Turbulence frequency spectrum

For large Reynolds numbers, the right-hand side of this expression will be large, thereby forcing the scalar dissipation rate to attain a stationary solution quickly. Thus, for a fully developed scalar spectrum, the scalar mixing rate is related to the turbulent frequency by... 

A detailed description of LES filtering is beyond the scope of this book (see, for example, Meneveau and Katz (2000) or Pope (2000)). However, the basic idea can be understood by considering a so-called sharp-spectral filter in wavenumber space. For this filter, a cut-off frequency kc in the inertial range of the turbulent energy spectrum is chosen (see Fig. 4.1), and a low-pass filter is applied to the Navier-Stokes equation to separate the... 

A method of discovering time scales associated with turbulent motion is Fourier analysis. Along with the frequency spectrum, the wave number... 

Longer nozzles tend to produce more degrees of freedom as indicated in results for an LjD = 6 case depicted in Fig. 27.12. Massflow pulsations are more complex and therefore yield a richer frequency spectrum. Increases in Reynolds number yield similar effects but it becomes challenging to compute these cases without incorporation of a turbulence model. The laminar-to-turbulent characteristics of this flowfield present substantial challenges for this flowfield as most two-equation turbulence models rely on turbulent inflow conditions to close the problem. Clearly this is an area ripe for future research. 

The a value depends on the flow velocity distribution. Variations in flow velocity will broaden the Doppler frequency spectrum and result in a large a value. Thus, the Doppler variance image can be an indicator of flow variations and can be used to study flow turbulences. In addition, standard deviation imaging can also be used to determine the transverse flow velocity [8]. 

The shear stress sensor for turbulent flow needs to accurately capture the complete turbulent fluctuation spectrum. Therefore, the shear stress sensor should possess a large bandwidth with flat and minimum frequency-phase relationship. For direct measurement, i.e., floating point sensors, the resonant frequency of the floating element and the fluidic damping determines the usable bandwidth. For the thermal sensor, the thermal inertia of the sensor element and the frequency-dependent heat conduction to the substrate influence the usable bandwidth. It is complicated to analytically predict the frequency response of the thermal sensor. Therefore, dynamic calibration is essential to characterize the frequency response of the sensor. 

Thus, it appeared naturally to assume that every interesting dynamical regime possesses a discrete frequency spectrum. In this connection, it is curious to note that Landau and Hopf had proposed quasiperiodic motions with a sufficiently large number of independent frequencies as the mathematical image of hydrodynamical turbulence (the number of the frequencies was supposed to increase to infinity as some structural parameter, such as the Reynolds number, increases). 

Pressure Fluctuation Turbulent pressure fluctuations which develop in the wake of a cylinder or are carried to the cylinder from upstream may provide a potential mechanism for tube vibration. The tubes respond to the portion of the energy spectrum that is close to their natural frequency. 

Note that the Kolmogorov power spectrum is unphysical at low frequencies— the variance is infinite at k = 0. In fact the turbulence is only homogeneous within a finite range—the inertial subrange. The modified von Karman spectral model includes effects of finite inner and outer scales. 

Further, an interesting question is how the kinetic energy of turbulence will be distributed according to various eddies/frequencies. Such a distribution of the energy among the eddies/frequencies is usually termed the energy spectrum. Our focus is now on the double correlation in the Karman-Howarth equation, and finally, the dynamic equation for the energy spectrum that is obtained by the Fourier transform of the double correlation is derived as... 

As described above, wet and dry particle-bound deposition are likely important for the accumulation of the higher chlorinated PCDD/Fs in aerial vegetation. The accumulation of particle-bound PCDD/Fs in plants is a function of a myriad of factors. The deposition rate itself is influenced by the particle size spectrum in the atmosphere and the distribution of the PCDD/Fs on the different particle size fractions, and further by the atmospheric turbulence, the canopy and plant properties, and the frequency and intensity of precipitation. The retention of the contaminants on the plant surface depends on the degree to which the particles are permanently retained on the plant and, for those particles which are not retained, the degree of transfer of PCDD/Fs from the particles to the plant cuticle. This is a very complex system that is not yet well understood. One approach that... 

An alternative approach is to impose random fluctuations upon the flow and then use Fourier analysis of the resultant current or potential fluctuations to obtain the transfer function. MartemYanov and Grafov [17, 87, 88] used a particularly simple method employing a paddle stirrer to generate a turbulent flow, with a uniform spectrum of fluctuations over the frequency range (<100 Hz). This methodology was termed hydroelec-... 

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