Gravity currents from a constant inflow on unbounded uniform slopes

AbstractIn this study we conducted laboratory experiments to examine the gravity currents produced from a constant inflow propagating on unbounded uniform slopes in the range 0∘≤θ≤15∘. In the experiments, the inlet Reynolds number and the slope angle were varied systematically. The study carried out dimensional analysis and quantified five dimensionless parameters, thereby characterizing the development of gravity currents. Top-view images shown in the experiments exhibited gravity currents in an elongated shape when propagating on steeper slopes larger than 6∘ but a round shape on milder slopes less than 3∘. The study finds that the five dimensionless parameters, which are functions of the slope angle, have near constant values for sufficiently large inlet Reynolds number, suggesting that the flow is approaching the regime of Reynolds number independence. The results from our experiments are expected to be applicable to gravity currents produced from a constant inflow on unbounded uniform slopes in larger scale natural or man-made environments.Keywords: Constant inflowdimensional analysisgravity currentsinclined bottomlaboratory experiments AcknowledgmentsThe authors would like to thank Mr L.-C. Hsu and Mr Y.-A. Li for help in running the experiments.Disclosure statementNo potential conflict of interest was reported by the author(s).Notationbmax=maximum width of spreading gravity currents (cm)b0=width of diffuser (cm)h=maximum head height (cm)h0=height of diffuser (cm)g=gravitational acceleration (cms−2)g′=reduced gravity (cms−2)Q0=volumetric inflow rate (cm3s−1)Re=Reynolds number (–)t=time (s)uf=front velocity of gravity currents (cms−1)Wp=buoyancy flux (cm4s−3)xf=front location (cm)xf,v=distance between the virtual origin and the front (cm)ν=kinematic viscosity of fluid (cm2s−1)π1=shape factor of the gravity currents in the spanwise direction (–)π2=shape factor of the gravity currents in the wall-normal direction (–)π3=dimensionless parameter relating front location and time (–)π4=dimensionless parameter relating maximum width and time (–)π5=dimensionless parameter relating the density difference in the head and front location (–)ρ0=density of ambient fluid (gcm−3)ρ1=density of inflow heavy fluid (gcm−3)θ=slope angle (–)Δρ=density excess of inflow heavy fluid (gcm−3)Δρf=density excess of the fluid in the head of the gravity currents (gcm−3)Additional informationFundingThe research was funded by National Taiwan University through grants 106R7739, 106R7830, 107L7830, 107L7734, 112L7826 and by Taiwan National Science and Technology Council through grants 107-2221-E-197-009, 108-2221-E-197-001-MY2, 111-2221-E-002-113-MY3.