Weak formulation and scaling properties of energy fluxes in three-dimensional numerical turbulent Rayleigh–Bénard convection

Abstract

We apply the weak formalism on the Boussinesq equations, to characterize scaling properties of the mean and the standard deviation of the potential, kinetic and viscous energy flux in very high resolution numerical simulations. The local Bolgiano-Oboukhov length L BO is investigated and it is found that its value may change of an order of magnitude through the domain, in agreement with previous results. We investigate the scale-by-scale averaged terms of the weak equations, which are a generalization of the Karman-Howarth-Monin and Yaglom equations. We have not found the classical Bolgiano-Oboukhov picture, but evidence of a mixture of Bolgiano-Oboukhov and Kolmogorov scalings. In particular, all the terms are compatible with a Bolgiano-Oboukhov local Hölder exponent for the temperature and a Kolmogorov 41 for the velocity. This behavior may be related to anisotropy and to the strong heterogeneity of the convective flow, reflected in the wide distribution of Bolgiano-Oboukhov local scales. The scale-by-scale analysis allows us also to compare the theoretical Bolgiano-Oboukhov length L BO computed from its definition with that empirically extracted through scalings obtained from weak analysis. The key result of the work is to show that the analysis of local weak formulation of the problem is powerful to characterize the fluctuation properties. †

Direct numerical simulation of bubble-induced turbulence

“…While energy spectra contain key information about the flow, they cannot be used to disentangle the different mechanisms leading to the observed scalings, and a scale-by-scale analysis can be particularly useful (Alexakis & Biferale 2018). For that purpose, we apply a coarse-graining approach (Duchon & Robert 2000;Eyink & Sreenivasan 2006b) linked to the filtering approach used in LES (Germano 1992), and recently applied to different turbulent configurations (Chen et al 2006b;Xiao et al 2009;Faranda et al 2018;Dubrulle 2019;Valori et al 2020). More specifically, we have applied this methodology to the velocity field, obtaining information about the energy flux and the dissipation.…”

Connecting boundary layer dynamics with extreme bulk dissipation events in Rayleigh-Bénard flow

“…Such a phase transition from Gaussian to intermittent derivative statistics has been investigated in more detail in isotropic turbulence [25,26,27,28], for Burgers turbulence [29], and for shear flows and thermal convection [30,20,31]. While this transition is sharp in isotropic box turbulence [28], the crossover of derivative statistics from the Gaussian to the intermittent regime is gradual and seems to be altered by increasingly intermittently appearing coherent structures which grow out of the boundary layers (BLs) near the walls, such as the rising and falling thermal plumes in convection [20,31,32]. Our goal here is to reveal the dynamical scenarios that are connected with the observed statistics as the larger magnitudes of the derivative moments of ∂u z /∂z are connected to rising and falling thermal plumes.…”

Heat-flux Fluctuations reveals regime transitions in Rayleigh-Bénard convection

“…Basilisk uses Finite-Volume numerical schemes, notably with Bell-Colella-Glaz advection scheme [3], and a pressure-correction scheme for the velocity-pressure coupling, with a global second-order precision. The code has been now comprehensively validated in turbulent flows, and most notably in Rayleigh-Bénard convection [6][7][8]48]. All simulations have been performed on a uniform Cartesian grid, and with a variable time-step that verifies the condition CFL < 0.5.…”