Multiscale heat transport with inertia and thermal vortices

Abstract In this paper, we present a Hamiltonian and thermodynamic theory of heat transport on various levels description. Transport is formulated within kinetic polarized phonons, unpolarized hydrodynamics phonons. These description are linked by Poisson reductions, where no linearizations made. Consequently, obtain new phonon that contains convective terms dependent vorticity the flux, which missing in standard theories hydrodynamics. Within zero-order Chapman-Enskog reduction, resulting hydrodynamic equations hyperbolic Galilean invariant, while first expansion gives additional viscous-like terms. The vorticity-dependent violate alignment flux with temperature gradient even stationary state, expressed Fourier-Crocco equation. Those also cause plays similar role as pressure aerodynamics, illustrated numerical simulations flow past cylinder. particular, show lead to colder spot just behind cylinder, for high-enough Reynolds numbers they von Kármán vortex street.