Departamento de Física and Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006 Badajoz, Spain.
Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba, Brazil.
Phys Rev E. 2018 May;97(5-1):052901. doi: 10.1103/PhysRevE.97.052901.
A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is carried out to identify the conditions for stability of a granular gas of rough hard spheres. The description is based on the results for the transport coefficients derived from the Boltzmann equation for inelastic rough hard spheres [Phys. Rev. E 90, 022205 (2014)PLEEE81539-375510.1103/PhysRevE.90.022205], which take into account the complete nonlinear dependence of the transport coefficients and the cooling rate on the coefficients of normal and tangential restitution. As expected, linear stability analysis shows that a doubly degenerate transversal (shear) mode and a longitudinal ("heat") mode are unstable with respect to long enough wavelength excitations. The instability is driven by the shear mode above a certain inelasticity threshold; at larger inelasticity, however, the instability is driven by the heat mode for an inelasticity-dependent range of medium roughness. Comparison with the case of a granular gas of inelastic smooth spheres confirms previous simulation results about the dual role played by surface friction: while small and large levels of roughness make the system less unstable than the frictionless system, the opposite happens at medium roughness. On the other hand, such an intermediate window of roughness values shrinks as inelasticity increases and eventually disappears at a certain value, beyond which the rough-sphere gas is always less unstable than the smooth-sphere gas. A comparison with some preliminary simulation results shows a very good agreement for conditions of practical interest.
对具有均匀冷却状态的流体力学方程进行线性稳定性分析，以确定粗糙硬球颗粒气体的稳定性条件。该描述基于从非弹性粗糙硬球的 Boltzmann 方程得出的输运系数的结果[Phys. Rev. E 90, 022205 (2014)PLEEE81539-375510.1103/PhysRevE.90.022205]，这些结果考虑了输运系数和冷却速率对法向和切向恢复系数的完全非线性依赖性。正如预期的那样，线性稳定性分析表明，横向（剪切）模式和纵向（“热”）模式在足够长的波长激发下是不稳定的。剪切模式在一定的非弹性阈值之上驱动不稳定性；然而，在较大的非弹性下，不稳定性由热模式驱动，其范围与中等粗糙度的非弹性有关。与非弹性光滑球颗粒气体的情况进行比较，证实了表面摩擦的双重作用的先前模拟结果：虽然小和大的粗糙度水平使系统比无摩擦系统更稳定，但在中等粗糙度时则相反。另一方面，这种中等粗糙度值的窗口随着非弹性的增加而缩小，最终在一定值处消失，超过该值，粗糙球气体总是比光滑球气体更稳定。与一些初步的模拟结果进行比较，对于实际感兴趣的条件，显示出非常好的一致性。
