A Validation Study of the Compressible Rayleigh–Taylor Instability Comparing the Ares and Miranda Codes

The initial perturbation spectrum given in Eq. (13)

The mixing width as a function of time computed from the Miranda simulations (a), the Ares simulations (b), and a comparison of the results from the highest resolution mesh, mesh D (c): (a) Miranda, (b) Ares, and (c) mesh D for Miranda and Ares

The mixedness as a function of time computed from the Miranda simulations (a), the Ares simulations (b), and a comparison of the results from the highest resolution mesh, mesh D (c): (a) Miranda, (b) Ares, and (c) mesh D for Miranda and Ares

The mixed mass as a function of time computed from the Miranda simulations (a), the Ares simulations (b), and a comparison of the results from the highest resolution mesh, mesh D (c): (a) Miranda, (b) Ares, and (c) mesh D for Miranda and Ares

Spectra of the turbulence kinetic energy at t/τ = 13 computed from the Miranda simulations (a), the Ares simulations (b), and a comparison of the results from the highest resolution mesh, mesh D (c). The thin black line above the spectra is thek^–5∕3 fiducial. (a) Miranda (b) Ares, and (c) mesh D for Miranda and Ares

Spectra of the mass fraction of the heavier fluid at t/τ = 13 computed from the Miranda simulations (a), the Ares simulations (b), and a comparison of the results from the highest resolution mesh, mesh D (c). The thin black line above the spectra is the k^−5∕3 fiducial.

The growth rate, α_b as a function of time, computed from the highest resolution Miranda (solid lines) and Ares (dotted lines) simulations, using Eq. (30) (thick lines) and Eq. (31) (thin lines)

The effective numerical viscosity as a function of the grid Reynolds number expression, similar to Fig. 15(b) from Ref. [56]. Blue symbols are data from Miranda and red are from Ares. The circle, square, triangle, and diamond values are calculated at t/τ = 0.5, 1, 1.5, and 3 respectively. See text for details.

The time dependence of the slope of the data points in Fig. 8. The black points are calculated from the highest resolution (mesh D) data, while the red, blue, and purple points are from mesh C, mesh B, and mesh A, respectively. The dashed gray line is at a slope of −1.4.

The equilibrium density profile given in Eq. (A5) as a function of z (solid line), with the values of g, M_H, M_L, T₀, and δ given in Sec. 2. The dashed line shows the density profile if the two fluids were not mixed across the interface initially, i.e., if there is a sharp transition between the heavy and light fluid.