Stabilization effect of elasticity on three-dimensional compressible vortex sheets
Stabilization effect of elasticity on three-dimensional compressible vortex sheets
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DOI：
10.1016/j.matpur.2023.01.005
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发表时间：
2023-01
期刊：
影响因子：
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通讯作者：
R. Chen;F. Huang;Dehua Wang;Difan Yuan
中科院分区：
文献类型：
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作者：
R. Chen;F. Huang;Dehua Wang;Difan Yuan
本文研究三维可压缩等熵弹性流动的涡面解。这是一个具有特征自由边界的非线性双曲型问题。与二维分析相比，这一增加的维度导致弹性效应和流体速度之间的更复杂的频率相互作用，使得稳定性分析更具挑战性。通过对线性化边值问题的Lopatinskirt行列式的细致研究，建立了平面涡面解的线性稳定性的充分必要条件。这些条件与弹性变形梯度的几何性质密切相关，并提供了证明三维弹性动力学中弹性对可压缩涡面的稳定作用的第一个稳定性判据。与二维等熵弹性流体相比，我们发现三维涡面的稳定性只在亚音速区域才能保持。
We are concerned with the vortex sheet solutions for the three-dimensional compressible isentropic elastic flows. This is a nonlinear hyperbolic problem with a characteristic free boundary. Compared with the analysis in two dimensions, this added dimension leads to more complicated frequency interactions between the effects of elasticity and the fluid velocity, making the stability analysis more challenging. Through a very delicate examination of the Lopatinskiĭ determinant of the linearized boundary value problem, necessary and sufficient conditions are established for the linear stability of the planar vortex sheet solutions. These conditions are closely related to the geometric properties of the elastic deformation gradient and provide the first stability criterion justifying the stabilization effect of elasticity on the compressible vortex sheets in the three-dimensional elastodynamics. In contrast to the two-dimensional isentropic elastic fluids, we find that the stability can only hold in the subsonic region for the three-dimensional vortex sheets.