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By DNS of Navier-Stokes turbulence, Goto-Saito-Kawahara (2017) showed thatturbulence consists of a self-similar hierarchy of anti-parallel pairs ofvortex tubes, in particular, stretching in larger-scale strain fields createssmaller-scale vortices. Inspired by their numerical result, we examine theGoto-Saito-Kawahara type of vortex-tubes behavior using the 3D incompressibleEuler equations, and show that such behavior induces energy cascade in theabsence of nonlinear scale-interaction. From this energy cascade, we prove amodified version of the zeroth-law. In the Appendix, we derive Kolmogorov's$-5/3$-law from the GSK point of view.

A remark on the zeroth law and instantaneous vortex stretching on the incompressible 3D Euler equations