2016/05/13 by Yantao Yang, Roberto Verzicco, Detlef Lohse · 42 citations
Engineering · Environmental Science · Physics and Astronomy · #Buoyancy #CO2 Sequestration and Geologic Interactions #Convection #Flow (mathematics) #Fluid Dynamics and Turbulent Flows #Nanofluid Flow and Heat Transfer #Nusselt number #Prandtl number #Rayleigh number #Reynolds number #Scalar (mathematics) #Scaling #physics.flu-dyn #physics.geo-ph
paper · pdf · open access · doi:10.1017/jfm.2016.484
published in Journal of Fluid Mechanics 802, 667-689 (Cambridge University Press)
arxiv created 2016/05/13 · openalex created_date 2016/06/24 · openalex publication_date 2016/08/08 · arxiv updated 2016/08/24 · openalex updated_date 2026/08/05
Direct numerical simulations are conducted for double diffusive convection (DDC) bounded by two parallel plates. The Prandtl numbers, i.e. the ratios between the viscosity and the molecular diffusivities of scalars, are similar to the values of seawater. The DDC flow is driven by an unstable salinity difference (here across the two plates) and stabilized at the same time by a temperature difference. For these conditions the flow can be in the finger regime. We develop scaling laws for three key response parameters of the system: the non-dimensional salinity flux NuS mainly depends on the salinity Rayleigh number RaS , which measures the strength of the salinity difference and exhibits a very weak dependence on the density ratio \unicode[STIX]x1D6EC , which is the ratio of the buoyancy forces induced by two scalar differences. The non-dimensional flow velocity Re and the non-dimensional heat flux NuT are dependent on both RaS and \unicode[STIX]x1D6EC . However, the rescaled Reynolds number Re\unicode[STIX]x1D6EC^\unicode[STIX]x1D6FCueff and the rescaled convective heat flux (NuT-1)\unicode[STIX]x1D6EC^\unicode[STIX]x1D6FCTeff depend only on RaS . The two exponents are dependent on the fluid properties and are determined from the numerical results as \unicode[STIX]x1D6FCueff=0.25± 0.02 and \unicode[STIX]x1D6FCTeff=0.75± 0.03 . Moreover, the behaviours of NuS and Re\unicode[STIX]x1D6EC^\unicode[STIX]x1D6FCueff agree with the predictions of the Grossmann–Lohse theory which was originally developed for the Rayleigh–Bénard flow. The non-dimensional salt-finger width and the thickness of the velocity boundary layers, after being rescaled by \unicode[STIX]x1D6EC^\unicode[STIX]x1D6FCueff/2 , collapse and obey a similar power-law scaling relation with RaS . When RaS is large enough, salt fingers do not extend from one plate to the other and horizontal zonal flows emerge in the bulk region. We then show that the current scaling strategy can be successfully applied to the experimental results of a heat–copper–ion system (Hage & Tilgner, Phys. Fluids , vol. 22, 2010, 076603). The fluid has different properties and the exponent \unicode[STIX]x1D6FCueff takes a different value 0.54± 0.10 .