Toward understanding the multiscale spatial spectrum of solar convection

Getling Alexander V., a.getling@mail.ru, Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow, 119991, Russia
Kolmychkov Vyacheslav V., ksv@keldysh.ru, Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047, Russia
Mazhorova Olga S., olgamazhor@mail.ru, Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047 Russia
Shcheritsa Olga V., shchery@keldysh.ru, Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047 Russia

Abstract
The structure of the convective-velocity field should have a profound effect on the operation of the solar and stellar MHD dynamos and on the structure of the magnetic fields produced. No convincing explanation has yet been given to the fact that the sizes of the convection cells observed in the near-photospheric layers of the Sun form a discrete spectrum. Convectively stable sublayers should not be present in the convection zone, so that confining the motions to height ranges much narrower than the whole convection-zone thickness can hardly be attributed to factors other than some specific features of the globally unstable stratification. This appears to be a nontrivial effect, especially if convection cells filling larger thickness intervals (up to the whole layer depth) are also present. We present an extensive study of the effects of specially chosen stratifications of a horizontal layer on the spectrum of convection by means of numerical simulations based on time-dependent equations of motion and energy. We consider a very simple two-dimensional, incompressible model and solve the equations for a rectangular domain with an aspect ratio of 5 x 3.14 = 15.7. The stratification can be controlled by appropriately specifying the temperature dependence of thermal diffusivity. In most cases, we assume a power-law form of this dependence so as to obtain a desired conductive temperature profile. The cases are considered in which the conductive temperature gradient is especially large in a narrow subsurface layer. Fairly wide ranges of Rayleigh and Prandtl numbers are explored. Under the conditions favourable for the development of a multiscale flow, the pattern of convection appears as a family of rolls with a certain basic scale, superposed with smaller cellular features. The latter are carried by the basic flow. We present movies illustrating these effects. The computed velocity and temperature as functions of the horizontal coordinate are Fourier transformed at several heights. The spectra exhibit, along a large-scale peak, some smaller-scale ones; in general, they are not overtones of the principal harmonic. We discuss different types of spectra (obtained for various stratifications) in the context of possible similarities between them and the spectrum of solar convection.