Turbulent cascade, bottleneck, and thermalized spectrum in hyperviscous flows
Rahul Agrawal, Alexandros Alexakis, Marc E. Brachet, Laurette S. Tuckerman
Abstract
High-resolution Direct Numerical Simulations of the Taylor-Green vortex using standard Navier-Stokes (NS) equations (order of the Laplacian $p=1$) and hyperviscosity ($p$ up to 100) show that evolution of the total energy and its dissipation are similar for the two simulations, but that the energy spectrum develops a more pronounced bottleneck. A link between this bottleneck and the thermalized (absolute equilibrium) state is demonstrated. The vortex tubes seen for the NS equations ($p=1$, above) are replaced by less elongated vortex ``blobs'' for the hyperviscous case ($p=10$, below).
Topics & Concepts
VortexHyperviscosityPhysicsDissipationTurbulenceEnergy spectrumSpectrum (functional analysis)Energy (signal processing)Steady state (chemistry)MechanicsClassical mechanicsVorticityStatistical physicsNoise (video)Laplace operatorField (mathematics)Computer simulationFluid Dynamics and Turbulent FlowsParticle Dynamics in Fluid FlowsCombustion and flame dynamics