Abstract

On the basis of the two-fluid hydrodynamics, an analogue of the well-known Rayleigh equation was obtained for the dynamics of a spherical cavity in superfluid helium. With the aim of choosing a correct set of variables, a thorough analysis of the momentum flux tensor and energy flux has been carried out. The mass flux density or the mass average velocity, associated with it, and the velocity of the normal component, were chosen as independent variables. Due to the nonlinear character of the momentum flux tensor, several additional terms appeared in the equation for the evolution of the interface in comparison with the classical Rayleigh equation. These additional terms led to fundamental difference in the dynamics of vapor film in comparison with a classical fluid. For instance, one of the new terms led to an interesting effect of anomalous suppression or, depending on the configuration, anomalous enhancement of oscillations of the interface, observed in many works. Besides the additional anomalous decay or anomalous enhancement, there is also additional pressure, associated with the relative velocity in superfluid helium. The result obtained indicates the need to revise some results on the dynamics of a cavity in superfluid helium.

中文翻译：

---

超流氦中的瑞利问题

摘要

在双流体流体动力学的基础上，获得了著名的瑞利方程的类似物，用于超流氦中球形腔的动力学。为了选择一组正确的变量，对动量通量张量和能量通量进行了彻底的分析。质量通量密度或与其相关的质量平均速度以及法向分量的速度被选为自变量。由于动量通量张量的非线性特性，与经典瑞利方程相比，在界面演化方程中出现了几个附加项。与经典流体相比，这些附加项导致汽膜动力学的根本差异。例如，其中一个新术语导致了异常抑制的有趣效果，或者根据配置，界面振荡的异常增强，在许多工作中观察到。除了额外的异常衰减或异常增强之外，还有额外的压力，与超流氦的相对速度有关。获得的结果表明需要修改超流氦中空腔动力学的一些结果。