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TURBULENT ENERGY DENSITY IN SCALE SPACE BASED ON FILTERED TWO-POINT CORRELATION

Fujihiro Hamba
Institute of Industrial Science, University of Tokyo Komaba, Meguro-ku, Tokyo 153-8505, Japan

Sinopsis

The energy spectrum must be useful in describing the energy transfer not only in homogeneous isotropic turbulence but also in inhomogeneous turbulence. Instead of the energy spectrum in the wavenumber space, the energy density in the scale space can be defined using the velocity structure function or the two-point velocity correlation in the physical space. In this work, a new expression for the energy density in the scale space was introduced on the basis of the filtered two-point velocity correlation. In contrast to the previous expressions for the energy density, this expression is expected to be non-negative in homogeneous directions. The transport equation for the energy density was derived and direct numerical simulation data of homogenous isotropic turbulence and turbulent channel flow was used to evaluate the energy transport in the scale space. It was shown that the energy density is positive in all scales and the energy transfer from large to small scales was adequately observed for the turbulent energy.