Resonant instability of tangential discontinuity in a compressible fluid

Abstract

The excitation and stability of surface waves on the interface of two compressible fluids moving with respect to each other in a two-dimensional channel is investigated. It is shown that in this case surface waves are always unstable. On the other hand, in this case the dispersion relation in the short and the long wavelength limits coincides with the dispersion relation in the compressible and the incompressible infinite fluid, respectively. Furthermore, surface wave excitation under resonant condition is investigated. It is concluded that due to the Cerenkov-like emission mechanism a sound wave propagates in the fluid at rest. In this case, the growth rate of the Cerenkov-like instability is compared with the growth rate of the instability for the excitation of the tangentially discontinuous surface wave. Likewise, using fluent software, surface wave excitation in two dimensions is simulated.

The effect of transition layer inhomogeneity on the stability of compressible MHD fluids

“…It is clear that the signs of N 1 and N 2 are opposite in the two pairs of relations (15), (17) and (15), (16). The surface wave is stable if the intersection of two inequalities in each pair of relations (15), (17) and (15), (16) are not empty and in this case two different modes propagate in two fluids. Without loss of generality by assuming v 1 = v 0 and v 2 = 0, the intersection of two intervals would not be empty under the following conditions…”

“…On the other hand, compressibility plays a significant role in stabilization or destabilization of the system. There exist various opinions about the effect of the compressibility on the stability [12][13][14][15]. Some authors believe that the results obtained by previous authors are invalid and the TD is absolutely unstable [14].…”

Early-time interface instabilities in high intensity aero-breakup of liquid drop

“…For KH instability, while the compressibility generally stabilize interface [5], the sound-wave resonance effect in bounded domain can lead to increase of growth rate for high-wavenumber disturbances [14]. The latter effect can explain the ripple-like waves between the primary bow shock and the upstream interface, and the high-wavenumber pattern within the water drop.…”

“…The evidence that these waves are relevant to KH instability is that they are almost eliminated in the modified simulation (not shown here). A simple prediction based on linear theory suggests that these waves do not contribute much due to the relative small growth rate [14]. For RT instability, the compressibility influences the growth rate by changing the density ratio [1,12].…”