Short- and Resonant-Range Interactions Between Scales in Turbulence and Their Applications
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摘要: 从Navier-Stokes方程出发，研究了湍流不同尺度间的相互作用规律，给出相近尺度间近程粘性应力的积分和微分表达式．引入极相近尺度之间共振相互作用的概念，得到共振粘性应力的微分表达式．利用共振粘性应力张量获得不含经验关系和常数、近似封闭的大涡模拟（LES）方程组．利用近程和共振粘性应力张量获得不含经验关系和常数、近似封闭的湍流多尺度方程组．讨论了湍流多尺度方程的性质及用于湍流计算的优点，尺度间相互作用的近程特性说明：多尺度模拟是湍流计算很有价值的方法，并列举了算例．Abstract: Interactions between different scales in turbulence were studied starting from the incompressible Navier-Stokes equations. The integral and differential formulae of the short-range viscous stresses, which express the short-range interactions between contiguous scales in turbulence, were given. A concept of the resonant-range interactions between extreme contiguous scales was introduced and the differential formula of the resonant-range viscous stresses was obtained. The short- and resonant-range viscous stresses were applied to deduce the large-eddy simulation (LES) equations as well as the multiscale equations, which are approximately closed and do not contain any empirical constants or relations. The properties and advantages of using the multiscale equations to compute turbulent flows were discussed. The short-range character of the interactions between the scales in turbulence means that the multiscale simulation is a very valuable technique for the calculation of turbulent flows. A few numerical examples were also given.
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