L. Biferale

We investigate numerically the model proposed in Sahoo et al. (2017 Phys. Rev. Lett. 118 , 164501) where a parameter λ is introduced in the Navier–Stokes equations such that the weight of homochiral to heterochiral interactions is varied while preserving all original scaling symmetries and inviscid invariants. Decreasing the value of λ leads to a change in the direction of the energy cascade at a critical value λ c ∼ 0.3 . In this work, we perform numerical simulations at varying λ in the forward energy cascade range and at changing the Reynolds number R e . We show that for a fixed injection rate, as λ → λ c , the kinetic energy diverges with a scaling law E ∝ ( λ − λ c ) − 2 / 3 . The energy spectrum is shown to display a larger bottleneck as λ is decreased. The forward heterochiral flux and the inverse homochiral flux both increase in amplitude as λ c is approached while keeping their difference fixed and equal to the injection rate. As a result, very close to λ c a stationary state is reached where the two opposite fluxes are of much higher amplitude than the mean flux and large fluctuations are observed. Furthermore,