This study investigated the weakly nonlinear propagation of pressure waves in compressible, flowing water with spherical microbubbles, considering various forces. Previous theoretical studies on nonlinear pressure waves in bubbly flows did not consider the forces acting on the bubbles, although the validity of ignoring these forces has not been demonstrated. We focused on every possible force such as drag, gravity, buoyancy, and Bjerknes (acoustic radiation) forces acting on bubbles and studied their effects on pressure waves in a one-dimensional setting. Using a singular perturbation method, the Korteweg–de Vries–Burgers equation describing wave propagation was derived. The following results were obtained: (i) Bjerknes force on the bubbles enhanced the nonlinearity, dissipation, and dispersion of the waves; (ii) Drag, gravity, and buoyancy forces acting on the bubbles increased wave dissipation; (iii) Thermal conduction had the most substantial dissipation effect, followed by acoustic radiation, drag, buoyancy, and gravity. We confirmed that the dissipation due to forces on gas bubbles was quantitatively minor.

中文翻译：

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各种力如何影响气泡流中的压力波？

本研究研究了压力波在具有球形微泡的可压缩流动水中的弱非线性传播，考虑了各种力。先前关于气泡流中非线性压力波的理论研究没有考虑作用在气泡上的力，尽管忽略这些力的有效性尚未得到证明。我们专注于作用在气泡上的每一种可能的力，例如阻力、重力、浮力和 Bjerknes（声辐射）力，并研究它们在一维环境中对压力波的影响。使用奇异摄动方法，推导出描述波传播的 Korteweg-de Vries-Burgers 方程。获得以下结果： (i) 气泡上的 Bjerknes 力增强了波的非线性、耗散和色散； (ii) 作用在气泡上的阻力、重力和浮力增加了波浪耗散； (iii) 热传导具有最显着的耗散效应，其次是声辐射、阻力、浮力和重力。我们证实，由于气泡上的力造成的耗散在数量上是很小的。