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Energy Spectrum for Buoyancy-Driven Turbulence

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Buoyancy-driven flows are often encountered in geophysics, astrophysics, atmospheric and solar physics, and engineering. In general, these flows come in two categories: stably stratified flows and Rayleigh-Bénard convection (RBC). Turbulent aspects of these flows are an active field of research. An important unsolved problem in this field is how to quantify the small-scale quantities, e.g., spectra and fluxes of kinetic energy (KE) and potential energy (PE) of these flows. Using direct numerical simulations performed at high resolution, we demonstrate that the stably stratified turbulence at moderate stratification exhibits Bolgiano-Obukhov scaling, due to the conversion of kinetic energy to potential energy via buoyancy. We show that the KE flux decreases with the wavenumber (k) which yield k and k{-7/5} scaling for KE and PE spectra respectively. For RBC , we performed simulation at grid resolution 4096^3 on a cubical box and have shown a delicate balance of dissipation and energy supply rate by buoyancy. This balance leads to a constant KE flux and rules out the Bolgiano-Obukhov scaling, and we observe Kolmogorov’s spectrum [1-3]. References: [1] Kumar, Chatterjee, and Verma, Phys. Rev. E, 90, 023016 (2014). [2] Kumar and Verma, Phys. Rev. E, 91, 043014 (2015). [3] Verma, Kumar, and Pandey, New J. Phys., 19, 025012 (2017).

This talk is part of the Fluid Mechanics (CUED) series.

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