Mixing efficiency in a run-down gravity current

Mixing efficiency in a run-down gravity current G. O. Hughes 1 and P. F. Linden 2 Department of Civil and Environmental Engineering, Imperial College London g.hughes@imperial.ac.uk Department of Applied Mathematics and Theoretical Physics, University of Cambridge p.f.linden@damtp.cam.ac.uk Abstract We present measurements of mixing efficiency in a run-down gravity current created by lock exchange in a channel. Experiments were designed to extend to particularly high Reynolds number (of order 10 5 , based on the current depth), at which mixing is no longer affected significantly by viscosity. Under these conditions, we observe that the run-down density profiles in the channel achieve full self-similarity and that the mixing efficiency asymptotes to a value of 0.08. Introduction Intense turbulence is a ubiquitous feature in gravity currents, but its dynamical impor- tance is not well understood. Most previous studies have concentrated on understanding the bulk characteristics of currents such as the speed of propagation and current depth, highlighting the existence of a number of flow regimes and dynamical balances (e.g. see Huppert and Simpson, 1980; Rottman and Simpson, 1983; Shin et al., 2004; Simpson, 1997, for an overview). Measurements have revealed rich density and velocity structure in a turbulent gravity current (e.g. Hacker et al., 1996; Hallworth et al., 1996; Kneller et al., 1999; Shin et al., 2004; Marino et al., 2005; Fragoso et al., 2013; Samasiri and Woods, 2015; Sher and Woods, 2015). Interestingly, although turbulent eddies exchange mass and momentum between the current and ambient fluid, resulting in additional drag on the current and mixing of the density field, the propagation speed and the effective current depth is usually still well-predicted by an energy-conserving theory (for instance, see Shin et al., 2004). Consequently, most previous theoretical models for gravity cur- rents also assume a highly idealized form based on lateral and/or depth averaging. ‘Box’ models are a common example of this approach (e.g. Huppert and Simpson, 1980), rep- resenting a two-dimensional current as a constant area rectangle that elongates along the boundary with time. Density and velocity structure in the current is not accounted for explicitly, these distributions instead being characterized as uniform. Even though bulk idealizations capture some dynamics associated with mixing (because the total buoyancy anomaly in the flow is conserved; Huppert, 2006), the internal structure of the current and its role in the overall flow remains a barely examined question. In this paper, we examine the energy budget of the flow with the aim of generating insight into the dynamics governing turbulent mixing in a gravity current. We restrict attention here to conceptually simple laboratory experiments examining lock exchange currents in the constant speed regime (Rottman and Simpson, 1983), where we expect turbulent mixing to also proceed at an approximately constant rate. We report measurements of the mixing for Reynolds number Re = U H/2ν ranging up to 70,000, where U is the current VIII th Int. Symp. on Stratified Flows, San Diego, USA, Aug. 29 - Sept. 1, 2016