When the material interface separating two different fluids is accelerated by shock wave, a hydrodynamic instability happens, which is well known as the Richtmyer-Meshkov instability (RMI) [1,2]. The physical mechanism for the occurrence of RMI is the deposition of baroclinic vorticity produced by the misalignment of the pressure gradient of the shock wave and the local density gradient at the interface (i.e.
0). Another type of instability is called the Kelvin-Helmholts instability (KHI) , which is because of the presence of tangential velocity jump at the interface. At late times of the RMI developing, because of the larger velocity difference at both sides of the spike and at the tip of the bubble, the KHI also starts to develop. The RMI is of importance in a wide range from man-made applications to natural phenomena such as inertial confinement fusion (ICF) and astrophysics. The KHI also has a prominent significance in plasma flow, radioactively driven molecular clouds , etc. So they have gained much attention for many years.