Causal Propagation of Heat and Thermohaline Instability in Quasi-static Phenomena

Abstract

Double diffusive convection is discussed in context of the simultaneity problem emerged from the thermal energy flux, where the temperature gradient (the cause) and the energy flux (the effect) appear at the same time. We used Cattaneo’s law, as a correction of the conventional Fourier’s law for thermal transport, in order to consider a delay time in the interaction, the so called relaxation time. For the sinking of a convective blob in a Newtonian fluid, Fourier’s equation describes a steady state flow, however the Cattaneo’s law predicts damped oscillations for times of the order of this relaxation time. Physical systems as the salt-finger phenomenon (for the Fourier regime), and the superfluid Helium II and pulsars micro-oscillations (for the Cattaneo regime) are studied through simulations of the temporal evolution of the speed of the convective blobs. Concluding that the dynamic of convective blobs in systems where the relaxation time is important presents quasi-static oscillations, even for degenerate matter. A further study about the complete description of the light curve of pulsars is suggested.