arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1206.5753physics.flu-dynmath.CA
收藏

N维气泡动力学

Bubble Dynamics in N Dimensions

Alexander R. Klotz

摘要:

空化和气泡动力学是工程、自然科学和流体力学数学中的中心概念。由于其动力学的非线性性质,控制方程是不完全可解的。在这里,一个球形气泡在N维流体中的动力学进行了讨论,希望检查气泡在N维的行为将增加洞察他们的行为在三维。气泡动力学中的几个典型的结果重新推导,包括瑞利崩溃时间,瑞利-Plesset方程,和Minnaert频率。数值模拟被用来检查发病的非线性行为。总的来说,气泡的动力学在更高的维度下更快,在更低的振幅下发生非线性行为。几个功能被发现是独特的三维,包括非线性行为的趋势和明显的时间尺度巧合。

英文摘要:

Cavitation and bubble dynamics are central concepts in engineering, the natural sciences, and the mathematics of fluid mechanics. Due to the nonlinear nature of their dynamics, the governing equations are not fully solvable. Here, the dynamics of a spherical bubble in an N-dimensional fluid are discussed in the hope that examining bubble behavior in N dimensions will add insight to their behavior in three dimensions. Several canonical results in bubble dynamics are re-derived, including the Rayleigh collapse time, the Rayleigh-Plesset equation, and the Minnaert frequency. Numerical simulations are used to examine the onset of nonlinear behavior. Overall, the dynamics of bubbles are faster at higher dimensions, with nonlinear behavior occurring at lower amplitudes. Several features are found to be unique to three dimensions, including the trend of nonlinear behaviour and apparent coincidences in timescales.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑