Analysis and direct numerical simulation of the flow at a gravity-current head. Part 1. Flow topology and front speed for slip and no-slip boundaries

Abstract

Direct numerical simulations are performed of gravity-current fronts in the lock-exchange configuration. The case of small density differences is considered, where the Boussinesq approximations can be adopted. The key objective of the investigation is a detailed analysis of the flow structure at the foremost part of the front, where no previous high-resolution data were available. For the simulations, high-order numerical methods are used, based on spectral and spectral-element discretizations and compact finite differences. A three-dimensional simulation is conducted of a front spreading along a no-slip boundary at a Reynolds number of about 750. The simulation exhibits all features typically observed in experimental flows near the gravity-current head, including the lobe-and-cleft structure at the leading edge. The results reveal that the flow topology at the head differs from what has been assumed previously, in that the foremost point is not a stagnation point in a translating system. Rather, the stagnation point is located below and slightly behind the foremost point in the vicinity of the wall. The relevance of this finding for the mechanism behind the lobe-and-cleft instability is discussed. In order to explore the high-Reynolds-number regime, and to assess potential Reynolds-number effects, two-dimensional simulations are conducted for Reynolds numbers up to about 30 000, for both no-slip and slip (i.e. shear-stress free) boundaries. It is shown that although quantitative Reynolds-number effects persist over the whole range examined, no qualitative changes in the flow structure at the head can be observed. A comparison of the two-dimensional results with laboratory data and the three-dimensional simulation provides evidence that a two-dimensional model is able to capture essential features of the flow at the head. The simulations also show that for the free-slip case the shape of the head agrees closely with the classical inviscid theory of Benjamin.

A nonhydrostatic version of FVCOM: 1. Validation experiments

“…At 10T, five vortices develop, and the left and right gravity current frontal heads move to the locations x/H = −6.47 and 6.7, respectively. The vortex numbers, locations of the gravity current frontal heads, and asymmetry of the speed of the left and right gravity current frontal heads compare well with those presented in Figure 11 of Härtel et al [2000].…”

Dynamics of the head of gravity currents

“…The development of gravity currents is typically an unsteady phenomenon, i.e., current kinematics and the inner density distribution are time varying, therefore the lockexchange setup is a simple and convenient way to investigating the flow features of these particular currents. Numerical modeling has also been used to investigate the evolution and impact of gravity currents [2,10,13,23,27,[33][34][35]44,47,59]. Although the motion of these currents is invariably three-dimensional, laboratory experiments and numerical results indicate that the large-scale features may be reasonably well described through a two-dimensional approach [27].…”

FINAL REPORT on Experimental Validation of Stratified Flow Phenomena, Graphite Oxidation, and Mitigation Strategies of Air Ingress Accidents

“…He also said that the characteristic head would control the mixing behavior, current velocity, and current profile. The current induced mixing is considered to be caused by two types of instabilities: billows, and lobes and clefts as shown in Figure 2 Hartel et al (2000) showed that the current can be explained using shallow-water theory if sufficiently accurate front conditions are prescribed for the nonhydrostatic flow at the head of the current.…”