scholarly journals A method of scaling up equipment from the viewpoint of energy spectrum function.

1986 ◽  
Vol 19 (4) ◽  
pp. 345-347 ◽  
Author(s):  
KOHEI OGAWA ◽  
CHIAKI KURODA ◽  
SHIRO YOSHIKAWA
Keyword(s):  
Energy Spectrum ◽  
Scaling Up ◽  
Spectrum Function ◽  
Energy Spectrum Function

Similarity and self-preservation in isotropic turbulence

1951 ◽  
Vol 243 (867) ◽  
pp. 359-386 ◽  
Keyword(s):  
Energy Spectrum ◽  
Isotropic Turbulence ◽  
Initial Period ◽  
Reynolds Numbers ◽  
Wave Number ◽  
Inertial Subrange ◽  
Local Similarity ◽  
Mean Flow ◽  
Spectrum Function ◽  
Energy Spectrum Function

Measurements of the double and triple velocity correlation functions and of the energy spectrum function have been made in the uniform mean flow behind turbulence-producing grids of several shapes at mesh Reynolds numbers between 2000 and 100000. These results have been used to assess the validity of the various theories which postulate greater or less degrees of similarity or self-preservation between decaying fields of isotropic turbulence. It is shown that the conditions for the existence of the local similarity considered by Kolmogoroff and others are only fulfilled for extremely small eddies at ordinary Reynolds numbers, and that the inertial subrange in which the spectrum function varies as k -35 ( k is the wave-number) is non-existent under laboratory conditions. Within the range of local similarity, the spectrum function is best represented by an empirical function such as k -a log k , and it is concluded that all suggested forms for the inertial transfer term in the spectrum equation are in error. Similarity of the large scale structure of flows of differing Reynolds numbers at corresponding times of decay has been confirmed, and approximate measurements of the Loitsianski invariant in the initial period have been made. Its value, expressed non-dimensionally, decreases slowly with grid Reynolds number within the range of observation. Turbulence-producing grids of widely different shapes are found to produce flows identical in energy decay and in structure of the smaller eddies. The largest eddies depend markedly on the grid shape and are, in general, significantly anisotropic. Within the initial period of decay, the greater part of the energy spectrum function is self-preserving, and this part has a shape independent of the shape of the turbulence-producing grid. The part that is not self-preserving contains at least one-third of the total energy, and it is concluded that theories postulating quasi-equilibrium during decay must be considered with great caution.

scholarly journals SOME ADDITIONAL SOLUTIONS OF CONFORMAL TURBULENCE

1993 ◽  
Vol 08 (07) ◽  
pp. 619-623 ◽  
Author(s):  
YUTAKA MATSUO
Keyword(s):  
Energy Spectrum ◽  
Careful Study ◽  
2D Turbulence ◽  
Spectrum Function ◽  
Energy Spectrum Function

We made a careful study of Polyakov’s Diofantian equations for 2D turbulence and found several additional CFTs which meet his criterion. This fact implies that we need further conditions for CFT in order to determine the exponent of the energy spectrum function.

scholarly journals An expression of energy spectrum function for wide wavenumber ranges.

1985 ◽  
Vol 18 (6) ◽  
pp. 544-549 ◽  
Author(s):  
KOHEI OGAWA ◽  
CHIAKI KURODA ◽  
SHIRO YOSHIKAWA
Keyword(s):  
Energy Spectrum ◽  
Spectrum Function ◽  
Energy Spectrum Function

Some Aspects of Gas-Solid Suspension Turbulence

1971 ◽  
Vol 93 (4) ◽  
pp. 631-635 ◽  
Author(s):  
P. S. H. Baw ◽  
R. L. Peskin
Keyword(s):  
Energy Spectrum ◽  
Continuous Medium ◽  
Solid Phase ◽  
Particle Energy ◽  
Solid Particles ◽  
Suspension Flow ◽  
Wave Number ◽  
Spectrum Function ◽  
Solid Suspension ◽  
Energy Spectrum Function

An analysis is given for the apparent particle energy spectrum function in addition to the analysis of the effect of particles on the fluid energy spectrum in a turbulent gas-solid suspension flow. The analysis assumes that the problem of the motion of a continuous medium containing solid particles can be treated as two interacting continuous media, namely, the gas—and the solid—phase. The results obtained show that upon introduction of the particles the energy density of the fluid decreases more rapidly than for the case of pure fluid as wave number increases.

On the transformation of a continuous spectrum by refraction

1957 ◽  
Vol 53 (1) ◽  
pp. 226-229 ◽  
Author(s):  
M. S. Longuet-Higgins
Keyword(s):  
Energy Spectrum ◽  
Broad Spectrum ◽  
Practical Importance ◽  
Two Dimensional ◽  
Sea Waves ◽  
Wave Direction ◽  
Dimensional Spectrum ◽  
Spectrum Function ◽  
Velocity Of Propagation ◽  
Ray Paths

When waves are propagated through a medium whose velocity of propagation varies gradually from place to place, the wave direction and intensity vary according to the laws of refraction. Although the geometry of ray-paths has been well explored, and so also the laws governing the intensity of a coherent train of waves, little attention has apparently been given to the variation in intensity of an incoherent beam having a broad spectrum. The transformation of the energy spectrum is of practical importance in branches of geophysics, for example, in the study of sea waves entering shallow water, or of microseismic waves propagated through inhomogeneous regions of the earth's crust. Accordingly, it seems worth while to state and prove the rule governing the transformation of the two-dimensional spectrum function of a wave disturbance undergoing refraction.

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