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COMPUTATIONAL STUDY OF RAILEIGH–TAYLOR INSTABILITY ON WATER-AIR INTERFACE

Two-fluid interface evolution is studied by direct simulations of Navier–Stokes and volume-fraction equations. To capture surface tension, the continuum surface force (CSF) model is used where the mollified volume-fraction function varies smoothly across the interface due to convolving the original function with the polynomial smooth kernel [1]. Tests for Rayleigh–Taylor instability (RTI) show that the average  y a of spike/bubble amplitudes (at the lateral domain sides) has an initial exponential growth, corresponding to a linear-instability stage with the constant growth rate n = d (ln  y a )/ dt .  This rate analysis shows that both viscosity and surface tension damp the RTI development in agreement with theory and measurements data [1]. For real fluids (water-air) good prediction is obtained for both linear-instability and nonlinear (with saturation of n )  stages. If density difference across the interface is not so large, the nonlinear stage shows Kelvin–Helmholtz instability effects leading to typical mushroom-like structures (as in [1] with ρ 1 = 2 ρ 2 ).  The similar convective structures are observed for one-phase stably stratified flow above the obstacle at high enough Reynolds/Schmidt numbers (when overturning and breaking internal waves produce unstable layers with strong density gradients), providing a source of quasi-steady turbulent patches [2]. For large density difference (e.g. water-air interface) the heavier fluid penetrates deeply into the lighter one and forms high columns as in [3,4]. Surface tension omission gives spurious distortion and fragmentation of the interface. The vortex-sheet method [4] yields under-estimation of n .  Application of the CSF model leads to the correct RTI evolution within the experimental data scatter. REFERENCES 1. Yakovenko, S.N., Chang, K.C., 2011, Thermophysics & Aeromechanics , Vol.18, No.3 . (accepted) 2. Yakovenko, S.N., Thomas, T.G., Castro, I.P., 2011, J. Fluid Mech. , Vol.677, pp.103-133. 3. Lewis, D.J., 1950, Proc. R. Soc. Lond. A , Vol.202. pp.81-96. 4. Pullin, D.I., 1982, J. Fluid Mech. , Vol.119. pp.507-532.