Modeling turbulent mixing and sand distribution in the bottom boundary layer

TL;DR

This paper develops analytical models for turbulent mixing and sand distribution in the bottom boundary layer, using observational data and theoretical functions to improve predictions of sediment concentration profiles.

Contribution

It introduces two new theoretical functions for mixing length based on turbulence observations and integrates them into a finite-mixing-length model for sediment transport.

Findings

The exponential decay model accurately describes turbulence intensity with height.

The lm1 function reproduces measured sediment concentration profiles for coarse sand.

The models differentiate the effects of mixing length formulations on sediment profile shapes.

Abstract

For the calculation of turbulent mixing in the bottom boundary layer, we present simple analytical tools for the mixing velocity wm and the mixing length lm. Based on observations of turbulence intensity measurements, the mixing velocity wm is represented by an exponential function decaying with z. We suggest two theoretical functions for the mixing length, a first lm1 obtained from the k-equation written as a constant modeled fluctuating kinetic energy flux and a second lm2 based on von K\'arm\'an's similarity hypothesis. These analytical tools were used in the finite-mixing-length model of Nielsen and Teakle (2004). The modeling of time-mean sediment concentration profiles C(z) over wave ripples shows that at the opposite of the second equation lm2 which increases the upward convexity of C(z), the first equation lm1 increases the upward concavity of C(z) and is able to reproduce the shape of the measured concentrations for coarse sand.