复杂结构平面波脉冲在非线性耗散介质中的衰减
The decay of plane wave pulses with complex structure in a nonlinear dissipative medium
摘要：
利用有限粘性Burgers方程研究了非线性平面声波在流体中的传播。本文研究了初始振幅为规则和随机的简单N脉冲以及单色和噪声载波脉冲的演化。在后一种情况下，初始脉冲的特征在于两个长度尺度。调制函数的长度尺度远大于载波的周期或长度尺度。随着时间的增加，初始脉冲发生变形，出现激波。有限的粘性导致有限的冲击宽度，它不依赖于初始脉冲的精细结构，并完全由冲击位置在零粘性极限。非零粘性的另一个影响是激波位置从零粘性位置的偏移。这种转变以及从非线性演化阶段转变为线性演化阶段的线性时间取决于初始脉冲的精细结构。它还表明，非线性的介质导致从一个初始的随机场与零平均值的非零平均场的产生。在非线性和线性阶段的光场的相对涨落进行了研究。
英文摘要：
Nonlinear plane acoustic waves propagating through a fluid are studied using Burgers' equation with finite viscosity. The evolution of a simple N-pulse with regular and random initial amplitude and of pulses with monochromatic and noise carrier is considered. In the latter case the initial pulses are characterized by two length scales. The length scale of the modulation function is much greater than the period or the length scale of the carrier. With increasing time the initial pulses are deformed and shocks appear. The finite viscosity leads to a finite shock width, which does not depend on the fine structure of the initial pulse and is fully determined by the shock position in the zero viscosity limit. The other effect of nonzero viscosity is the shift of the shock position from the position at zero viscosity. This shift, as well as the linear time, at which the nonlinear stage of evolution changes to the linear stage, depends on the fine structure of the initial pulse. It is also shown that the nonlinearity of the medium leads to generation of a nonzero mean field from an initial random field with zero mean value. The relative fluctuation of the field is investigated both at the nonlinear and the linear stage.
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