Abstract

Abstract

Highlights

  • Density-driven, predominantly horizontal flows in the form of gravity currents play a central role in a host of natural processes, as well as in numerous engineering applications 916 A30-1R

  • We have explored the removal of a dense fluid layer above a horizontal bottom wall by a lock-release gravity current, via 2-D Navier–Stokes simulations in the Boussinesq limit

  • As the two dominant dimensionless quantities governing this problem, we identify a thickness parameter for the dense bottom layer, and the density ratio given by the differences between the densities of the bottom layer, the gravity current and the ambient fluid

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Summary

Introduction

Density-driven, predominantly horizontal flows in the form of gravity currents play a central role in a host of natural processes, as well as in numerous engineering applications. We note that the situation sketched in figure 1 differs in several key aspects from the one in which all of the fluid initially to the left of the gate is of the same intermediate density, so that a dense bottom layer exists only to the right of the gate This set-up has been explored in some detail, going back to the early experimental investigations by Holyer & Huppert (1980) and Britter & Simpson (1981), and it can exhibit interesting symmetry properties. By its very nature, the configuration sketched in figure 1 with a dense fluid layer to the left of the gate cannot give rise to corresponding geometric or dynamical flow symmetries, since it does not produce a left-propagating countercurrent along the bottom wall It represents an interesting subject of exploration in its own right.

Governing equations
Initial and boundary conditions
Numerical method
Two-dimensional versus three-dimensional simulations
Flow regimes
Effective bore height
Amplitude and wavelength of the undular bore waves
Vorticity-based model
Energy budget
Conclusions
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