Abstract Details
| Name: Abhishek Kumar Affiliation: Indian Institute of Technology Kanpur Conference ID: ASI2017_1166 Title : Energy spectrum for buoyancy-driven turbulence Authors and Co-Authors : Abhishek Kumar and Mahendra K. Verma, Department of Physics, IIT Kanpur Abstract Type : Oral Abstract Category : Sun and the Solar System Abstract : Gravity or buoyancy plays an important role in astrophysical flows. The flow is destabilized when heavier or colder fluid is on top of a lighter or hotter fluid, often seen in thermal convection. Convection plays a significant role in interiors of many planets and stars, and it is one of the mechanisms for the generation of a magnetic field. Conversely, the flow is stabilized when a lighter fluid sits on top of a heavier fluid, for example, in Earth’s atmosphere. An important unsolved problem in this field is how to quantify the spectra and fluxes of kinetic energy and potential energy, respectively, of buoyancy-driven flows. According to Kolmogorov, for hydrodynamic turbulence, a constant energy flux flows across the intermediate length scales, called the inertial range, of the system. However, for stably stratified flows, Bolgiano and Obukhov conjectured that buoyancy will convert the kinetic energy (KE) to the potential energy (PE) at all scales, thus making the kinetic energy flux in the inertial range a decreasing function of wavenumber. Further, Procaccia and Zeitak and L’vov and Falkovich proposed that the Bolgiano and Obukhov scaling of stably stratified flows would also be applicable to the turbulent convection. Using high-resolution direct numerical simulations (DNS) and arguments based on the kinetic energy flux [1,2], we demonstrate that the Rayleigh-Benard convection, an idealized model of thermal convection, follows Kolmogorov’s spectrum. We show that the kinetic energy flux increases briefly, and then becomes constant due to a delicate balance of dissipation and energy supply rate. Due to the constancy of energy flux, the turbulent RBC exhibits Kolmogorov’s spectrum rather than Bolgiano and Obukhov’s spectrum. We performed the aforementioned simulation for the extreme Rayleigh number approximately 10^{11} in a closed cubical box of $4096^3$ grid [3]. We also performed DNS for the stably stratified turbulence at moderate stratification and exhibited Bolgiano-Obukhov spectrum with k^{-4/5} scaling for the KE flux. Further, we constructed a unified shell-model for buoyancy-driven turbulence, which yields similar results as obtained from DNS, albeit at extreme parameters [4]. References: [1] A. Kumar, A. G. Chatterjee, and M. K. Verma. Energy spectrum of buoyancy- driven turbulence. Phys. Rev. E, 90:023016, 2014. [2] M. K. Verma, A. Kumar, and A. G. Chatterjee. Energy spectrum and flux of buoyancy-driven turbulence. Physics Focus, AAPPS Bulletin, 25, 2015. [3] M. K. Verma, A. Kumar, and A. Pandey, Phenomenology of buoyancy-driven turbulence: recent results, Under review in New Journal of Physics, (2016). [4] A. Kumar and M. K. Verma. Shell model for buoyancy-driven turbulence. Phys. Rev. E, 91:043014, 2015. |