Triadic resonances in numerical simulations of a precessing cylinder

In the framework of the project DRESDYN (DREsden Sodium facility for DYNamo and thermohydraulic studies) a next generation dynamo experiment is under construction at the Helmholtz-Zentrum Dresden-Rossendorf. In this experiment a fluid flow of liquid sodium in a cylindrical container, solely driven by precession, is considered as a possible source for magnetic field generation.

Precession has long been discussed as a complementary energy source for driving the geodynamo, and dynamo action generated by precession driven flows has been found in various numerical simulations in a sphere, ellipsoid, cube and cylinder. In the current study we perform hydrodynamic simulations of the three-dimensional non-linear Navier-Stokes equation in cylindrical geometry including weakly precessional forcing. The main focus is put on the development of the non-axisymmetric time-dependent instabilities that could be responsible for dynamo action like triadic resonances.

Our simulations reveal clear triads at aspect ratios and frequencies close to predictions from the linear inviscid theory with an amplitude below the forced m=1 mode so that most of the flow energy remains in the fundamental forced mode. Next step will be kinematic simulations in order to test the ability of the triades to provide for dynamo action.