Mathematical Sciences: Semi-Strong Turbulence

数学科学：半强湍流

• 批准号: 9423245
• 负责人: Philip Saffman
• 金额: $ 5万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-05-01 至 1997-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9423245&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Semi; Strong; Turbulence

DMS-9423245 Saffman and Meiron In the 60s scientists began to study so called weak turbulence which can be described by a so called kinetic equation for waves, similar to the Boltzmann kinetic equation for particles. Such turbulence represents a dynamics of many dispersive waves weakly interacting with each other (like nonlinear waves on the sea surface). We have found that there is a well defined intermediate situation between weak and strong turbulence which we call {\it semi-strong turbulence}. In this situation the turbulence represents the dynamics of a system of weakly interacting waves, but the wave kinetic equation is inapplicable, no matter how small the wave amplitudes are (this happens, for example, when the waves are non-dispersive, like acoustic waves). We are going to develop the theory of semi-strong turbulence from first principles and apply the results to several practical problems, e.g. acoustic turbulence, the turbulence of shallow water gravity waves, the suppression of short wave turbulence by long waves, angular distribution of the sea wave turbulence, turbulence in optical fibers, magneto-hydrodynamic turbulence, etc. In addition we are going to implement some computational and real experiments to check the predictions of the theory. We also intend to develop a new formalism for nonlinear waves, which will allow us to simplify the description of semi-strong turbulence.

DMS-9423245 Saffman和Meiron在60年代，科学家们开始研究所谓的弱湍流，这种湍流可以用所谓的波动力学方程来描述，类似于粒子的玻尔兹曼动力学方程。这种湍流代表了许多色散波彼此弱相互作用的动力学（如海面上的非线性波）。我们发现在弱湍流和强湍流之间有一个很好的中间状态，我们称之为半强湍流。 在这种情况下，湍流表示弱相互作用波系统的动力学，但波动力学方程是不适用的，无论波的振幅有多小（例如，当波是非色散的，如声波时，就会发生这种情况）。 我们将从第一性原理出发，发展半强湍流理论，并将其应用于几个实际问题，如声湍流、浅水重力波湍流、长波对短波湍流的抑制、海浪湍流的角分布、光纤中的湍流、磁流体动力学湍流、此外，我们将实施一些计算和真实的实验来检查理论的预测。我们还打算发展一种新的形式主义的非线性波，这将使我们能够简化半强湍流的描述。