Local wave-number model for inhomogeneous two-fluid mixing.

Area of Science:

• Fluid Dynamics
• Turbulence Modeling
• Plasma Physics

Background:

• Rayleigh-Taylor (RT) instability arises from density stratification relaxation.
• Two-point spectral closure models like LWN are used for turbulence analysis.
• Accurate modeling of RT instability is crucial for various scientific and engineering applications.

Purpose of the Study:

• To analyze the local wave-number (LWN) model for Rayleigh-Taylor (RT) instability.
• To validate LWN model outcomes against 3D RT instability simulations.
• To investigate model enhancements for capturing specific turbulence dynamics and asymptotic states.

Main Methods:

• Application of the local wave-number (LWN) model to RT instability.
• Validation of model results using 3D simulation data.
• Analysis of minimal model terms and source term formulations for density-specific-volume covariance.

Main Results:

• The minimal LWN model captures key global quantities like mix-width and Reynolds stress.
• The simple model fails to reproduce the asymptotic behavior of density-specific-volume covariance.
• An enhanced LWN model with a calibrated or uncalibrated source term accurately captures all dynamical quantities, including covariance evolution.

Conclusions:

• The LWN model, particularly with enhancements, provides a robust framework for simulating RT instability.
• Improved source term formulations are key to accurately predicting turbulence evolution and asymptotic states.
• The study demonstrates the model's capability to capture inhomogeneous mixing and key dynamical quantities.