  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 $Ma$.
