Lyapunov exponents and information dimension of the mass distribution in turbulent compressible flows

Turbulent density fluctuations in isothermal highly compressible turbulent flows are highly clumped and can be quantified by the scaling properties of powers of the mass distribution. This Eulerian quantity can be related to Lagrangian properties of the system given by the Lyapunov exponents of tracer particles advected with the flow. Using highly resolved numerical simulations, we show that the Kaplan-Yorke conjecture holds within numerical uncertainties.