We study the vortex-accelerated secondary baroclinic vorticity deposition
(VAVD) at late-intermediate times, and dynamics of sinusoidal single-mode Richtmyer–Meshkov interfaces in two dimensions. Euler simulations using a piecewise parabolic method are conducted for three post-shock Atwood numbers (A∗),
0.2, 0.635, and 0.9, with Mach number (M
) of 1.3. We initialize the sinusoidal interface with a slightly “diffuse
” or small-but-finite
thickness interfacial transition layer to facilitate comparison with experiment and avoid ill-posed phenomena associated with evolutions of an inviscid vortex sheet. The thickness of the interface is chosen so that there are no secondary structures along the interface prior to the multivalue time tM,
which is defined as the time when the extracted
medial axis of an interfacial layer first becomes multivalued. For an interval of 11tM
the simulations reveal nearly monotonic strong growth of both positive and negative baroclinic circulation in a vortex bilayer pattern inside the complex roll-up region. The circulations grow and secondary baroclinic circulation dominates at intermediate times, especially for higher A∗.
This vorticity deposition is due to misalignment of density gradient across the interface and vortex-centripetal acceleration (secondary baroclinic
), and enhanced by the intensification of interfacial density gradient arising from the vortex-induced strain. Our simulation results for A∗ = 0.635
agree with the recent air–sulfur hexafluoride (SF6)
experiment of Jacobs and Krivets [Proceedings of the 23rd International Symposium on Shock Waves, Fort Worth, Texas, (2001)], including several large-scale features of the evolving mushroom structure: The usual interface spike-bubble amplitude growth rate
and the dimensions of the spike roll-up cavity. VAVD plays an important role in the intermediate time dynamics of the interfaces. Our amplitude growth rate disagrees
with the O(t−1)
result of Sadot et al. [Phys. Rev. Lett. 80
, 1654 (1998)]. Instead, it approaches a constant which increases with A∗( ⩽ 0.9).
periodic single point vortex model which uses the calculated net circulation magnitude and its location, gives excellent results for the amplitude growth rates to late-intermediate times at low Atwood numbers (A∗ = 0.2,0.635).
The evolution of enstrophy, vorticity skewness, and flatness are quantified for the entire run duration, and one-dimensional averaged kinetic-energy spectra are presented at several times. © 2003 American Institute of Physics.