Journal of Fluid Mechanics Webinar Series: Chris Howland, Netherlands and Shingo Motoki, Japan

Speaker: Chris Howland, University of Twente, Netherlands

Date/Time: Friday 28th May 2021 4:00pm BST/11am EST

Title: Quantifying mixing in simulations of stratified flows

Abstract: Turbulent mixing exerts a significant influence on many physical processes in the ocean. In a stably stratified Boussinesq fluid, this irreversible mixing describes the conversion of available potential energy (APE) to background potential energy (BPE). In some settings the APE framework is difficult to apply and approximate measures are used to estimate irreversible mixing. For example, numerical simulations of stratified turbulence often use triply periodic domains to increase computational efficiency. In this set-up, however, BPE is not uniquely defined and the method of Winters et al. (J. Fluid Mech., vol. 289, 1995, pp. 115–128) cannot be directly applied to calculate the APE. We propose a new technique to calculate APE in periodic domains with a mean stratification. By defining a control volume bounded by surfaces of constant buoyancy, we can construct an appropriate background buoyancy profile b∗(z,t) and accurately quantify diapycnal mixing in such systems. This technique also permits the accurate calculation of a finite-amplitude local APE density in periodic domains. The evolution of APE is analysed in various turbulent stratified flow simulations. We show that the mean dissipation rate of buoyancy variance χ provides a good approximation to the mean diapycnal mixing rate, even in flows with significant variations in local stratification. We discuss how best to interpret these results in the context of quantifying diapycnal diffusivity in real oceanographic flows.

Enjoy free access to papers in support of Howland' webinar, courtesy of the Journal of Fluid Mechanics.

Speaker: Shingo Motoki, Osaka University, Japan

Date/Time: Friday 28th May 2021 4:30pm BST/11:30am EST

Title: Multi-scale steady solutions representing classical and ultimate scaling in thermal convection

Abstract: Rayleigh–Bénard convection is one of the most canonical flows widely observed in nature and engineering applications. The effect of buoyancy on a flow is characterised by the Rayleigh number Ra, and the flow becomes turbulent eventually as Ra increases. One of the primary interests in convective turbulence is the scaling law of the Nusselt number Nu (dimensionless vertical heat flux) with Ra. A one-third power law for Nu with Ra, referred to as the 'classical' scaling, has been reported in many experiments and numerical simulations. On the other hand, a one-half power law, referred to as the 'ultimate' scaling, has not been observed yet in conventional Rayleigh–Bénard convection (buoyancy-driven convection between horizontal impermeable walls with a constant temperature difference). In this talk, I will first discuss a multi-scale steady solution in the conventional Rayleigh–Bénard convection. It is a three-dimensional steady solution to the Boussinesq equations, found using a homotopy from the wall-to-wall optimal transport solution (Motoki et al. 2018 J. Fluid Mech., 851, R4). The exact coherent thermal convection exhibits the classical scaling and reproduces structural and statistical properties of convective turbulence. Next, I will draw attention to thermal convection between permeable walls. The permeable wall is a simple model mimicking a Darcy-type porous wall (Jiménez et al. 2001 J. Fluid Mech. 442, 89-117). The wall permeability leads to the ultimate scaling, meaning that a wall heat flux being independent of thermal conductivity, although the heat transfer on the wall is dominated by thermal conduction. Finally, I will discuss the physical mechanisms of classical and ultimate scaling.

Read Motoki's recent papers here and here, both published in the JFM Special Volume in celebration of the George Batchelor centenary.