On the Oscillation in Model Z

Summary

The paper deals with nonlinear decaying oscillations appearing in model Z. A method, based on the balance equations, is proposed which allows us to estimate whether or not the time behaviour of the solutions is correct. For this purpose the balance equation of energy and a new variable J = B_θ/s are used. The equation for J has conservative form. The oscillatory solution is characterized by two time scales. We speculate that the small time scale (the period of the oscillations) is connected to diffusion of azimuthal field through the boundary layer while the large time scale (the decay time of the oscillations) is linked to the diffusion of the meridional field (created in the boundary layer) into the volume of the core. The large meridional convection at the core-mantle boundary (CMB) plays a crucial role in this process.

INTRODUCTION

The solution of model Z has been found in many cases with account taken of both viscous and electromagnetic core-mantle coupling (Braginsky 1978; Braginsky & Roberts 1987; Braginsky 1988; Braginsky 1989; Cupal & Hejda 1989). Apart from Braginsky (1989), the time evolution of the solution was used simply as an aid to obtain the steady-state solution. Cupal & Hejda (1992) found numerically a transient solution of model Z having the form of a decaying oscillation. The accuracy of such solutions depends on the numerical method used, on the density of space and time discretization, and for that matter, on the character of the solution itself. An important question is which characteristics of the time behaviour of the solution reflect the real (physical) behaviour of the system and which follow from the limitations of the numerical method.