Late-time growth rate, mixing and anisotropy in the multimode narrowband Richtmyer--Meshkov Instability: the $\theta$-Group Collaboration

摘要: Turbulent Richtmyer--Meshkov instability (RMI) is investigated through a series of high resolution three dimensional smulations two initial conditions with eight independent codes. The simulations are initialised narrowband perturbation such that growth due to non-linear coupling/backscatter from the energetic modes, thus generating lowest expected rate pure RMI. By independently assessing results each algorithm, and computing ensemble averages multiple algorithms, allow quantification key flow properties as well uncertainty differing numerical approaches. A new analytical model predicting layer for multimode presented, along models linear regime combined. Overall, exponent determined $\theta=0.292 \pm 0.009$, in good agreement prior studies; however, decaying slowly time. $\theta$ shown be relatively insensitive choice mixing width measurement. asymptotic integral molecular measures $\Theta=0.792\pm 0.014$, $\Xi=0.800 0.014$ $\Psi=0.782\pm 0.013$ which lower than some experimental measurements but within range studies. field persistently anisotropic all at latest time having between 49\% 66\% higher kinetic energy shock parallel direction compared perpendicular does not show any return isotropy. plane averaged volume fraction profiles different instants collapse reasonably when scaled by width, implying can described single length scale $\theta$. Quantitative data given both individual algorithms provide useful benchmark future research.