Heat vortices and the vorticity triplet in kinetic phonon transport: a fluid-dynamical perspective

Abstract

From a novel fluid-dynamical perspective, the present study investigates the heat-current vortices and heat vorticity in heat conduction process of solid materials. The heat vorticity $\bmω$, defined as the curl of the heat-flux field, is decomposed into the orbital-rotation $\bm{R}$ and spin $\bm{S}$, which collectively constitute the heat-vorticity triplet $(\bm{R},\bm{S},\bmω)$, extending beyond the existing single-vorticity research paradigm. As an illustrative example, kinetic phonon transport in a 2D porous solid structure is examined based on the numerical solutions of the Peierls-Boltzmann equation under the Callway dual-relaxation-time approximation. The physical characteristics of heat vortices and the vorticity triplet patterns are analyzed across different kinetic regimes in the phase diagram of the normal (N) and resistive (R) scattering processes.... In the hydrodynamic limit, the boundary generation mechanism of heat vorticity is further elucidated based on the Guyer-Krumhansl (G-K) equation generated from the truncated Chapman-Enskog (C-E) expansion. The boundary heat vorticity flux (BHVF) is proposed as a new concept for describing the local rate at which heat vorticity is generated at the boundary of a solid material. The general expression for the BHVF is rigorously derived for phonon hydrodynamics, and for the 2D steady hydrodynamic phonon transport case, we find that the BHVF is solely attributed to the tangential component of the net heat flux deviating from the classical Fourier heat flux. Furthermore, we show that the total vorticity contained in a control volume arises from the spatiotemporal accumulation of the BHVF, weighted by the memory kernel arising from the R scattering. The proposed theory and findings herein could be valuable for understanding the diverse vortical-flow phenomena in condensed matter systems.