On the dynamics of gravity current motion in a stratified ambient

Abstract

AbstractThis study presents LES results of lock-release propagating gravity current (GC) at the base of a linearly stratified ambient. The focus of the study is to investigate the effect of ambient stratification on GC motion for both subcritical and supercritical regimes. The effects of Reynolds number and the ratio of the fluid depth in the lock to the total ambient fluid depth on GC front velocity are also examined. Also, the effect of stratification strength on mixing is evaluated. It is found that both subcritical and supercritical GCs have a constant-velocity phase. This phase terminates due to the current interaction with the internal waves (IWs) for the former, while for the latter, it is due to the decay of the head buoyancy. The duration of the constant-velocity phase increases with increasing stratification strength when the current is supercritical. For weak stratification the turbulence is considerable, while it is suppressed with stronger stratification. Mixing is more intense for supercritical GCs; however, mixing efficiency is much higher for subcritical GCs.Keywords: Gravity currentslarge-eddy simulationlock-exchangemixingstratification AcknowledgementsThe simulations for this work have been performed using the Aristotle University of Thessaloniki (AUTh) High Performance Computing Infrastructure and Resources.Disclosure statementNo potential conflict of interest was reported by the author(s).Data availability statementData can be provided upon reasonable request to the authors.NotationC=concentration (–)Cave=spanwise average concentration (–)C¯=current volume average concentration (–)D=depth of the fluid in the lock(m)Ed,ν=dissipation energy due to viscosity (m5 s−2)Ed,SGS=dissipation energy due to SGS viscosity (m5 s−2)Ed,num=numerical dissipation energy (m5 s−2)Ed,tot=total dissipation energy (m5 s−2)F=Froude number (–)g′=reduced gravity acceleration (m s−2)H=total fluid depth (m)I=internal energy due to density diffusion (m5 s−2)K=kinetic energy (m5 s−2)L=tank length (m)L0=lock length (m)N=buoyancy frequency (s−1)nc=cumulative mixing efficiency (–)p*=the pressure minus the hydrostatic pressure (kg m−1 s−2)P=potential energy (m5 s−2)P0=initial potential energy (m5 s−2)P0str=initial potential energy due to initial fluid stratification (m5 s−2)Pb=background energy (m5 s−2)Pa=available potential energy (m5 s−2)Rb=Reynolds number (–)S=ambient stratification strength (–)Sc=Schmidt number (–)Sc,t=turbulent Schmidt number (–)Sij=deformation tensor component ij (s−1)Ttr=transition time (s)ub=buoyancy velocity (m s−1)ui (u, v, w)=filtered velocity component of the i-direction (m s−1)Uf=current front velocity (m s−1)W=tank width (m)Xtr=transition distance (m)xf=current front position (m)Γ=molecular diffusivity (m2 s−1)ΓSGS=subgrid-scale molecular diffusivity (m2 s−1)ϵ=dissipation rate (m5 s−3)ν=kinematic viscosity (m2 s−1)νSGS=subgrid-scale kinematic viscosity (m2 s−1)ρc=density of the fluid in the lock (kg m−3)ρ0=density at the top of the tank (kg m−3)ρb=density at the bottom of the tank (kg m−3)φz=vertical buoyancy flux (m5 s−3)φi=rate of conversion from internal to potential energy (m5 s−3)φd=rate of change of the background energy (m5 s−3)φz=vertical buoyancy flux (m5 s-3)φ’z=local value of the vertical buoyancy flux (m2 s-3)φi=rate of conversion from internal to potential energy (m5 s-3)φ’i=local value of the rate of conversion from internal to potential energy (m2 s-3)Additional informationFundingThis project is part of the first author’s doctoral thesis. The implementation of the doctoral thesis is co-financed by Greece and the European Union (European Social Fund-ESF) through the Operational Programme “Human Resources Development, Education and Lifelong Learning” in the context of the Act “Enhancing Human Resources Research Potential by undertaking a Doctoral Research” Sub-action 2: IKY Scholarship Programme for PhD candidates in the Greek Universities.