通过吸积盘中湍流涨落激发螺旋密度波I：WKBJ理论
The excitation of spiral density waves through turbulent fluctuations in accretion discs I: WKBJ theory
摘要：
本文研究和阐明了差动旋转湍流中螺旋密度波的激发机理。我们制定了一套波动方程的源，只有非零的湍流波动的存在。我们解决了这些剪切盒域使用WKBJ方法。据发现，对于一个特定的方位角波长，波激发发生通过一系列规则间隔的摆动，在此期间，波的变化，从领先的尾随形式。这是一个一般的过程，预计将发生在剪切盘与湍流。产生沿相反方向传播的等振幅的尾波，它们都产生向外的角动量通量，我们给出了作为圆盘参数和方位波长的函数的表达式。通过数值求解波振幅方程，我们证明了WKBJ方法的开普勒旋转定律的所有参数制度的利益。为了完全量化波浪激励，需要指定重要的波源项。假设弱非线性的条件下，这些可以被识别，并与有关的位涡量，是唯一的幸存者在线性制度。在源在长方位波长处具有平坦功率谱的附加假设下，发现产生的最佳方位波长仅由WKBJ响应确定，并且估计为2 π H，其中H是标称盘刻度高度。
英文摘要：
We study and elucidate the mechanism of spiral density wave excitation in a differentially rotating turbulent flow. We formulate a set of wave equations with sources that are only non-zero in the presence of turbulent fluctuations. We solve these in a shearing box domain using a WKBJ method. It is found that, for a particular azimuthal wave length, the wave excitation occurs through a sequence of regularly spaced swings during which the wave changes from leading to trailing form. This is a generic process that is expected to occur in shearing discs with turbulence. Trailing waves of equal amplitude propagating in opposite directions are produced, both of which produce an outward angular momentum flux that we give expressions for as functions of the disc parameters and azimuthal wave length. By solving the wave amplitude equations numerically we justify the WKBJ approach for a Keplerian rotation law for all parameter regimes of interest. In order to quantify the wave excitation completely the important wave source terms need to be specified. Assuming conditions of weak nonlinearity, these can be identified and are associated with a quantity related to the potential vorticity, being the only survivors in the linear regime. Under the additional assumption that the source has a flat power spectrum at long azimuthal wave lengths, the optimal azimuthal wave length produced is found to be determined solely by the WKBJ response and is estimated to be 2 pi H, with H being the nominal disc scale height.
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