turbulence和类太阳振荡之间的耦合：一种组合拉格朗日PDF/SPH方法。II -模态驱动、阻尼和模态表面效应
Coupling between turbulence and solar-like oscillations: A combined Lagrangian PDF/SPH approach. II - Mode driving, damping and modal surface effect
摘要：
本系列的第一篇论文建立了类太阳p模的线性随机波动方程，正确地考虑了湍流的影响。在这第二篇论文中，我们的目的是推导出与任何给定的p模式相关的激励率，阻尼率和模态表面效应的同时表达式，作为湍流速度场的统计特性的显式函数。对于系统的正常振荡模式，我们将随机波动方程简化为复振幅方程。然后，我们推导出等效的Fokker-Planck方程的所有振荡模式的实际振幅和相位的同时。湍流波动的有限记忆时间（相当于模式的周期）对模式本身的影响是一致的，严格占，通过简化的振幅方程形式主义。这种形式主义充分考虑了相互线性模式耦合，然后我们转向特殊的单模情况。这使我们能够推导出每个模式的平均能量和平均相位的演化方程，从中自然产生激励率，阻尼率和模态表面效应。我们表明，模式的激发率的表达式是相同的，通过不同的建模方法获得的结果，从而支持这里提出的形式主义的有效性。我们还恢复了这样一个事实，即阻尼率和模态表面效应对应于同一个单一的复数量的实部和虚部。我们明确地分离不同的物理贡献，这些可观的，特别是湍流压力的贡献和压力率的应变相关性和湍流耗散的联合效应。我们表明，前者占主导地位的高频模式和后者的低频模式。
英文摘要：
The first paper of this series established a linear stochastic wave equation for solar-like p-modes, correctly taking the effect of turbulence thereon into account. In this second paper, we aim at deriving simultaneous expressions for the excitation rate, damping rate, and modal surface effect associated with any given p-mode, as an explicit function of the statistical properties of the turbulent velocity field. We reduce the stochastic wave equation to complex amplitude equations for the normal oscillating modes of the system. We then derive the equivalent Fokker-Planck equation for the real amplitudes and phases of all the oscillating modes of the system simultaneously. The effect of the finite-memory time of the turbulent fluctuations (comparable to the period of the modes) on the modes themselves is consistently and rigorously accounted for, by means of the simplified amplitude equation formalism. This formalism accounts for mutual linear mode coupling in full, and we then turn to the special single-mode case. This allows us to derive evolution equations for the mean energy and mean phase of each mode, from which the excitation rate, the damping rate, and the modal surface effect naturally arise. We show that the expression for the excitation rate of the modes is identical to previous results obtained through a different modelling approach, thus supporting the validity of the formalism presented here. We also recover the fact that the damping rate and modal surface effect correspond to the real and imaginary part of the same single complex quantity. We explicitly separate the different physical contributions to these observables, in particular the turbulent pressure contribution and the joint effect of the pressure-rate-of-strain correlation and the turbulent dissipation. We show that the former dominates for high-frequency modes and the latter for low-frequency modes.
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