论文标题
湍流与太阳能振荡之间的耦合：Lagrangian PDF/SPH的组合方法。 II-模式驾驶，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
论文作者
论文摘要
该系列的第一篇论文建立了一个线性随机波方程，用于太阳能p模型，正确考虑了湍流的效果。在第二篇论文中，我们旨在得出与任何给定p模式相关的激发率，阻尼率和模态表面效应的同时表达式，作为湍流速度场统计特性的明确函数。我们将随机波方程减少到系统正常振荡模式的复杂振幅方程。然后，我们为同时的所有振荡模式的实际振幅和相位得出等效的fokker-planck方程。通过简化的振幅方程形式主义，始终如一，严格地解释了模式本身的湍流波动（与模式周期相当）的有限记忆时间的影响。这种形式主义解释了完全线性模式的完整耦合，然后我们转向特殊的单模案例。这使我们能够得出每种模式的平均能量和平均相位的进化方程，从中，激发率，阻尼率和模态表面效应自然出现。 我们表明，模式的激发率的表达与通过不同的建模方法获得的先前结果相同，从而支持此处介绍的形式主义的有效性。我们还恢复了一个事实，即阻尼速率和模态表面效应对应于同一单个复合量的真实和虚构部分。我们明确将不同的物理贡献分离为这些可观察物，特别是湍流压力的贡献和压力率相关性和湍流耗散的关节效应。我们表明，前者以高频模式为主导，而后者则是低频模式。
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.
