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arXiv 1109.2907astro-ph.EP
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吸积盘turbulence激发螺旋密度波的弱非线性理论

A Weakly nonlinear theory for spiral density waves excited by accretion disc turbulence

Tobias Heinemann, John C. B. Papaloizou

摘要:

我们发展了一个解析理论来描述弱非线性区域中剪切圆盘中螺旋密度波的传播。通常发现这种波在湍流吸积盘的模拟中被激发,特别是如果所述湍流由磁旋转不稳定性(MRI)引起的话。我们推导出一个修改后的Burgers方程的动力学,其中包括非线性陡化,分散,和体积粘度的影响,以支持冲击。我们近似地求解这个方程,得到在后期渐近有效的非线性非线性解。在这个极限下,发现激波的存在导致波幅随时间减小1/t^2。通过对全非线性运动方程的直接数值求解,证实了解析描述的有效性。的状态变量的波形的渐近形式也被发现发生在MRI模拟表明,耗散由于冲击起着重要的作用,除了从直接耦合到湍流所产生的任何影响。

英文摘要:

We develop an analytic theory to describe spiral density waves propagating in a shearing disc in the weakly nonlinear regime. Such waves are generically found to be excited in simulations of turbulent accretion disks, in particular if said turbulence arises from the magneto-rotational instability (MRI). We derive a modified Burgers equation governing their dynamics, which includes the effects of nonlinear steepening, dispersion, and a bulk viscosity to support shocks. We solve this equation approximately to obtain nonlinear sawtooth solutions that are asymptotically valid at late times. In this limit, the presence of shocks is found to cause the wave amplitude to decrease with time as 1/t^2. The validity of the analytic description is confirmed by direct numerical solution of the full nonlinear equations of motion. The asymptotic forms of the wave profiles of the state variables are also found to occur in MRI simulations indicating that dissipation due to shocks plays a significant role apart from any effects arising from direct coupling to the turbulence.

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