Variable energy flux in turbulence


Verma, Mahendra K.

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In three-dimensional hydrodynamic turbulence forced at large length scales, a constant energy flux Πu flows from large scales to intermediate scales, and then to small scales. It is well known that for multiscale energy injection and dissipation, the energy flux Πu varies with scales. In this review we describe this principle and show how this general framework is useful for describing a variety of turbulent phenomena. Compared to Kolmogorov's spectrum, the energy spectrum steepens in turbulence involving quasi-static magnetofluid, Ekman friction, stable stratification, magnetohydrodynamics, and solution with dilute polymer. However, in turbulent thermal convection, in unstably stratified turbulence such as Rayleigh–Taylor turbulence, and in shear turbulence, the energy spectrum has an opposite behaviour due to an increase of energy flux with wavenumber. In addition, we briefly describe the role of variable energy flux in quantum turbulence, in binary-fluid turbulence including time-dependent Landau–Ginzburg and Cahn–Hillianrd equations, and in Euler turbulence. We also discuss energy transfers in anisotropic turbulence.

Verma, M. K. (2021). Variable energy flux in turbulence. Journal of Physics A: Mathematical and Theoretical, 55(1), 013002. doi:10.1088/1751-8121/ac354e

For writing this review I drew heavily from the discussions and idea exchanges I had with my collaborators, namely, Franck Plunian, Rodion Stepanov, Ravi Samtaney, Daniele Carati, Stephan Fauve, Jai Sukhatme, Sanjay Puri, K R Sreenivasan, Alexandros Alexakis, Gaurav Dar, Vinayak Eswaran, and Bernard Knaepen. I am very grateful to them for the same. In addition, I received critical inputs and ideas from many past and present doctoral and master students—Abhishek Kumar, Shashwat Bhattacharya, Roshan Samuel, Mohammad Anas, Shadab Alam, Soumyadeep Chatterjee, Pankaj Mishra, Satyajit Barman, Manohar Sharma, Shubhadeep Sadhukhan, Olivier Debliquy, Bogdan Teaca, Thomas Lessinness, Valerii Titov, Ambrish Pandey, Sandeep Reddy, Anando Chatterjee, Arvind Ayyer, and V Avinash. I also thank J K Bhattacharjee, Peter Frick, Annick Pouquet, Arnab Rai Choudhuri, Avinash Khare, P K Yeung, Diego Donzis, Xavier Albets, Itamar Procaccia, Maurice Rossi, Andrei Teimurazov, Andrei Sukhanovskii, Marc Brachet, Gregory Eyink, Luca Moriconi, Sagar Chakraborty, Supratik Banerjee, Sonakshi Sachdev, Akanksha Gupta, and Luca Biferale for useful discussions. I also thank the anonymous referees and an Editorial Board Member for useful suggestions. I gratefully acknowledge the support of Indo-French projects 4904-1 and 6104-1 from CEFIPRA, IFCAM project MA/IFCAM/19/90, Indo-Russian project INT/RUS/RSF/P-03 from Department of Science and Technology India, and SERB project SERB/F/3279/2013-14 that made the collaborative work and idea exchanges possible. Some of the results presented in the review have been generated using SHAHEEN II of KAUST (project K1052) and HPC2013 of IIT Kanpur.

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