Srikanth Toppaladoddi

Roughness as a Route to the Ultimate Regime of Thermal Convection

We use highly resolved numerical simulations to study turbulent Rayleigh-Bénard convection in a cell with sinusoidally rough upper and lower surfaces in two dimensions for Pr=1 and Ra=[4×10^{6},3×10^{9}]. By varying the wavelength λ at a fixed amplitude, we find an optimal wavelength λ_{opt} for which the Nusselt-Rayleigh scaling relation is (Nu-1∝Ra^{0.483}), maximizing the heat flux. This is consistent with the upper bound of Goluskin and Doering [J. Fluid Mech. 804, 370 (2016)JFLSA70022-112010.1017/jfm.2016.528] who prove that Nu can grow no faster than O(Ra^{1/2}) as Ra→∞, and thus with the concept that roughness facilitates the attainment of the so-called ultimate regime. Our data nearly achieve the largest growth rate permitted by the bound. When λ≪λ_{opt} and λ≫λ_{opt}, the planar case is recovered, demonstrating how controlling the wall geometry manipulates the interaction between the boundary layers and the core flow. Finally, for each Ra, we choose the maximum Nu among all λ, thus optimizing over all λ, to find Nu_{opt}-1=0.01×Ra^{0.444}.

Tailoring boundary geometry to optimize heat transport in turbulent convection

By tailoring the geometry of the upper boundary in turbulent Rayleigh-Benard convection we manipulate the boundary layer-interior flow interaction, and examine the heat transport using the lattice ...

Theory of the Sea Ice Thickness Distribution.

We use concepts from statistical physics to transform the original evolution equation for the sea ice thickness distribution g(h) from Thorndike et al. into a Fokker-Planck-like conservation law. The steady solution is g(h)=N(q)h(q)e(-h/H), where q and H are expressible in terms of moments over the transition probabilities between thickness categories. The solution exhibits the functional form used in observational fits and shows that for h≪1, g(h) is controlled by both thermodynamics and mechanics, whereas for h≫1 only mechanics controls g(h). Finally, we derive the underlying Langevin equation governing the dynamics of the ice thickness h, from which we predict the observed g(h). The genericity of our approach provides a framework for studying the geophysical-scale structure of the ice pack using methods of broad relevance in statistical mechanics.

Statistical Mechanics and the Climatology of the Arctic Sea Ice Thickness Distribution

We study the seasonal changes in the thickness distribution of Arctic sea ice, g(h), under climate forcing. Our analytical and numerical approach is based on a Fokker–Planck equation for g(h) (Toppaladoddi and Wettlaufer in Phys Rev Lett 115(14):148501, 2015), in which the thermodynamic growth rates are determined using observed climatology. In particular, the Fokker–Planck equation is coupled to the observationally consistent thermodynamic model of Eisenman and Wettlaufer (Proc Natl Acad Sci USA 106:28–32, 2009). We find that due to the combined effects of thermodynamics and mechanics, g(h) spreads during winter and contracts during summer. This behavior is in agreement with recent satellite observations from CryoSat-2 (Kwok and Cunningham in Philos Trans R Soc A 373(2045):20140157, 2015). Because g(h) is a probability density function, we quantify all of the key moments (e.g., mean thickness, fraction of thin/thick ice, mean albedo, relaxation time scales) as greenhouse-gas radiative forcing,

Turbulent Transport Processes at Rough Surfaces with Geophysical Applications

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Turbulent transport at rough surfaces

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Penetrative convection at high Rayleigh numbers

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