arXiv 1809.022022018-09-06physics.flu-dyn

非线性声波的谱能量级联与衰减

Spectral energy cascade and decay in nonlinear acoustic waves

Prateek Gupta, Carlo Scalo

DOI：: 10.1103/PhysRevE.98.033117

摘要：

本文对标准温度和压力下单组分理想气体中衰减的有限振幅平面声波的非线性谱能量级联进行了数值和理论研究。我们分析了各种一维规范流配置：传播行波（TW），一个驻波（SW），和随机初始化的声波湍流（AWT）。本文采用激波分辨网格自适应直接数值模拟方法对一维完全可压缩纳维-斯托克斯方程进行了非线性声波谱能量级联的数值模拟。我们还导出了一组新的非线性声学方程截断到二阶和相应的扰动能量推论产生一个新的扰动能量范数$E^{(2)}$的表达式。它的空间平均，< $E^{(2)}$ >满足定义的李雅普诺夫函数，正确地捕获的非粘性（或无损）扩大的频谱能量在初始阶段的演变-类似于动能的演变过程中的流体动力学预锻分解的三维相干涡-导致形成较小的规模。在谱能量级联饱和时，即完全加宽的能谱时，粘性损失的开始导致时间上的单调衰减< $E^{(2)}$ >。

英文摘要：

We present a numerical and theoretical investigation of nonlinear spectral energy cascade of decaying finite-amplitude planar acoustic waves in a single-component ideal gas at standard temperature and pressure (STP). We analyze various one-dimensional canonical flow configurations: a propagating traveling wave (TW), a standing wave (SW), and randomly initialized Acoustic Wave Turbulence (AWT). We use shock-resolved mesh-adaptive direct numerical simulations (DNS) of the fully compressible one-dimensional Navier-Stokes equations to simulate the spectral energy cascade in nonlinear acoustic waves. We also derive a new set of nonlinear acoustics equations truncated to second order and the corresponding perturbation energy corollary yielding the expression for a new perturbation energy norm $E^{(2)}$. Its spatial average, <$E^{(2)}$> satisfies the definition of a Lyapunov function, correctly capturing the inviscid (or lossless) broadening of spectral energy in the initial stages of evolution -- analogous to the evolution of kinetic energy during the hydrodynamic break down of three-dimensional coherent vorticity -- resulting in the formation of smaller scales. Upon saturation of the spectral energy cascade i.e. fully broadened energy spectrum, the onset of viscous losses causes a monotonic decay of <$E^{(2)}$> in time.

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