吸积盘中涡旋的形成、生存和破坏
Formation, Survival, and Destruction of Vortices in Accretion Disks
摘要：
二维流体动力圆盘是非线性不稳定的旋涡形成。一旦形成，这些漩涡基本上永远存在。在三维空间里会发生什么？我们与伪谱模拟表明，在3D中的一个漩涡在一个短的盒子的形式和生存就像在2D。但是在一个高盒子里的漩涡是不稳定的，会被摧毁。在我们的模拟中，不稳定的旋涡衰减成一个瞬态的类顺磁状态，以几乎恒定的速率向外传输角动量数百个轨道时间。破坏旋涡的三维不稳定性是形成旋涡的二维不稳定性的推广。通过计算线性模之间的耦合，我们导出了这些非线性不稳定性发生作用的条件，从而导出了涡旋在三维中和在二维中一样存在的判据：涡旋的方位角范围必须大于吸积盘的尺度高度。当这个准则被违反时，旋涡是不稳定的并且衰减。由于涡旋在方位角上的长度比径向长度长，其系数与其过量涡旋成反比，因此具有给定径向长度的涡旋只有在足够弱时才能在3D盘中存活。这个违反直觉的结果解释了为什么以前的3D模拟总是产生衰减的漩涡：它们的漩涡太强了。我们的结论是，在原行星盘中，弱涡旋可以捕获尘埃，并作为行星形成的温床。衰减的强涡旋可能是造成吸积盘吸积所需的角动量向外输送的原因。
英文摘要：
Two dimensional hydrodynamical disks are nonlinearly unstable to the formation of vortices. Once formed, these vortices essentially survive forever. What happens in three dimensions? We show with pseudospectral simulations that in 3D a vortex in a short box forms and survives just as in 2D. But a vortex in a tall box is unstable and is destroyed. In our simulation, the unstable vortex decays into a transient turbulent-like state that transports angular momentum outward at a nearly constant rate for hundreds of orbital times. The 3D instability that destroys vortices is a generalization of the 2D instability that forms them. We derive the conditions for these nonlinear instabilities to act by calculating the coupling between linear modes, and thereby derive the criterion for a vortex to survive in 3D as it does in 2D: the azimuthal extent of the vortex must be larger than the scale height of the accretion disk. When this criterion is violated, the vortex is unstable and decays. Because vortices are longer in azimuthal than in radial extent by a factor that is inversely proportional to their excess vorticity, a vortex with given radial extent will only survive in a 3D disk if it is sufficiently weak. This counterintuitive result explains why previous 3D simulations always yielded decaying vortices: their vortices were too strong. We conclude that in protoplanetary disks weak vortices can trap dust and serve as the nurseries of planet formation. Decaying strong vortices might be responsible for the outwards transport of angular momentum that is required to make accretion disks accrete.
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