Turbulence Theory: Bounds and Higher-Order Statistics

本研究的目的是开发 湍流近似提供了上界和下界， 物理兴趣的数量。这项工作是在精神 霍华德和Busse的边界理论，但从一个 抽取方案，其中仅流的模式的子集 系统被明确对待。 其余的隐式模式是 由随机强迫项表示， 在无穷组力矩约束中， 动力学 为了找到边界，建议寻求解决方案， 在一个有限的子集下， 这些限制，加上可实现性 不等式 由于约束是精确的，因此 建造将是严格的。第四，订单统计在 在边界发展中发挥着至关重要的作用。 这些统计数据 由于最近的纳维尔斯托克斯， 模拟研究显示了均方的有趣行为 螺旋度和总非线性项的均方。 是 建议用抽取方案研究四阶统计量。 利用积分法可以减少计算的复杂性 而不是详细形式的四阶矩约束。

The objective of this research is the development of turbulence approximations which provide upper and lower bounds on quantities of physical interest. This work is in the spirit of the bounding theory of Howard and Busse but proceeds from a decimation scheme in which only a subset of the modes of the flow system are treated explicitly. The remaining, implicit modes are represented by stochastic forcing terms which are subject to an in infinite set of moment constraints taken from the exact dynamics. To find bounds, it is proposed to seek solutions which extremalize the chosen quantities under a restricted subset of these constraints, imposed together with realizability inequalities. Since the constraints are exact, bounds so constructed would be rigorous. Fourth.order statistics play an essential role in the development of bounds. These statistics are additionally important because of recent Navier.Stokes simulation studies which show interesting behavior of mean.square helicity and the mean square of the total nonlinear term. It is proposed to study 4th.order statistics by the decimation scheme. The complexity of the work can be reduced by using integral rather than detailed forms of 4th.order moment constraints.