Large-scale effects on the decay of rotating helical and non-helical turbulence

Turbulent mixing in geophysics is often affected by the presence of rotation, which renders the flow anisotropic at large scales. Helicity (correlation between the velocity and its curl) has relevance for atmospheric and astrophysical flows and can also affect mixing. In this paper, decaying three-dimensional (3D) turbulence is studied via direct numerical simulations (DNS) for an isotropic non-rotating flow and for rotating flows with and without helicity. We analyze the cases of moderate Rossby number and large Reynolds number, focusing on the behavior of the energy spectrum at large scales and studying its effect on the time evolution of the energy and integral scales for E(k)~k4 initial conditions. In the non-rotating case, we observe the classical energy decay rate t−10/7 and a growth of the integral length proportional to t2/7 in agreement with the prediction obtained assuming conservation of the Loitsyanski integral. In the presence of rotation we observe a decoupling in the decay of the modes perpendicular to the rotation axis from the remaining 3D modes. These slow modes show a behavior similar to that found in two-dimensional (2D) turbulence, whereas the 3D modes decay as in the isotropic case. We phenomenologically explain the decay considering integral conserved quantities that depend on the large-scale anisotropic spectrum. The decoupling of modes is also observed for a flow with a net amount of helicity. In this case, the 3D modes decay as an isotropic fluid with a constant, constrained integral length and the 2D modes decay as a constrained rotating fluid with maximum helicity.