## Compressible Turbulent Mixing

We have investigated the influence of different three-dimensional multi-mode initial
conditions on the rate of growth of a mixing layer initiated via a Richtmyer-Meshkov
instability through a series of well-controlled numerical experiments. Results have been
obtained for large-eddy simulation of narrowband and broadband perturbations at
grid resolutions up to 3 x 10^{9} points using two completely different numerical methods (Eulerian and Lagrangian),
and comparisons are made with theory and experiments. The key conclusion is that the growth of the resultant mixing layer is strongly dependent on initial conditions.

Furthermore, we have investigated turbulent mixing due to the interaction of a shock wave with an inclined material interface. The interface between the two gases is modeled by geometrical random multimode perturbations represented by different surface perturbation power spectra with the same standard deviation. Simulations of the Richtmyer-Meshkov instability and associated turbulent mixing have been performed using high-resolution implicit large eddy simulations. The key integral properties have been examined for different interface perturbations. It is shown that turbulent mixing is reduced when the initial perturbations are concentrated at short wavelengths. The form of the initial perturbation has strong effects on the development of small-scale flow structures, but this effect is diminished at late times.

We have also studied reshocked turbulent mixing layer using high-order accurate Implicit Large-Eddy-Simulations (ILES). Existing theoretical approaches have been extended to predict the behaviour of a reshocked mixing layer formed initially from a shock interacting with a broadband instability. Simulations have been conducted for broadband and narrowband initial perturbations and results for the growth rate of the reshocked layer and the decay rate of turbulent kinetic energy show excellent agreement with the extended theoretical approach. Reshock causes a marginal decrease in mixing parameters for the narrowband layer, but a significant increase for the broadband initial perturbation. The layer properties are observed to be very similar post-reshock, however, the growth rate exponent for the mixing layer width is higher in the broadband case, indicating that the reshocked layer still has a dependence (although weakened) on the initial conditions. The high-resolution ILES will guide the Unsteady Reynolds Averaged Navier Stokes modelling of such instabilities.

#### References

- B. Thornber, D. Drikakis, D. L. Youngs, R. J. R. Williams, The influence of initial conditions on turbulent mixing due to Richtmyer-Meshkov instability, Journal of Fluid Mechanics, 654, 99-139, 2010.
- M. Hahn, D. Drikakis, D. L. Youngs, R. J. R Williams, Richtmyer-Meshkov turbulent mixing arising from an inclined material interface with realistic surface perturbations and reshocked flow, Physics of Fluids, Vol. 23, 4, 046101, 2011.
- D. Drikakis, M. Hahn, A. Mosedale, B. Thornber, Large Eddy Simulation Using High Resolution and High Order Methods, Philosophical Transactions Royal Society A, 367, 2985-2997, 2009.
- Thornber, D. Drikakis, D.L. Youngs, R.J.R. Williams, Physics of the single-shocked and reshocked RichtmyerMeshkov instability, Journal of Turbulence, Vol. 13, 10, 1-17, 2012.
- B. Thornber, D. Drikakis, D.L. Youngs, R.J.R. Williams, Growth of a Richtmyer-Meshkov turbulent layer after reshock, Physics of Fluids, 095107, 2011.
- B. Thornber, D. Drikakis, D. Youngs, Large-eddy simulation of multi-component compressible turbulent flows using high resolution methods, Computers and Fluids, 37(7), 867-876, 2008.
- D. Drikakis, . Youngs, F. Grinstein, Symmetry-breaking and instabilities in Fluid Mechanics, Progress in Aerospace Sciences, 41, 609-641, 2005.
- A. Mosedale, D. Drikakis, Assessment of very high-order of accuracy in LES models, ASME Journal of Fluids Engineering, Vol. 129(12), 1497-1503, 2007.
- Oggian, D. Drikakis, D. Youngs, R. Williams, A hybrid compressible-incompressible CFD method for Richtmyer-Meshkov mixing, ASME J. Fluids Eng., 2014, accepted (in print).
- M. G. Probyn, B. Thornber, D. Drikakis, D. Youngs, R. Williams, An Investigation into Non-Linear Growth Rate of 2D and 3D Single-Mode Richtmyer-Meshkov Instability, ASME J. Fluids Eng., 2014, accepted (in print).