Special three-dimensional helical turbulence produced by two-dimensional turbulence

Based on an exact solution to incompressible Navier–Stokes equations, a special three-dimensional flow is theoretically constructed with an arbitrarily given two-dimensional flow with or without rotation and forcing. In particular, a corresponding three-dimensional helical turbulence can be produced by an arbitrary two-dimensional turbulence. This helical turbulence is anisotropic with a solely inverse energy cascade, which is described by a special energy spectrum that is generally distinct from the classical Kolmogorov '−5/3' law. A few more detailed properties of the helical turbulence are derived, and their implications for magnetohydrodynamic turbulence and turbulence modelling in general are discussed.