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In three dimensional turbulence there is on average a cascade of kineticenergy from the largest to the smallest scales of the flow. While the dominantidea is that the cascade occurs through the physical process of vortexstretching, evidence for this is debated. In the framework of theKarman-Howarth equation for the two point turbulent kinetic energy, we derive anew result for the average flux of kinetic energy between two points in theflow that reveals the role of vortex stretching. However, the result shows thatvortex stretching is in fact not the main contributor to the average energycascade; the main contributor is the self-amplification of the strain-ratefield. We emphasize the need to correctly distinguish and not conflate theroles of vortex stretching and strain-self amplification in order to correctlyunderstand the physics of the cascade, and also resolve a paradox regarding thediffering role of vortex stretching on the mechanisms of the energy cascade andenergy dissipation rate. Direct numerical simulations are used to confirm theresults, as well as provide further results and insights on vortex stretchingand strain-self amplification at different scales in the flow. Interestingly,the results imply that while vortex stretching plays a sub-leading role in theaverage cascade, it may play a leading order role during large fluctuations ofthe energy cascade about its average behavior.

Is vortex stretching the main cause of the turbulent energy cascade?