# On the modelling of shallow turbidity flows

## TL;DR

This paper introduces a simple hyperbolic model for shallow turbidity flows that incorporates turbulence, sediment entrainment, and water mixing, validated against experimental data and capable of capturing various flow behaviors.

## Contribution

A novel, minimal-parameter hyperbolic model for shallow turbidity flows that accounts for turbulence, sediment dynamics, and mixing, validated through experiments and analytical solutions.

## Key findings

- Model accurately fits experimental data
- Special solutions include travelling and self-similar flows
- Unsteady simulations show long-term asymptotic states

## Abstract

In this study we investigate shallow turbidity density currents and underflows from mechanical point of view. We propose a simple hyperbolic model for such flows. On one hand, our model is based on very basic conservation principles. On the other hand, the turbulent nature of the flow is also taken into account through the energy dissipation mechanism. Moreover, the mixing with the pure water along with sediments entrainment and deposition processes are considered, which makes the problem dynamically interesting. One of the main advantages of our model is that it requires the specification of only two modeling parameters - the rate of turbulent dissipation and the rate of the pure water entrainment. Consequently, the resulting model turns out to be very simple and self-consistent. This model is validated against several experimental data and several special classes of solutions (such as travelling, self-similar and steady) are constructed. Unsteady simulations show that some special solutions are realized as asymptotic long time states of dynamic trajectories.