Seminář se koná každé úterý v 10:40 v posluchárně ÚTF MFF UK
v 10. patře katedrové budovy v Tróji, V Holešovičách 2, Praha 8
We describe ab initio statistical theory of turbulence allowing calculation of moments of the invariant measure (IM) of the dynamical system (DS) corresponding to the Navier-Stokes equations (NSE).First we transform the NSE for flow in a closed volume, e.g. a long cylindrical pipe, into a system of N ordinary differential equations for N unknown functions. This defines a DS on the N-dimensional state space whose points correspond 1:1 to kinematic states of the fluid. In general the IM of this DS is not unique. To eliminate the IMs corresponding to unstable laminar solutions of NSE we take into account the small but really existing thermal noise and add the relevant term to the equations. This makes the equation for IM density second order elliptic with unique and smooth solution. To find the IM we expand its density into Hermite functions and show that the expansion coefficients are equal to long-time mean values of Hermite polynomials, from which we can calculate e.g. the mean turbulent velocity at any point. We derive a system of linear algebraic equations for these mean values, show that its matrix is block-tridiagonal and write an analytical expression for its solution.
Gravity waves are low frequency fluid oscillations restored by buoyancy forces in planetary and stellar interiors. Despite their ubiquity, the importance of gravity waves in evolutionary processes and asteroseismology has only recently been appreciated. For instance, Kepler asteroseismic data has revealed gravity modes in thousands of red giant stars, providing unprecedented measurements of core structure and rotation. I will show how gravity modes (or lack thereof) can also reveal strong magnetic fields in the cores of red giants, and I will demonstrate that strong fields appear to be common within "retired" A stars but are absent in their lower-mass counterparts. In the late phase evolution of massive stars approaching core-collapse, vigorous convection excites gravity waves that can redistribute huge amounts of energy within the star. I will present preliminary models of this process, showing how wave energy redistribution can drive outbursts and enhanced mass loss in the final years of massive star evolution, with important consequences for the appearance of subsequent supernovae.
Jiří Horáček Jiří Bičák