Phenomenology of two-dimensional stably stratified turbulence under large-scale forcing


Kumar, Abhishek
Verma, Mahendra K.
Sukhatme, Jai

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In this paper, we characterise the scaling of energy spectra, and the interscale transfer of energy and enstrophy, for strongly, moderately and weakly stably stratified two-dimensional (2D) turbulence, restricted in a vertical plane, under large-scale random forcing. In the strongly stratified case, a large-scale vertically sheared horizontal flow (VSHF) coexists with small scale turbulence. The VSHF consists of internal gravity waves and the turbulent flow has a kinetic energy (KE) spectrum that follows an approximate k−3 scaling with zero KE flux and a robust positive enstrophy flux. The spectrum of the turbulent potential energy (PE) also approximately follows a k−3 power-law and its flux is directed to small scales. For moderate stratification, there is no VSHF and the KE of the turbulent flow exhibits Bolgiano–Obukhov scaling that transitions from a shallow k−11/5 form at large scales, to a steeper approximate k−3 scaling at small scales. The entire range of scales shows a strong forward enstrophy flux, and interestingly, large (small) scales show an inverse (forward) KE flux. The PE flux in this regime is directed to small scales, and the PE spectrum is characterised by an approximate k−1.64 scaling. Finally, for weak stratification, KE is transferred upscale and its spectrum closely follows a k−2.5 scaling, while PE exhibits a forward transfer and its spectrum shows an approximate k−1.6 power-law. For all stratification strengths, the total energy always flows from large to small scales and almost all the spectral indicies are well explained by accounting for the scale-dependent nature of the corresponding flux.

Kumar A, Verma MK, Sukhatme J (2017) Phenomenology of two-dimensional stably stratified turbulence under large-scale forcing. Journal of Turbulence 18: 219–239. Available:

We thank Anirban Guha for useful discussions. Our numerical simulations were performed on Chaos clusters of IIT Kanpur and ‘Shaheen II’ at KAUST supercomputing laboratory, Saudi Arabia. This work was supported by a research grant (Grant No. SERB/F/3279) from Science and Engineering Research Board, India, computational project k1052 from KAUST, and the grant PLANEX/PHY/2015239 from Indian Space Research Organisation (ISRO), India. Jai Sukhatme would also like to acknowledge support fromthe IISc ISROSpace Technology Cell project ISTC0352 and the Ministry of Earth Sciences Monsoon Mission grant IITM/MAS/DSG/0001. Science and Engineering Research Board, India [grant number SERB/F/3279]; Computational project from King Abdullah University of Science and Technology [project number k1052]; Indian Space Research Organisation (ISRO), India [grant number PLANEX/PHY/2015239]; IISc ISRO Space Technology Cell [project number ISTC0352]; Ministry of Earth Sciences Monsoon Mission [grant number IITM/MAS/DSG/0001].

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