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

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The local wave-number (LWN) model accurately predicts Rayleigh-Taylor (RT) instability dynamics, including mix-width and turbulent mass flux. Enhancements to the model capture density-specific-volume covariance evolution, improving turbulence simulation.

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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.