Understanding the role of wave-like turbulent structures in tornadic supercells through an electromagnetic-hydrodynamic analogy

Despite enormous strides in our understanding and identification of key characteristics that distinguish tornadic from non-tornadic supercell thunderstorms, there remain questions regarding the evolution of the low and mid-level vorticity fields that lead to tornadogenesis. The downdrafts of supercell thunderstorms in particular have been the focus of much study in the search for mechanisms which generate and redistribute vorticity near the surface. This process seems intimately linked to the detailed structures of turbulence and the organization of these structures inside a mesocyclone into a tornadic vortex. Through the analogy between Navier-Stokes hydrodynamic theory and Maxwell's equations for electromagnetic fields, the theory of turbulence can be reformulated from a functional relationship between statistical moments of the velocity field to a physical theory of wave turbulence. In this theoretical framework, the vorticity and Lamb vector fields continuously interweave and respond in an electromagnetic wave-like fashion to quantities which can be called turbulent charge sources and the currents of these charge sources. Through numerical simulation of super-cell thunderstorms using the University of Wisconsin Non-Hydrostatic Modeling System these turbulent charges and their currents are tracked and used as input to obtain wave-like eigenmode turbulent solutions. These vorticity-Lamb vector waves are not the unstable modes of some laminar mean flow, but rather an inherent feature of high Reynolds number flows. These represent turbulent structures which do not necessarily transfer energy downscale but rather serve to induce, maintain, or even strengthen a tornadic vortex (and its associated vorticity gradient) through convergence of this turbulent wave activity.