On the propagation of waves exhibiting both positive and negative nonlinearity
On the propagation of waves exhibiting both positive and negative nonlinearity
复制标题
关于表现出正非线性和负非线性的波的传播
DOI：
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发表时间：
1984
影响因子：
3.7
通讯作者：
A. Kluwick
中科院分区：
文献类型：
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作者：
M. Cramer;A. Kluwick
研究了基导数符号局部值变化的一维小振幅波。未扰动的介质被认为是一种静止的、具有均匀压力和密度的Navier-Stokes流体，使得基本导数很小。发展了处理无粘性运动的弱激波理论，并用多尺度方法导出了控制弱耗散波演化的非线性抛物方程。后者用于计算粘性激波结构。令人感兴趣的新现象包括冲击波在冲击波强度中具有四级熵跳跃，冲击波在激波的上游或下游具有音速条件，以及膨胀和压缩激波之间的碰撞。结果表明，当无扰动介质的基导数为零时，单符号脉冲的最终衰减量与传输时间的负1/3次方成正比。
One-dimensional small-amplitude waves in which the local value of the fundamental derivative changes sign are examined. The undisturbed medium is taken to be a Navier–Stokes fluid which is at rest and uniform with a pressure and density such that the fundamental derivative is small. A weak shock theory is developed to treat inviscid motions, and the method of multiple scales is used to derive the nonlinear parabolic equation governing the evolution of weakly dissipative waves. The latter is used to compute the viscous shock structure. New phenomena of interest include shock waves having an entropy jump of the fourth order in the shock strength, shock waves having sonic conditions either upstream or downstream of the shock, and collisions between expansion and compression shocks. When the fundamental derivative of the undisturbed media is identically zero it is shown that the ultimate decay of a one-signed pulse is proportional to the negative 1/3-power of the propagation time.