Viscoelastodynamics of a stratified, compressible planet: incremental field equations and short- and long-time asymptotes
Viscoelastodynamics of a stratified, compressible planet: incremental field equations and short- and long-time asymptotes
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DOI：
10.1111/j.1365-246x.1991.tb02520.x
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发表时间：
1991-02
影响因子：
2.8
通讯作者：
D. Wolf
中科院分区：
文献类型：
--
作者：
D. Wolf
摘要我们考虑了一个化学上和熵上分层的、可压缩的、旋转的流体行星，并研究了流体静力初态的引力-粘弹性扰动。利用拉格朗日公式，我们首先导出了控制微扰的增量场方程和连续性条件。然后，在扰动开始后，我们推导出方程在短时间和长时间的渐近线。这些短时渐近方程称为广义弹性动力学的增量场方程和连续条件。它们包括作为零级近似的传统弹性动力学方程。该长时间渐近方程符合牛顿粘性流体动力学的增量场方程和连续性条件。特别是，增量本构方程的长时间渐近线上出现的增量热力学压力满足相应的增量状态方程。最后，我们引入了广义增量不可压缩条件。在此基础上，我们导出了等化学区、等熵区和可压缩区重力-粘弹性摄动的近似增量场方程。
SUMMARY We consider a chemically and entropically stratified, compressible, rotating fluid planet and study gravitational-viscoelastic perturbations of a hydrostatic initial state. Using the Lagrangian formulation, we first derive the incremental field equations and continuity conditions governing the perturbations. Following this, we deduce the asymptotes to the equations for short and long times after the onset of the perturbations. The short-time asymptotic equations are referred to as the incremental field equations and continuity conditions of generalized elastodynamics. They include the equations of conventional elastodynamics as zeroth-order approximations. The long-time asymptotic equations agree with the incremental field equations and continuity conditions of Newtonian-viscous fluid dynamics. In particular, the incremental thermodynamic pressure appearing in the long-time asymptote to the incremental constitutive equation satisfies the appropriate incremental state equation. Finally, we introduce the generalized incremental incompressibility condition. Based on it, we derive approximate incremental field equations for gravitational-viscoelastic perturbations of isochemical, isentropic and compressible regions.