximately two times as thick as the velocity mixing layer. Scaling of velocity fluctuations is attempted using combinations of KH and RT scales. It is found that the proposed KHRT velocity scale, obtained using the combined mixing-layer growth equation, is appropriate for intermediate stages of the flow when both KH and RT dynamics are comparable. Probability density functions (p.d.f.s) for different fluctuating quantities are presented. Multiple peaks in p.d.f.s are qualitatively explained from the development of coherent KH roll-ups and their subsequent transition into turbulent pockets. The evolution of energy spectra indicates that density fluctuations start to show an inertial subrange from earlier times compared to velocity fluctuations. The spectra exhibit a slightly steeper slope than the Kolmogorov–Obukhov five-thirds law.

Two-length-scale turbulence model for self-similar buoyancy-, shock-, and shear-driven mixing

“…By observing where the simulations deviate from these reference lines, the space can be divided into KH-dominated mixing for Ri 0.01, RT-dominated mixing for Ri 0.25, and transitional mixing for 0.01 < Ri < 0.25. These ranges are in reasonable agreement with experimental results by Akula et al [52], who observe the transition point to RT-dominated mixing occurring for Ri = 0.17-0.56.…”

“…The k-2L-a model, with model coefficients given in Table I, is now applied to the simulation of combined RT/KH instability. In the case of combined RT/KH instability, the relative strength of buoyancy to shear effects LLNL-JRNL-740721-DRAFT 11 Submitted to Physical Review E is given by the Richardson number [52] Ri = − g ∂ρ/∂y…”

“…While much experimental [17][18][19][20][21][22][23][24][25][26][27][28][29] and computational [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49] work exists studying RT, RM, and KH instabilities in isolation, fewer studies have been performed to investigate combined RT/KH or RM/KH instability. Recent experimental studies by Akula and collaborators [50][51][52] have investigated the dynamics of the combined RT/KH instability in a wind tunnel at Atwood numbers ranging from 0.04 to 0.73. Work has also been performed recently at the National Ignition Facility (NIF) [53] and on the OMEGA laser [54] to provide data on shear-dominated RM/KH instability in the high energy density physics (HEDP) regime.…”

Discrete Boltzmann modeling of unsteady reactive flows with nonequilibrium effects

“…As an essential physical mechanism in turbulence and fluids mixing process, the KHI has been studied extensively with experimental [55][56][57], theoretical [40,41,58], and computational [42][43][44][45] methods during the past decades. In this section, we further utilize the DBM to simulate and investigate the compressible KHI with both hydrodynamic and thermodynamic nonequilibriun effects.…”

Kinetic Simulation of Nonequilibrium Kelvin-Helmholtz Instability

“…Examples include waves on a windblown ocean or sand dune, swirling cloud billows, the stream structure of solar corona, the helical wave motion in ionized comet tails, the Great Red Spot in Jupiters atmosphere, the Eagle Nebula in astrophysics, the reacting mixing layers in combustion, and the ignition in inertial confinement fusion. The KHI is one of the most fundamental and famous instabilities in fluid dynamics, and it is often coupled with other instabilities, such as Rayleigh-Taylor Instability [6,7], Richtmyer-Meshkov instability [8,9], etc. Hence, due to its great importance, the KHI has been studied extensively in experimental [7,10,11], theoretical [6], and numerical fields [12,13].…”