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首页> 外文期刊>ZAMP: Zeitschrift fur Angewandte Mathematik und Physik: = Journal of Applied Mathematics and Physics: = Journal de Mathematiques et de Physique Appliquees >Nonlinear stability of oscillatory core-annular flow: A generalized Kuramoto-Sivashinsky equation with time periodic coefficients
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Nonlinear stability of oscillatory core-annular flow: A generalized Kuramoto-Sivashinsky equation with time periodic coefficients

机译：振荡核-环流的非线性稳定性：具有时间周期系数的广义Kuramoto-Sivashinsky方程

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摘要

In this paper the nonlinear stability of two-phase core-annular flow in a pipe is examined when the acting pressure gradient is modulated by time harmonic oscillations and viscosity stratification and interfacial tension is present. An exact solution of the Navier-Stokes equations is used as the background state to develop an asymptotic theory valid for thin annular layers, which leads to a novel nonlinear equation describing the spatio-temporal evolution of the interface. The evolution equation is an extension of the equation found for constant pressure gradients and generalizes the Kuramoto-Sivashinsky equation with dispersive effects found by Papageorgiou, Maldarelli and Rumschitzki, Phys. Fluids A 2(3), 340-352 (1990), to a similar system with time periodic coefficients. The distinct regimes of slow and moderate flow are considered and the corresponding evolution is derived. Certain solutions are described analytically in the neighborhood of the first bifurcation point by use of multiple scales asymptotics. Extensive numerical experiments, using dynamical systems ideas, are carried out in order to evaluate the effect of the oscillatory pressure gradient on the solutions in the presence of a constant pressure gradient.
机译：在本文中，当通过时间谐波振荡调节作用压力梯度并且存在粘度分层和界面张力时，研究了管道中两相芯环流的非线性稳定性。 Navier-Stokes方程的精确解被用作背景状态，以开发适用于薄环形层的渐近理论，从而得出描述界面时空演化的新型非线性方程。演化方程是为恒定压力梯度找到的方程的扩展，并推广了Papageorgiou，Maldarelli和Rumschitzki，Phys发现的具有分散效应的Kuramoto-Sivashinsky方程。流体A 2（3），340-352（1990），流向具有时间周期系数的类似系统。考虑慢速和中速流量的不同状态，并得出相应的演变。通过使用多尺度渐近线，在第一分叉点附近分析性地描述了某些解决方案。为了评估在恒定压力梯度存在下振荡压力梯度对溶液的影响，使用动力学系统思想进行了广泛的数值实验。

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