[Paper Review] Effects of the initial perturbations on the Rayleigh-Taylor-Kelvin-Helmholtz instability system

Feng Chen, Aiguo Xu+4 more|arXiv (Cornell University)|Dec 29, 2021

Fluid Dynamics and Turbulent Flows79 references22 citations

TL;DR

This study investigates the influence of initial perturbation shapes on the Rayleigh-Taylor-Kelvin-Helmholtz instability (RTKHI) system using a multiple-relaxation-time discrete Boltzmann model. It reveals that sharper initial interfaces significantly accelerate RTI growth, while KHI evolution is largely insensitive to initial shape; the critical shear velocity for RTKHI transitions depends on bilateral (θ₁) and middle (θ₂) contact angles, with inverted parabolic/ellipse interfaces delaying the KHI-to-RTI transition more than others.

ABSTRACT

In the paper, the effects of initial perturbations on the Rayleigh-Taylor instability (RTI), Kelvin-Helmholtz instability (KHI), and the coupled Rayleigh-Taylor-Kelvin-Helmholtz instability (RTKHI) systems are investigated using a multiple-relaxation-time discrete Boltzmann model. Six different perturbation interfaces are designed to study the effects of the initial perturbations on the instability systems. Based on the mean heat flux strength $D_{3,1}$, the effects of initial interfaces on the coupled RTKHI are examined in detail. The research is focused on two aspects: (i) the main mechanism in the early stage of the RTKHI, (ii) the transition point from KHI-like to RTI-like for the case where the KHI dominates at earlier time and the RTI dominates at later time. It is found that the early main mechanism is related to the shape of the initial interface, which is represented by both the bilateral contact angle $ heta_{1}$ and the middle contact angle $ heta_{2}$. The influence of inverted parabolic and inverted ellipse perturbations ($ heta_{1}<90$) on the transition point of the RTKHI system is greater than that of other interfaces.

Motivation & Objective

• To analyze the impact of diverse initial perturbation morphologies on RTI, KHI, and coupled RTKHI systems.
• To determine how interface shape influences the early-stage dominant mechanism in RTKHI.
• To identify the conditions under which the RTKHI system transitions from KHI-like to RTI-like behavior.
• To quantify the role of initial amplitude and contact angles (θ₁, θ₂) in delaying or advancing the transition point.

Proposed method

• A multiple-relaxation-time discrete Boltzmann model (MRT-DLB) is employed to simulate hydrodynamic instabilities with high accuracy and stability.
• Six distinct initial interface shapes—sinusoidal, parabolic, inverted parabolic, sawtooth, ellipse, and inverted ellipse—are numerically designed and simulated.
• The mean heat flux strength D3,1 is used as a diagnostic to assess the relative contributions of RTI and KHI in the coupled system.
• Contact angles θ₁ (bilateral) and θ₂ (middle) are used to characterize interface geometry and correlate with critical shear velocity.
• Parametric studies vary initial amplitude (a₀ = 2, 3.6) and interface morphology to assess their effects on transition timing.
• The model preserves isotropy in viscous stress and heat flux through modified collision terms (ˆA8, ˆA9) in moment space.

Experimental results

Research questions

• RQ1 How does the initial interface shape affect the growth rate and evolution of RTI in isolation?
• RQ2 To what extent does the initial interface morphology influence the development of KHI?
• RQ3 What determines the critical shear velocity for the onset of RTKHI, and how do θ₁ and θ₂ affect it?
• RQ4 How do initial interface shape and amplitude influence the transition point from KHI-dominated to RTI-dominated behavior in RTKHI?
• RQ5 Why do inverted parabolic and inverted ellipse interfaces cause a more pronounced delay in the transition point compared to other shapes?

Key findings

• Sharper initial interfaces, such as parabolic and inverted parabolic shapes, lead to faster RTI bubble and spike growth compared to sinusoidal or sawtooth interfaces.
• The critical shear velocity for RTKHI increases with increasing bilateral contact angle θ₁ when θ₂ ≈ 90°, reaching a maximum for the elliptical interface.
• For θ₂ ≈ 90° and θ₁ < 90° (inverted parabolic/ellipse), the critical shear velocity remains nearly constant and lower than for sinusoidal or sawtooth shapes.
• The transition point from KHI-like to RTI-like behavior is significantly delayed when the bilateral contact angle θ₁ is smaller, with inverted ellipse interfaces showing the latest transition.
• Increasing the initial disturbance amplitude (a₀) shortens the linear growth stage and advances the transition point, especially for inverted parabolic and inverted ellipse interfaces.
• The effect of amplitude on transition timing is most pronounced for inverted parabolic and inverted ellipse interfaces, with the inverted ellipse showing the greatest advancement under higher amplitudes.