Hydrodynamic stability of rotationally supported flows: Linear and nonlinear 2D shearing box results
Hydrodynamic stability of rotationally supported flows: Linear and nonlinear 2D shearing box results
复制标题
旋转支撑流的水动力稳定性：线性和非线性二维剪切盒结果
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
O. Regev
中科院分区：
文献类型：
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作者：
O. Umurhan;O. Regev
本文给出了用剪切盒方法研究旋转支撑的绕星流的流体动力稳定性的分析和数值结果。系统地导出了证明剪切盒近似的渐近标度参数，指出存在两个极限，我们称之为小剪切盒（SSB）和大剪切盒（LSB）。简要讨论了这两个极限的物理意义以及它们与前人所实现的模型方程的关系。二维（2D）的SSB动力学进行了探索，并显示包含瞬态增长（TG）的线性模式，其性质是第一次讨论的范围内的线性理论。完全非线性政权在2D数值研究非常高的雷诺数（Re）。发现了表现出长期动力学活动的解决方案，并表现出短暂但重复的TG行为，这些与相干涡旋的形成和长期生存有关。这种时空复杂性的寿命取决于Re数和初始扰动的强度和性质。有限Re解的动力学活动最终衰减的特征时间与Re增加。然而，对于足够大的Re和适当的初始扰动，大量的TG情节重现之前，任何粘性衰减开始清楚地表现出来。在名义上Re = ∞的情况下（即仅由数值截断误差引起的任何耗散），动力学活动在整个模拟期间持续存在（数百个盒轨道）。由于SSB近似等效于二维不可压缩流，因此动力学不依赖于科里奥利力。因此，需要三维（3D）模拟，以确定该力是否确实抑制剪切盒近似中旋转支撑盘中的非线性流体动力学不稳定性，以及复发性TG行为是否仍然可以在三维中持续-可能导致亚临界过渡到长期时空复杂性。
We present here both analytical and numerical results of hydrodynamic stability investigations of rotationally sup- ported circumstellar flows using the shearing box formalism. Asymptotic scaling arguments justifying the shearing box approxi- mation are systematically derived, showing that there exist two limits which we call small shearing box (SSB) and large shearing box (LSB). The physical meaning of these two limits and their relationship to model equations implemented by previous in- vestigators are discussed briefly. Two dimensional (2D) dynamics of the SSB are explored and shown to contain transiently growing (TG) linear modes, whose nature is first discussed within the context of linear theory. The fully nonlinear regime in 2D is investigated numerically for very high Reynolds (Re) numbers. Solutions exhibiting long-term dynamical activity are found and manifest episodic but recurrent TG behavior and these are associated with the formation and long-term survival of coherent vortices. The life-time of this spatio-temporal complexity depends on the Re number and the strength and nature of the initial disturbance. The dynamical activity in finite Re solutions ultimately decays with a characteristic time increasing with Re. However, for large enough Re and appropriate initial perturbation, a large number of TG episodes recur before any viscous decay begins to clearly manifest itself. In cases where Re = ∞ nominally (i.e. any dissipation resulting only from numerical truncation errors), the dynamical activity persists for the entire duration of the simulation (hundreds of box orbits). Because the SSB approximation used here is equivalent to a 2D incompressible flow, the dynamics can not depend on the Coriolis force. Therefore, three dimensional (3D) simulations are needed in order to decide if this force indeed suppresses nonlinear hydro- dynamical instability in rotationally supported disks in the shearing box approximation, and if recurrent TG behavior can still persist in three dimensions as well - possibly giving rise to a subcritical transition to long-term spatio-temporal complexity.