A Unified Instability Region for the Extended Taylor-Goldstein Problem of Hydrodynamic Stability

We consider inviscid,incompressible shear flows with variable density and variable cross section.For this problem,we derived a new estimate for the growth rate of an unstable mode and a parabolic instability region which intersects semiellipse instability region under some condition.

Stability of stratified shear flows in channels with variable cross sections

For the instability problem of density stratified shear flows in sea straits with variable cross sections, a new semielliptical instability region is found.Furthermore, the instability of the bounded shear layer is studied in two cases:(i) the density which takes two different constant values in two layers and(ii) the density which takes three different constant values in three layers.In both cases, the dispersion relation is found to be a quartic equation in the complex phase velocity.It is found that there are two unstable modes in a range of the wave numbers in the first case, whereas there is only one unstable mode in the second case.

Stability of plane-parallel flow of magnetic fluids under external magnetic fields

In this work,we present a theoretical study on the stability of a two-dimensional plane Poiseuille flow of magnetic fluids in the presence of externally applied magnetic fields.The fluids are assumed to be incompressible,and their magnetization is coupled to the flow through a simple phenomenological equation.Dimensionless parameters are defined,and the equations are perturbed around the base state.The eigenvalues of the linearized system are computed using a finite difference scheme and studied with respect to the dimensionless parameters of the problem.We examine the cases of both the horizontal and vertical magnetic fields.The obtained results indicate that the flow is destabilized in the horizontally applied magnetic field,but stabilized in the vertically applied field.We characterize the stability of the flow by computing the stability diagrams in terms of the dimensionless parameters and determine the variation in the critical Reynolds number in terms of the magnetic parameters.Furthermore,we show that the superparamagnetic limit,in which the magnetization of the fluids decouples from hydrodynamics,recovers the same purely hydrodynamic critical Reynolds number,regardless of the applied field direction and of the values of the other dimensionless magnetic parameters.

Short wave stability of homogeneous shear flows with variable topography

For the stability problem of homogeneous shear flows in sea straits of arbitrary cross section, a sufficient condition for stability is derived under the condition of inviscid flow. It is shown that there is a critical wave number, and if the wave number of a normal mode is greater than this critical wave number, the mode is stable.

Supersonic gas jet stabilization in laser–plasma acceleration

Supersonic gas jets generated via a conical nozzle are widely applied in the laser wakefield acceleration of electrons.The stability of the gas jet is critical to the electron injection and the reproducibility of the wakefield acceleration.Here we discussed the role of the stilling chamber in a modified converging-diverging nozzle to dissipate the turbulence and to stabilize the gas jets.By the fluid dynamics simulations and the Mach-Zehnder interferometer measurements,the instability originating from the nonlinear turbulence is studied and the mechanism to suppress the instability is proposed.Both the numerical and experimental results prove that the carefully designed nozzle with a stilling chamber is able to reduce the perturbation by more than 10% compared with a simple-conical nozzle.