  Density gradients aligned at an angle to pressure gradients result in
baroclinic torque in fluid flows, generating vorticity. In this work, we study
the vorticity generated by the baroclinic torque exerted by the interaction of
pressure jumps across random two-dimensional shock waves with density
gradients. A field of random two-dimensional shock waves has acoustic spectral
energy scaling as {\epsilon}^{2/3}{\ell}^{-1/3}k^{-2} where k is the
wavenumber, {\epsilon} is the energy dissipation, and \ell is the integral
length scale of the field. Since the acoustic energy is broadband, pressure and
velocity gradients exist in a wide range of length scales. We study the
interaction of these broadband gradients with isobaric thermal gradients
localized at a length scale in the spectral space. We show that the method of
generating shock waves or injection of wave energy in the system governs the
baroclinic interactions. For stochastically forced shock waves, baroclinic
termsare negligible. Broadband vorticity with energy at least two orders of
magnitude smaller is generated due to continuous variation in curvature of
shock waves caused by stochastic forcing. On the other hand, shock waves
maintained by energy rescaling result in the generation of coherent vorticity.
We also discuss the relative magnitude of the baroclinic torque generated due
to total density gradients compared to the one generated due to non-isentropic
density gradients within the shock waves interacting with the pressure
gradients.
