C224 不変量空間における圧縮性乱流の統計数理

概要

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The evolution equations of the invariants P, Q and R (which correspond to the incompressible ones when P=0) are reproduced with the coefficients m and n of the characteristic equation. Here, the characteristic equation is modified to ξ^3+3mξ+n=0. The line, which divides real solutions from complex solutions, is given by n^2+4m^3=0. The cusp points are degenerated on the origin of m-n space. Evolution equations of the m(t) and n(t) are given as follows; dm/dt=4/3Pm-n;dn/dt=6m^2+2Pn. The quantities of m(t) and n(t) are expressed in terms of elliptic functions. A robust feature in the tensor invariant space of simulated compressible turbulence is explained by the solution trajectories, especially around the singular point where a fluid particle represented by the velocity gradient tensor Aij remains for a long time.
日本流体力学会の論文
2000-07-25