Numerical Investigation of the Atmosphere-Like Flows in the Spherical Geometry

• Applicant: Dr.-Ing. Vadim Travnikov
• Subject Area: Fluid Mechanics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 439798763

Numerical Investigation of the Atmosphere-Like Flows in the Spherical Geometry (continuation)Buoyancy-driven convective flows play a crucial role in geophysics and meteorology for global heat and momentum transport. Simplified planetary and stellar atmospheres can be described by a spherical gap geometry with special boundary conditions. Besides, radial gravitational acceleration and rotational effects have to be taken into account. The investigation of such a configuration is complex to be realized by a laboratory experiment. However, the numerical study is favored in this proposal, keeping in mind to implement physically relevant boundary conditions. The dielectrophoretic effect is used in the spherical gap to synthesize the radial gravity field and causes a convective flow. Additionally, lateral thermal boundary conditions are used to model the solar radiation at the equator and the poles. The temperature has a maximum value on the equator and becomes colder near the poles. Due to the temperature dependence on the polar angle ϑ, the basic flow occurs that has to be calculated. The influence of the Coriolis and centrifugal forces should be taken into account in the case of a rotating gap. First, we performed the classification of the two-dimensional axisymmetric basic flow. Secondly, linear stability theory is used in investigating the stability of the basic flow. The main results of this investigation are:The range in which the flow is stable to infinitesimal perturbations, bounded by the intervals (0,Ta_c), 〖(0,Ra〗_Ec) and the stability curve. The basic flow becomes unstable regarding non-axisymmetric perturbations. Equatorially symmetric and equatorially antisymmetric perturbations are responsible for the instability.In all cases considered, the instability sets in as an oscillating bifurcation. The drift velocity is always negative, i.e., the perturbative flow moves in a retrograde direction.The three-dimensional flows will be calculated due to the direct numerical simulation (DNS) to perform the bifurcation analysis and must be expanded on the large Rayleigh numbers to analyze various scenarios and transitions. The next issue is the analysis of the heat transfer. Numerical calculations in the supercritical region will be performed using a 3D pseudo-spectral numerical code developed by R. Hollerbach and MagIC pseudo-spectral code.

• DFG Programme: Research Grants