相位畸变在高超声速平行流边界层不稳定声学模态非线性饱和中的作用
Role of phase distortion in nonlinear saturation of the unstable acoustic modes in hypersonic parallel flow boundary layer
AI总结：
本文分析二维高超声速平行流边界层中不稳定Mack模态非线性饱和时相对相位的作用，发现平均流非线性畸变导致的相位畸变占主导，通过渐近重构和能量收支计算，结合数值模型与DNS对比，揭示高次谐波作用极小及粘性效应的关键影响。
摘要：
我们分析了二维（2D）高超声速平行流边界层中不稳定Mack模态非线性饱和过程中相对相位的作用。随着线性不稳定的Mack模态从平均流中提取能量，扰动能量级联到高次谐波和平均流中。稳态时高次谐波的能量占总扰动能量的比例<0.5%，表明其在2D中作用极小。此外，高次谐波与不稳定模态的相速度相同，说明存在波陡化和相干能量级联。由于扰动能量持续提取到行波模态以及这些模态的粘性耗散，平均流发生减速和加热。与经典流体力学中的不稳定模态不同，我们发现平均流非线性畸变导致的流向速度与法向速度间的相对相位畸变占主导地位。通过不稳定本征模态的渐近重构，我们计算了线性和非线性区域的扰动能量收支。能量收支分析表明，壁面层和临界层的粘性效应足以捕捉平均流畸变引起的相位畸变。随后，我们将其整合到数值模型中，用于计算2D高超声速平行流边界层中不稳定Mack模态非线性饱和后的稳态扰动能量和平均流畸变。全文中，我们将近似理论分析结果与2D直接数值模拟（DNS）结果进行了比较。
英文摘要：
We analyze the role of the relative phasing in the nonlinear saturation of the unstable Mack modes in a hypersonic parallel flow boundary layer in two dimensions (2D). As the linearly unstable Mack modes extract energy from the mean flow, the perturbation energy cascades into higher harmonics as well as the mean flow. The higher harmonics are generated with < 0.5% of total perturbation energy at steady state, indicating a very small role of higher harmonics in 2D. Additionally, the higher harmonics propagate with the same phase speed as the unstable mode, indicating wave steepening and a coherent energy cascade. The mean flow gets decelerated and heated due to the continuous extraction of the perturbation energy into traveling modes and the viscous dissipation of these modes. Unlike unstable modes in classical hydrodynamics, we show that the distortion in relative phasing between the streamwise velocity and wall-normal velocity due to nonlinear distortion of the mean flow is dominant. Using asymptotic reconstruction of the unstable eigenmodes, we compute the perturbation energy budgets in the linear and nonlinear regimes. Through energy budgets, we show that the viscous effects in the wall layer and the viscous effects in the critical layer sufficiently capture the distortion in phase due to the mean-flow distortion. We then combine this in a numerical model for calculating the steady-state perturbation energy and mean-flow distortion through the nonlinear saturation of unstable Mack modes in a hypersonic parallel flow boundary layer in 2D. Throughout, we compare the results of approximate theoretical analysis with 2D direct numerical simulations (DNS).
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