Double diffusive convection in the finger regime for different Prandtl and Schmidt numbers
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RESEARCH PAPER
Double diffusive convection in the finger regime for different Prandtl and Schmidt numbers Yantao Yang1 Received: 18 April 2020 / Revised: 1 June 2020 / Accepted: 10 June 2020 © The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this work fingering double diffusive convection, i.e. the buoyancy-driven flow with fluid density being affected by two different scalar components, is investigated numerically with special efforts on the influences of the physical properties of two scalar components. We show that different scalar properties can affect the global transport behaviors. The concentration flux exhibits different exponents in their power-law scalings for different combinations of scalar components. The scaling exponents of heat flux, however, depend mainly on the ratio of the diffusivities of two scalars. If one uses the local parameters of the finger layer in the bulk, the behaviors are very similar to those found in the fully periodic simulations. The horizontal width of the fingers is consistent with the wavelength of the fast growing mode. For one case we observe evidences of the thermohaline staircase, namely, the typical width of the flow structures changes significantly in different layers within the flow domain. Keywords Double diffusive convection · Convection turbulence · Turbulent mixing
1 Introduction Double diffusive convection (DDC) refers to the buoyancydriven convection flow where the fluid density depends on two scalar components with very different molecular diffusivities. DDC occurs in many natural environments and engineering applications, including astrophysics [1,2], geoscience [3,4], and process engineering [5]. The most relevant terrestrial environment is the ocean since the density of seawater is determined by both temperature and salinity, and their diffusivities differ by two orders of magnitude. Indeed, DDC has been widely observed in oceans [6–9]. It is estimated that over 40% of the Earth ocean favors the occurrence of DDC [10]. DDC can greatly enhance the diapycnal mixing [7], and may even have influences on ocean climate [11]. Therefore, it has drawn a lot of research interests in the past [12,13]. A comprehensive review can be found in the recent book of Radko [14].
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Yantao Yang [email protected] SKLTCS and Department of Mechanics and Engineering Science, BIC-ESAT, College of Engineering, and Institute of Ocean Research, Peking University, Beijing 100871, China
A key point which distinguishes DDC from the normal Rayleigh–Bénard convection is that the two scalar components have very different diffusivities. The difference in diffusivity allows various new instability mechanisms to develop even when the overall density is stably stratified. In the upper part of the (sub-)tropic oceans, both temperature and salinity decrease with depth and fingering instability can occur [15]. Here the flow is driven by the unstable salinity gradient and stabilized by the temperature gradien
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