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Models for dual cascades in power-spectra for fully three-dimensional (3D) incompressible turbulence are summarized. The basic equations for 3D incompressible flows are expanded in terms of the eigenfunctions for the curl-operator. The possibilities for forward and inverse cascades in 3D fluid turbulence are illustrated and quantified. Conditions for dual- and forward-energy cascades in wavenumber space are presented. The forward or unidirectional cascade is found to dominate, a result consistent with the basic physical arguments formulated by vortex-line stretching. For inhomogeneous conditions, the inverse cascade can be dominating in a transient time inetrval.
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This page is a summary of: On the Possibility of a Dual Cascade in Three-Dimensional Incompressible Turbulent Flows, Physics, January 2026, MDPI AG,
DOI: 10.3390/physics8010013.
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