Effects of the Mach number on the evolution of vortex-surface fields in compressible Taylor--Green flows

TL;DR

This study examines how Mach number influences vortex-surface field evolution in compressible Taylor-Green flows, revealing stage-dependent effects including vortex contraction, reconnection, and energy dissipation.

Contribution

It extends vortex-surface field analysis from incompressible to compressible flows and introduces a mass-based renormalization method for better characterization.

Findings

Higher Mach numbers lead to earlier vortex reconnection.

Shocklets induce vortex surface contraction and distortion.

Increased Mach number accelerates energy dissipation and suppresses vortex twisting.

Abstract

We investigate the evolution of vortex-surface fields (VSFs) in compressible Taylor--Green flows at Mach numbers ($Ma$) ranging from 0.5 to 2.0 using direct numerical simulation. The formulation of VSFs in incompressible flows is extended to compressible flows, and a mass-based renormalization of VSFs is used to facilitate characterizing the evolution of a particular vortex surface. The effects of the Mach number on the VSF evolution are different in three stages. In the early stage, the jumps of the compressive velocity component near shocklets generate sinks to contract surrounding vortex surfaces, which shrink vortex volume and distort vortex surfaces. The subsequent reconnection of vortex surfaces, quantified by the minimal distance between approaching vortex surfaces and the exchange of vorticity fluxes, occurs earlier and has a higher reconnection degree for larger $Ma$ owing to the dilatational dissipation and shocklet-induced reconnection of vortex lines. In the late stage, the positive dissipation rate and negative pressure work accelerate the loss of kinetic energy and suppress vortex twisting with increasing $Ma$.