λ-Navier-Stokes turbulence

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 [Formula: see text]. In this work, we perform numerical simulations at varying λ in the forward energy cascade range and at changing the Reynolds number [Formula: see text]. We show that for a fixed injection rate, as [Formula: see text], the kinetic energy diverges with a scaling law [Formula: see text]. 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 [Formula: see text] is approached while keeping their difference fixed and equal to the injection rate. As a result, very close to [Formula: see text] 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, we show that intermittency as [Formula: see text] is approached is reduced. The possibility of obtaining a statistical description of regular Navier-Stokes turbulence as an expansion around this newly found critical point is discussed. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.