A hypothesis of turbulent energy spectrum

1970 ◽  
Vol 26 (5) ◽  
pp. 296-299 ◽  
Author(s):  
Tosio Nan-Niti
Keyword(s):  
Energy Spectrum ◽  
Turbulent Energy

A model for the turbulent energy spectrum

1983 ◽  
Vol 26 (5) ◽  
pp. 1228 ◽  
Author(s):  
Richard J. Driscoll
Keyword(s):  
Energy Spectrum ◽  
Turbulent Energy

A consequence of the zero fourth cumulant approximation

1962 ◽  
Vol 13 (3) ◽  
pp. 369-382 ◽  
Author(s):  
Edward E. O'Brien ◽  
George C. Francis
Keyword(s):  
Energy Spectrum ◽  
Numerical Computation ◽  
Root Mean Square ◽  
Isotropic Turbulence ◽  
Initial Conditions ◽  
Passive Scalar ◽  
Turbulent Energy ◽  
Length Scale ◽  
Mean Square ◽  
Stationary Turbulence

Recent investigations by Kraichnan (1961) and Ogura (1961) have raised doubts concerning the usefulness of the zero fourth cumulant approximation in turbulence dynamics. It appears extremely tedious to examine, by numerical computation, the consequences of this approximation on the turbulent energy spectrum although the appropriate equations have been established by Proudman & Reid (1954) and Tatsumi (1957). It has proved possible, however, to compute numerically the sequences of an analogous assumption when applied to an isotropic passive scalar in isotropic turbulence.The result of such computation, for specific initial conditions described herein, and for stationary turbulence, is that the scalar spectrum does develop negative values after a time approximately $2 \Lambda | {\overline {(u^2)}} ^{\frac {1}{2}}$, Where Λ is a length scale typical of the energy-containing components of both the turbulent and scalar spectra and $\overline {(u^2)}^{\frac {1}{2}}$ is the root mean square turbulent velocity.

scholarly journals Turbulent Energy Spectrum via an Interaction Potential

2020 ◽  
Vol 30 (6) ◽  
pp. 3057-3087
Author(s):  
Rafail V. Abramov
Keyword(s):  
Energy Spectrum ◽  
Interaction Potential ◽  
Turbulent Energy

scholarly journals Scale-space energy density for inhomogeneous turbulence based on filtered velocities

2021 ◽  
Vol 931 ◽  
Author(s):  
Fujihiro Hamba
Keyword(s):  
Energy Spectrum ◽  
Energy Density ◽  
Channel Flow ◽  
Isotropic Turbulence ◽  
Turbulent Energy ◽  
Scale Space ◽  
Scale Dependence ◽  
Order Structure ◽  
Homogeneous Isotropic Turbulence ◽  
Inhomogeneous Turbulence

The energy spectrum is commonly used to describe the scale dependence of turbulent fluctuations in homogeneous isotropic turbulence. In contrast, one-point statistical quantities, such as the turbulent kinetic energy, are mainly employed for inhomogeneous turbulence models. Attempts have been made to describe the scale dependence of inhomogeneous turbulence using the second-order structure function and two-point velocity correlation. However, unlike the energy spectrum, expressions for the energy density in the scale space fail to satisfy the requirement of being non-negative. In this study, a new expression for the scale-space energy density based on filtered velocities is proposed to clarify the reasons behind the negative values of the energy density and to obtain a better understanding of inhomogeneous turbulence. The new expression consists of homogeneous and inhomogeneous parts; the former is always non-negative, while the latter can be negative because of the turbulence inhomogeneity. Direct numerical simulation data of homogeneous isotropic turbulence and a turbulent channel flow are used to evaluate the two parts of the energy density and turbulent energy. It was found that the inhomogeneous part of the turbulent energy shows non-zero values near the wall and at the centre of a channel flow. In particular, the inhomogeneous part of the energy density changes its sign depending on the scale. A concave profile of the filtered-velocity variance at the wall accounts for the negative value of the energy density in the region very close to the wall.

Similarity and the Turbulent Energy Spectrum

1967 ◽  
Vol 10 (4) ◽  
pp. 855 ◽  
Author(s):  
J. L. Lumley
Keyword(s):  
Energy Spectrum ◽  
Turbulent Energy
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