Covariance of physical quantities in fluid-turbulence theory and their governing equations under generalized coordinate transformation is discussed. It is shown that the velocity fluctuation and its governing law have a covariance under far wider group of coordinate transformation than that of conventional Euclidean invariance, and, as a natural consequence, various correlations and their governing laws are shown to be formulated in covariant manners under this wider transformation group. In addition, it is also shown that the covariance of the Reynolds stress is tightly connected to the objectivity of the mean flow.
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|Publication status||Published - 2015 May 4|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics