吸积盘中对流对螺旋密度波的激发
Excitation of spiral density waves by convection in accretion discs
摘要：
受\citet{Lesur_Ogilvie10}关于原行星盘中不可压缩对流输运性质的最新结果的启发，本文研究了可压缩性以及另一种基本模式--螺旋密度波--在盘中对流不稳定性中的作用。本文用局部剪切盒方法分析了具有超绝热垂直层结的开普勒圆盘中非轴对称对流和螺旋密度波的线性动力学。结果表明，与开普勒微分旋转相关的剪切引入了一种新的现象，它导致这两种扰动模式耦合：在演化过程中，对流模式产生（拖尾）螺旋密度波，因此可以被视为圆盘中螺旋密度波的一个新的源。这里研究的波的产生过程中，由于其存在的唯一剪切盘的差分旋转，是一个更一般的线性模式耦合现象普遍发生在一个不均匀的速度剖面流的一个特殊表现。我们量化的螺旋密度波产生的对流作为这些模式的方位角和垂直波数的函数的效率，并发现它是最大的和最强大的，当这两个长度尺度是可比的光盘规模的高度。我们还表明，不像对流模式，这往往是运输角动量向内的线性制度，螺旋密度波运输角动量向外。基于这些研究结果，我们认为，在非线性政权的螺旋密度波产生的对流可能会发挥作用，在增强角动量的传输，由于单独的对流模式，这实际上是由非线性向外改变，如上述最近的事态发展。
英文摘要：
Motivated by the recent results of \citet{Lesur_Ogilvie10} on the transport properties of incompressible convection in protoplanetary discs, in this paper we study the role of compressibility and hence of another basic mode -- spiral density waves -- in convective instability in discs. We analyse the linear dynamics of non-axisymmetric convection and spiral density waves in a Keplerian disc with superadiabatic vertical stratification using the local shearing box approach. It is demonstrated that the shear associated with Keplerian differential rotation introduces a novel phenomenon, it causes these two perturbation modes to become coupled: during evolution the convective mode generates (trailing) spiral density waves and can therefore be regarded as a new source of spiral density waves in discs. The wave generation process studied here owes its existence solely to shear of the disc's differential rotation, and is a special manifestation of a more general linear mode coupling phenomena universally taking place in flows with an inhomogeneous velocity profile. We quantify the efficiency of spiral density wave generation by convection as a function of azimuthal and vertical wavenumbers of these modes and find that it is maximal and most powerful when both these length-scales are comparable to the disc scale height. We also show that unlike the convective mode, which tends to transport angular momentum inwards in the linear regime, the spiral density waves transport angular momentum outwards. Based on these findings, we suggest that in the non-linear regime spiral density waves generated by convection may play a role in enhancing the transport of angular momentum due the convective mode alone, which is actually being changed to outward by non-linearity, as indicated by above-mentioned recent developments.
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