Simulations of two-dimensional single-mode Rayleigh-Taylor Instability using front-tracking/ghost-fluid method: comparison to experiments and theory

TL;DR

The paper investigates two-dimensional single-mode Rayleigh-Taylor instability between immiscible fluids at $A=0.29$ with surface tension, using front-tracking/ghost-fluid method (FT/GFM) combined with a fifth-order WENO scheme to solve the compressible Euler equations. The FT/GFM framework enforces sharp interface conditions while suppressing spurious oscillations, and is implemented in FronTier with surface-tension capabilities. Validation against Renoult et al. experiments shows good agreement in interface profiles, bubble/spike penetration, and amplitude growth characterized by $\alpha \approx 0.073$, with velocity fields consistent with single-wavelength theory and rotational near-interface dynamics. The results demonstrate the method’s robustness for capturing both linear and nonlinear RTI dynamics in the presence of surface tension, providing quantitative insights into the role of tension during nonlinear development.

Abstract

Two-dimensional single-mode Rayleigh-Taylor Instability (RTI) is simulated using an accurate and robust front-tracking/ghost-fluid method (FT/GFM) with high-order weighted essentially non-oscillatory (WENO) scheme. We compare our numerical results with the single-mode RTI experiments of Renoult, Rosenblatt and Carles (2015). The time evolution of the interface between two immiscible fluids and the effects of surface tension on the growth of the amplitude and asymmetry of the perturbed interface are examined for the initial wavelength 1 cm and the Atwood number A=0.29. The important features of RTI flows such as interface profiles, bubble/spike penetration and velocities show good agreement between experiments and simulations of immiscible fluids with surface tension. The velocity vector fields for the bubble and spike in the linear and nonlinear regimes are consistent with the theory for the single wavelength perturbation.

Figures (5)

• Figure 1: Interface profile showing the development of immiscible RTI with a surface tension $\sigma= 7.74~\text{dyn}\cdot\text{cm}^{-1}$ and an initial wavelength $\lambda_0=1$ cm at a grid resolution $192 \times 512$. There is a 16.7 ms between two consecutive interface.
• Figure 2: Bubble penetration versus scaled acceleration distance for $\lambda_0=1$ cm at a grid resolution $192\times 512$. The growth parameter $\alpha=0.073$ is obtained by fitting a line to the numerical simulation data.
• Figure 3: Comparison of spike (left) and bubble (right) velocities for solutions of the compressible Euler equations with and without a surface tension on a fine grid resolution $192 \times 512$ for 3 waves (top) and single wave (bottom).
• Figure 4: Velocity vector field for the spike (left) and bubble (right) on a grid resolution $192\times 512$ in the linear regime at early time $t=16.7~ms$.
• Figure 5: Velocity vector field for the spike (left) and bubble (right) on a grid resolution $192\times 512$ in the non-linear regime at late time $t=153$ ms.