ABSTRACT The double-averaging methodology is used in this paper for deriving equations for the second-order velocity moments (i.e. turbulent and dispersive stresses) that emerge in the double-averaged momentum equation for incompressible Newtonian flows over mobile boundaries. The starting point in the derivation is the mass and momentum conservation equations for local (at a point) instantaneous variables that are up-scaled by employing temporal and spatial averaging. First, time-averaged conservation equations for mass, momentum, and turbulent stresses for mobile bed conditions are derived. Then, the double-averaged hydrodynamic equations obtained by spatial averaging the time-averaged equations are proposed. The derived second-order equations can serve as a basis for the construction of simplified mathematical and numerical models and for interpretation of experimental and simulation data when bed mobility is present. Potential applications include complex flow situations such as free-surface flows over vegetated or mobile sedimentary beds and flows through tidal and wind turbine arrays.

中文翻译：

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移动粗糙层上的空间平均流量：二阶速度矩方程

摘要 本文使用双平均方法来推导二阶速度矩（即湍流和色散应力）的方程，这些方程出现在移动边界上不可压缩牛顿流的双平均动量方程中。推导的起点是局部（在一个点）瞬时变量的质量和动量守恒方程，这些变量通过使用时间和空间平均来放大。首先，推导出移动床条件下质量、动量和湍流应力的时间平均守恒方程。然后，提出了对时间平均方程进行空间平均得到的双平均水动力方程。推导出的二阶方程可以作为构建简化数学和数值模型的基础，以及当存在床层流动性时解释实验和模拟数据的基础。潜在的应用包括复杂的流动情况，例如在植被或移动沉积层上的自由表面流动，以及通过潮汐和风力涡轮机阵列的流动。