The variation of flow and turbulence across the sediment–water interface

Abstract

A basic framework characterising the interaction between aquatic flows and permeable sediment beds is presented here. Through the permeability Reynolds number ($Re_{K}=\sqrt{K}u_{\ast }/\unicode[STIX]{x1D708}$, where$K$is the sediment permeability,$u_{\ast }$is the shear velocity and$\unicode[STIX]{x1D708}$is the fluid viscosity), the framework unifies two classical flow typologies, namely impermeable boundary layer flows ($Re_{K}\ll 1$) and highly permeable canopy flows ($Re_{K}\gg 1$). Within this range, the sediment–water interface (SWI) is identified as a transitional region, with$Re_{K}$in aquatic systems typically$O(0.001{-}10)$. As the sediments obstruct conventional measurement techniques, experimental observations of interfacial hydrodynamics remain extremely rare. The use of refractive index matching here allows measurement of the mean and turbulent flow across the SWI and thus direct validation of the proposed framework. This study demonstrates a strong relationship between the structure of the mean and turbulent flow at the SWI and$Re_{K}$. Hydrodynamic characteristics, such as the interfacial turbulent shear stress, velocity, turbulence intensities and turbulence anisotropy tend towards those observed in flows over impermeable boundaries as$Re_{K}\rightarrow 0$and towards those seen in flows over highly permeable boundaries as$Re_{K}\rightarrow \infty$. A value of$Re_{K}\approx 1{-}2$is seen to be an important threshold, above which the turbulent stress starts to dominate the fluid shear stress at the SWI, the penetration depths of turbulence and the mean flow into the sediment bed are comparable and similarity relationships developed for highly permeable boundaries hold. These results are used to provide a new perspective on the development of interfacial transport models at the SWI.