Richtmyer–Meshkov instability of arbitrary shapes.

We consider the effect of a shock passing through an arbitrarily shaped interface y(x,0) between two fluids. The evolution of the interface into a new shape, written formally as y(x,t)=y(x,0)+tF(x), is found by applying the linear, classical Richtmyer–Meshkov instability result to each mode in the Fourier expansion of the original interface. We provide several examples where the new shape F(x) can be found analytically. For any interface y(x,0) we define an associated dual interface ydual(x,0) and show that F(x)=dydual(x,0)/dx. Representing a shock by a new mathematical operator we find how y(x,0), ydual(x,0), and F(x) transform under the effect of a shock. Kink-singularities are found in F(x) when and where y(x,0) has a discontinuous change in its first derivative. These are the locations where jetting occurs. We briefly discuss the effects of nonlinearity, compressibility, viscosity, etc., all of which suppress kink-singularities, and present hydrocode simulations of shock tube and high-explosive-driven experiments to highlight the influence of compressibility, nonlinearity, and material strength. [ABSTRACT FROM AUTHOR]