Energetics of Turbulence Explains Physical Transport Processes in the Environment

Abstract

The indispensability of turbulent transport processes in environmental flows for a broad spectrum of applications, such as river restoration, sediment transport, and wetland design, is a widely acknowledged fact. Notably, turbulent eddies exert a substantial influence on transport phenomena, warranting novel approaches that account for their energetic impact on bulk flow variables. In this vein, the present study endeavors to explore and expound upon such approaches, with a specific focus on the transport of sediments in turbulent flows.This dissertation consists of six chapters, with Chapter 1 serving as an introduction and overview. Chapter 2 focuses on the development of a co-spectral budget model to account for the pressure-redistribution effect in modeling turbulent shear stress. The model proposed incorporates a modified spectral linear Rotta scheme that considers isotropization of production and interactions between turbulent eddies and bed roughness. The result is a mathematical derivation of a modified Nikuradse curve that links the friction factor to Reynolds number and wall roughness.Chapter 3 extends the co-spectral budget model to link the incipient motion of sediments to turbulent eddies. A mathematical derivation is presented to elucidate the scaling properties of an empirical diagram between a densimetric Froude number and relative roughness, connecting sediment motion to turbulent energetics.Chapter 4 centers on representing the energetics of multiple turbulent eddies in modeling the suspended particle distribution in turbulent flows. A noval formulation is developed that considers all characteristic scales, Reynolds number, and Schmidt number effects, based on established spectral shapes of the turbulent vertical velocity and closure model constants. Chapter 5 examines the turbulent settling velocity of suspended particles, accounting for two often-neglected effects: the unsteady vortices caused by grain movement (Basset history term) and the displacement of water mass due to grain movement (virtual mass term). The inclusion of these terms addresses inconsistencies between resent laboratory experiments and previous theories on grain settling velocities in turbulence where density contrasts between water and grain is not too large.The findings of this research have potential to enhance the design and management of river systems and other flow-related infrastructure. Some of these applications are discussed in the concluding Chapter 6.