Artículos de revistas
Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence
Fecha
2013Registro en:
Zeitschrift für angewandte mathematik und physik, Basel, n.64, p.599-620, 2013
10.1007/s00033-012-0251-7
Autor
Grebenev, V. N.
Oberlack, M.
Grishkov, A. N.
Institución
Resumen
We deal with homogeneous isotropic turbulence and use the two-point velocity correlation tensor field (parametrized
by the time variable t) of the velocity fluctuations to equip an affine space K3 of the correlation vectors by a family
of metrics. It was shown in Grebenev and Oberlack (J Nonlinear Math Phys 18:109–120, 2011) that a special form of this
tensor field generates the so-called semi-reducible pseudo-Riemannian metrics ds2(t) in K3. This construction presents the
template for embedding the couple (K3, ds2(t)) into the Euclidean space R3 with the standard metric. This allows to introduce
into the consideration the function of length between the fluid particles, and the accompanying important problem to
address is to find out which transformations leave the statistic of length to be invariant that presents a basic interest of the
paper. Also we classify the geometry of the particles configuration at least locally for a positive Gaussian curvature of this
configuration and comment the case of a negative Gaussian curvature.