Lyubimova T P, Lyubimov D V, Sadilov E S, Popov D M
Institute of Continuous Media Mechanics, UB RAS, 1 Koroleva Street, 614013 Perm, Russia.
Perm State University, 15 Bukireva Street, 614990 Perm, Russia.
Phys Rev E. 2017 Jul;96(1-1):013108. doi: 10.1103/PhysRevE.96.013108. Epub 2017 Jul 17.
The stability of the horizontal interface of two immiscible viscous fluids in a Hele-Shaw cell subject to gravity and horizontal vibrations is studied. The problem is reduced to the generalized Hill equation, which is solved analytically by the multiple scale method and numerically. The long-wave instability, the resonance (parametric resonance) excitation of waves at finite frequencies of vibrations (for the first three resonances), and the limit of high-frequency vibrations are studied analytically under the assumption of small amplitudes of vibrations and small viscosity. For finite amplitudes of vibrations, finite wave numbers, and finite viscosity, the study is performed numerically. The influence of the specific natural control parameters and physical parameters of the system on its instability threshold is discussed. The results provide extension to other results [J. Bouchgl, S. Aniss, and M. Souhar, Phys. Rev. E 88, 023027 (2013)10.1103/PhysRevE.88.023027], where the authors considered a similar problem but took into account viscosity in the basic state and did not consider it in the equations for perturbations.
研究了在重力和水平振动作用下，Hele-Shaw盒中两种不混溶粘性流体水平界面的稳定性。该问题被简化为广义希尔方程，通过多尺度方法进行解析求解并进行数值求解。在振动幅度小和粘度小的假设下，对长波不稳定性、有限振动频率下波的共振（参数共振）激发（前三个共振）以及高频振动极限进行了解析研究。对于有限的振动幅度、有限的波数和有限的粘度，进行了数值研究。讨论了系统特定自然控制参数和物理参数对其不稳定性阈值的影响。结果扩展了其他结果[J. Bouchgl, S. Aniss, and M. Souhar, Phys. Rev. E 88, 023027 (2013)10.1103/PhysRevE.88.023027]，其中作者考虑了类似问题，但在基本状态中考虑了粘度，而在微扰方程中未考虑。
