Burgers' turbulence with self-consistently evolved pressure

The Burgers' model of compressible fluid dynamics in one dimension is exten ded to include the effects of pressure back-reaction The system consists of two coupled equations: Burgers' equation with a pressure gradient (essenti ally the one-dimensional;Navier-Stokes equation) and an advection-diffusion equation for the pressure held. It presents a minimal model of both adiaba tic gas dynamics and compressible magnetohydrodynamics. From the magnetic p erspective, it is the simplest possible system which allows for "Alfvenizat ion," i.e., energy transfer between the fluid and magnetic field excitation s. For the special case of equal fluid viscosity and (magnetic) diffusivity , the system is completely integrable, reducing to two decoupled Burgers' e quations in the characteristic variables v+/-v(sound) (v+/-v(Alfven)) For a rbitrary diffusivities, renormalized perturbation theory is used to calcula te the effective transport coefficients for forced "Burgerlence." It is sho wn that energy equidissipation, not equipartition, is fundamental to the tu rbulent state. Both energy and dissipation are localized to shocklike struc tures, in which wave steepening is inhibited by small-scale forcing and by pressure back reaction. The spectral forms predicted by theory are confirme d by numerical simulations.