Anisotropy in rapidly rotating helical flows
Date and time:
Thursday, November 10, 2011 - 4:00pm
Rapidly rotating fluid flow is characterized by the emergence of columnar structures that are representative of quasi-two dimensional behavior of the flow. It is known that when energy is injected into the fluid at scale lf , it cascades towards both smaller and larger scales. Besides, arguably for the first time, we also observe signature of an inverse helicity transfer to large scales. We are interested in analyzing the flow at larger scales at a fixed Rossby number, Rof ≈ 0.03. We argue that the nature of the large-scale energy spectrum may show a departure from traditional Kolmogorov theory depending on the type of external forcing, i.e. helical vs non-helical type. We show that in the case of helical forcing, the linear time scales associated with global rotation (inertial waves) and shear are comparable and dominate the initial dynamics of the flow during it’s transition towards the slow manifold; in the slow manifold the dominant time scale is the shear time scale τsh which is sustained by a weak reverse helicity transfer to large scales. We then present a dimensional argument to further support evidence, from numerical simulations, of a k-1 energy spectrum based on the respective linear time scales that drives the flow both during it’s transition to the slow manifold and in the slow manifold. In case of non-helical forcing, the time scale that defines the flow at large scales is the nonlinear time scale τnl thereby resulting in a conventional Kolmogorov energy spectrum, k-5⁄3 . The results are based on a Large Eddy Simulation that includes the effect of helicity on the transport coefficients while modelling the small scales and explicitly solves for the large scales unlike hyperviscosity models that truncate the very small scales.
In this talk, I will begin by presenting a brief review of wave turbulence theory that is the current state of the art in understanding the emergence of anisotropic structures in the context of rotating flows. However, this theory cannot explain the inverse cascade phenomenon owing to a singularity in the solution of wave turbulence equation in the slow manifold and the two dimensional manifold and hence provides scope for further research in this direction. In addition, shear in turbulent flows is known to be present in small scales. I will formally derive the conservation of helicity flux in the slow manifold from the helicity evolution equation and argue that shear is transported from the small scales to the large scales by a weak helicity transfer to large scales, thereby influencing the overall dynamics of the flow at large scales.