Minimum enstrophy states and bifurcations in 2D Euler flows around a central obstacle

Abstract

International audienceRod bundle flows inside nuclear cores of pressurized water reactors (PWR) are mainly aligned with the direction parallel to the rods. In the planes orthonormal to this direction, some secondary flows occur and play an important role in the thermal mixing characteristics. These flows exhibit spontaneous reorganisations that seem comparable to the phase transitions observed between meta-stable states of the Northern Hemisphere atmosphere (Corvellec [5]). In order to put forward an explanation of this phenomenon, equilibrium states of the 2D Euler equations are computed from a variational problem consisting in minimizing the total enstrophy function (related to entropy) while conserving kinetic energy and circulation inside the domain. This method can be related to MRS theory ([7, 9]). We obtain the most probable equilibrium states depending on control parameters and geometry here restricted to the representative configuration of a ring-shaped domain. We have solved numerically this problem and obtained the different caloric curves and phase diagrams. A bifurcation between 1-eddy solution (’zonal’) and 2-eddy solution (’blocked’) has been identified confirming the existence of meta-stable states in flows containing a central obstacle