Self-similarity of a Rayleigh–Taylor mixing layer at low Atwood number with a multimode initial perturbation

ABSTRACT

High-fidelity large eddy simulation (LES) of a low-Atwood number (A = 0.05) Rayleigh–Taylor mixing layer is performed using the 10th-order compact difference code Miranda. An initial multimode perturbation spectrum is specified in Fourier space as a function of mesh resolution such that a database of results is obtained in which each successive level of increased grid resolution corresponds approximately to one additional doubling of the mixing layer width, or generation. The database is then analysed to determine approximate requirements for self-similarity, and a new metric is proposed to quantify how far a given simulation is from the limit of self-similarity. It is determined that mixing layer growth reaches a high degree of self-similarity after approximately 4.5 generations. Statistical convergence errors and boundary effects at late time, however, make it impossible to draw similar conclusions regarding the self-similar growth of more sensitive turbulence parameters. Finally, self-similar turbulence profiles from the LES database are compared with one-dimensional simulations using the k-L-a and BHR-2 Reynolds-averaged Navier–Stokes models. The k-L-a model, which is calibrated to reproduce a quadratic turbulence kinetic energy profile for a self-similar mixing layer, is found to be in better agreement with the LES than BHR-2 results.

KEYWORDS:

• Turbulent mixing
• turbulence modelling
• Rayleigh–Taylor instability
• large-eddy simulation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344.