Семинар в ИВТ СО РАН 24 сентября 2013 года

24 сентября 2013 года в конференц-зале Института вычислительных технологий СО РАН  (5 этаж) состоятся 3 заседания  семинара "Законы сохранения и инварианты для уравнений гидродинамического типа".
Доклады будут сделаны немецкими коллегами.

Первый доклад: 14:30-15:45
Тема: Helical flows: new conservation laws and may it be considered a dimensionally reduced model for turbulence
Докладчик: Martin Oberlack (Technical University Darmstadt, Germany)
Аннотация: Helically invariant reductions due to a reduced set of independent variables (t, r, \xi) with \xi = a z + b \phi emerging from a cylindrical coordinate system of viscous and inviscid time-dependent fluid flow equations, with all three velocity components generally nonzero, are considered in primitive variables and in the vorticity formulation. Full sets of equations are derived. Local conservation laws of helically invariant systems are systematically sought through the direct construction method. Various new sets of conservation laws for both inviscid and viscous flows, including families that involve arbitrary functions, are derived. For both Euler and Navier–Stokes flows, infinite sets of vorticity-related conservation laws are derived. In particular, for Euler flows, we obtain a family of conserved quantities that generalize helicity. The special case of two-component flows, with zero velocity component in the invariant direction, is additionally considered, and special conserved quantities that hold for such flows are computed. In particular, it is shown that the well-known infinite set of generalized enstrophy conservation laws that holds for plane flows also holds for the general two-component helically invariant flows and for axisymmetric two-component flows.

Второй доклад: 16:00 - 17:00Тема: New statistical symmetries identified to compute higher order multi-point statistics for turbulent shear flows
 Докладчик: Martin Oberlack (Technical University Darmstadt, Germany)
Аннотация: Beginning in the late 90th the present author established the notion that turbulent scaling laws are exact solutions of the multi-point correlation equations (MPCE) of invariant type based on Lie symmetries. Though solutions for arbitrary moments were generated only the mean velocities clearly followed the theory suggesting that key characteristics were missing. This gap was partially closed in 2010 with the finding of an infinite set of statistical symmetries and finally fully completed recently with the derivation of a further extended set of statistical symmetries valid for wall-bounded shear flows. Combining these symmetries the new solutions for the higher moments exhibit an excellent match for a broad variety of canonical wall bounded shear flows such as boundary layer, Poiseulle and Couette flow inlcuding those with rotation and transpiration. Other then originally suggested for the mean velocity, higher order moments do not follow the maximum symmetry principle. Instead certain statistical symmetries are on active if the mean velocity in the correspondent is non-zero and hence, these symmetries are of conditional nature.

Третий доклад: 17:15 - 18:00
Тема: On the Hopf characteristic functional approach and Lundgren-Monin-Novikov hierarchy for multipoint pdf's of turbulence: new symmetries and solutions
Докладчик: Marta Waclawczyk (Technical University Darmstadt, Germany)
Аннотация: There exists three alternative mathematical approaches which may provide a full description of turbulence. First possibility is to investigate the infinite system of equations for the multi-point correlations of velocity. Second, the Lundgren-Monin-Novikov (LMN) hierarchy for the multipoint probability density functions can be considered and finally the third method is the Hopf characteristic functional approach. In this work, the two latter methods are a subject of our interest. First, the distortion of the pdf's induced by the new statistical symmetries of the LMN hierarchy will be discussed. Second, the symmetries of the Hopf functional formulation of the Burgers equations and its special solutions will be presented. The link between the symmetry transformations in all three aforementioned approaches to the description of turbulence will be discused.

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