Rethinking missing mass theory

We perform a series of investigations, both theoretical and numerical, intended to establish a foundational, quantitative understanding of the material outflows generated when a strong shock is driven through an imperfect ("defected") metal surface. Our investigation is limited to tin surfaces with symmetric defects subject to sufficiently strong shock pressures (∼28 GPa) such that the tin completely changes to fluid phase and Richtmyer-Meshkov instability produces outflows of mass from surface defects. Outflow masses are non-dimensionalized by dividing by the "missing mass," which is the product of the pre-shock solid metal density and the pre-shock defect volume. We examine the effects of defect shape, defect aspect ratio, distance between defects, and bump-type defects on outflow mass variability with 2D simulations. Rectangular, triangular, elliptical, and sinusoidal defect shapes are investigated. Bump-type defects are normalized by added mass. Our results suggest that, while missing and added masses are useful quantities for non-dimensionalizing outflow mass, new theories of outflow mass variability should attempt to assimilate patterns of baroclinic variability (the degree of misalignment of density and pressure gradients during shock transit).