一个将湍流涡旋与槽道流中悬浮泥沙浓度联系起来的共谱收支模式
A co-spectral budget model links turbulent eddies to suspended sediment concentration in channel flows
摘要：
悬浮泥沙浓度的垂向分布与水力学、水文学、生态学和水质控制等诸多问题密切相关，一直是研究的热点。在过去的90年里，许多经典理论都是使用有效混合长度或涡扩散系数来描述湍流对悬浮泥沙（SS）的影响，而没有明确说明湍流涡旋的能量。为了解决这一差距，沉积物的湍流通量推导使用的共谱预算（CSB）模型，可以迫切地用于SS和其他细颗粒物传输模型。CSB关闭的压力再分布效应，使用修改后的光谱线性Rotta计划，包括对流层的生产和湍流涡旋和沉积物颗粒之间的相互作用，通过修改后的尺度相关的去相关时间。其结果是一个公式的复杂性类似于广泛使用的劳斯方程，但所有的特征尺度，雷诺数，施密特数的影响来自完善的垂直速度的频谱形状和公认的常数从湍流模型。最后，所提出的CSB模型可以恢复Prandtl和Rouse方程的限制条件。
英文摘要：
The vertical distribution of suspended sediment concentration (SSC) remains a subject of active research given its relevance to a plethora of problems in hydraulics, hydrology, ecology, and water quality control. Much of the classical theories developed over the course of 90 years represent the effects of turbulence on suspended sediments (SS) using an effective mixing length or eddy diffusivity without explicitly accounting for the energetics of turbulent eddies across scales. To address this gap, the turbulent flux of sediments is derived using a co-spectral budget (CSB) model that can be imminently used in SS and other fine particle transport models. The CSB closes the pressure-redistribution effect using a spectral linear Rotta scheme modified to include isotropoziation of production and interactions between turbulent eddies and sediment grains through a modified scale-dependent de-correlation time. The result is a formulation similar in complexity to the widely used Rouse's equation but with all characteristic scales, Reynolds number, and Schmidt number effects derived from well-established spectral shapes of the vertical velocity and accepted constants from turbulence models. Finally, the proposed CSB model can recover Prandtl's and Rouse's equations under restricted conditions.
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