Turbulence frequency definition

The two-point one time correlation functions, in the form presented in the preceding discussion, are not suitable for analyzing motions at different scales and specifically they are not suitable for understanding relations between movements of fluid characterized by different length and time scales. That is why it is better to use the 3D Fourier transforms of two-point correlations and to decompose them into waves of different frequencies or wave numbers. Turbulence has by definition a 3D character so it is obvious that the spectrum has to be 3D as well, to characterize turbulence properly. The ID spectrum of Taylor (see, e.g., [66]) oversimplifies the observed features of turbulence and may give misleading interpretations of the 3D held (see also, [113], p. 18). The differences and consequences of ID and 3D spectrum analysis are discussed by Hinze ([66], sects. 1-12 and 3-4) and Pope ([121], sect. 6.5). 

Although at first sight turbulence seems to be structureless and randomized, studies" of oscillographs like that in Fig. 3.3 show that this is not quite so. The randomness and unpredictability of the fluctuations, which are nonetheless constrained between definite limits, exemplify the behavior of certain mathematical chaotic nonlinear functions. Such functions, however, have not yet proved useful in quantitatively characterizing turbulence. This is done by statistical analysis of the frequency distributions. 

Harmonic vibration is the period of vibration in tall towers which is resonant with the period of vortexing of eddy currents downstream from the tower. With smooth cylindrical columns, a turbulent vortex is formed on the downwind side which, because of the circular motion of the vortex, will shift to the left or right of the wind direction. When this shifting reaches a limiting off-center distance, the eddy current will reverse direction and shift to the opposite side of the axis of the wind direction. In other words, there is an eddy current downstream from the tower that oscillates from left to right of the wind direction, and this oscillation has a definite frequency controlled by the wind velocity, tower diameter and tower roughness. 

This function, which is simply the area under the/( ) curve up to a given value of n, shows what fraction of the turbulent kinetic energy is contained in oscillations of lower frequency. By definition, the value of F n) must approach 1 as n becomes very large. 

The collision frequency and the breakage probability are determined by consideration of the interactions between drops in a field of turbulent pulsations. Their definition represents an independent problem. The problem of drop interactions in an emulsion will be considered in detail in Section V. 

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