Abstract
The movement of heat in a convecting system is typically described by the nondimensional Nusselt number, which involves an average over both space and time. In direct numerical simulations of turbulent flows, there is considerable variation in the contributions to the Nusselt number, both because of local spatial variations due to plumes and because of intermittency in time. We develop a statistical approach to more completely describe the structure of heat transfer, using an exit-distance extracted from Lagrangian tracer particles, which we call the Lagrangian heat structure. In a comparison between simulations of homogeneous turbulence driven by Boussinesq convection, the Lagrangian heat structure reveals significant non-Gaussian character, as well as a clear trend with Prandtl number and Rayleigh number. This has encouraging implications for simulations performed with the goal of understanding turbulent convection in natural settings such as Earth’s atmosphere and oceans, as well as planetary and stellar dynamos.
Highlights
Convection occurs in many natural settings, including the oceans, the atmosphere, and the interior of the Earth and the stars
To understand in better detail the transport of heat in convective turbulence and to supplement the information from the average Nusselt number, we define the Lagrangian heat structure. We develop this as an exit-distance statistic, similar in spirit to the finite-time Lyapunov exponent (FTLE) which is used to calculate Lagrangian coherent structures (LCS) [47]
After studying the intermittency of the Nusselt number in our simulations of homogeneous turbulent convection, we develop an exit-distance statistic, the Lagrangian heat structure, to quantify properties of heat transfer in a way that is less susceptible to noise and intermittency effects
Summary
Convection occurs in many natural settings, including the oceans, the atmosphere, and the interior of the Earth and the stars. The use of an exit-distance statistic has the advantage, documented in Lagrangian descriptions of turbulence [18], that it permits us to compare fluid particles that have transported the same amount in temperature, rather than particles that have diffused for the same length of time This removes contamination due to crossover from other temperature scales, a quality that has helped to clarify intermittent behavior in hydrodynamic turbulence (e.g., as discussed in [25]). Examination of this statistic provides higher-order information about the heat transfer from a different perspective, supplementing a straightforward global average like the Nusselt number.
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