Turbulent vertical velocity

I designed an instrument that measured vertical gustiness and provided the vertical component of air movements (Figure 6.3.A). Vertical gustiness (Gz) is a ratio of turbulent vertical velocity divided by wind velocity. 

Gustiness is the ratio of turbulent vertical velocity and wind velocity. Recall the relation Area A = K/D . For two areas Ajr and A2 with corresponding dosages T>i and T>i. 

Development in recent years of fast-response instruments able to measure rapid fluctuations of the wind velocity (V ) and of fhe tracer concentration (c ), has made it possible to calculate the turbulent flux directly from the correlation expression in Equation (41), without having to resort to uncertain assumptions about eddy diffusivities. For example, Grelle and Lindroth (1996) used this eddy-correlation technique to calculate the vertical flux of CO2 above a foresf canopy in Sweden. Since the mean vertical velocity w) has to vanish above such a flat surface, the only contribution to the vertical flux of CO2 comes from the eddy-correlation term c w ). In order to capture the contributions from all important eddies, both the anemometer and the CO2 instrument must be able to resolve fluctuations on time scales down to about 0.1 s. 

Temporal sequence of OH-LIF measurements captures a localized extinction event in a turbulent nonpremixed CH4/H2/N2 jet flame (Re 20,000) as a vortex perturbs the reaction zone. The time between frames is 125 ps. The velocity field from PIV measurements is superimposed on the second frame and has the mean vertical velocity of 9m/s subtracted. (From Hult, J. et al.. Paper No. 26-2, in 10th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, 2000. With permission.)... 

The Grashof number given by Eq. (40) appears to have a weaker theoretical basis than that given by Eq. (37), since it is based on an analysis that approximates the profile of the vertical velocity component in free convection, for example, by a quadratic function of the distance to the electrode. The choice of an appropriate Grashof number, as well as the experimental conditions in the work of de Leeuw den Bouter et al. (DIO) and Marchiano and Arvia (M3), has been reviewed critically by Wragg and Nasiruddin (W10). They measured mass transfer by combined thermal and diffusional, turbulent, free convection at a horizontal plate [see Eq. (31) in Table VII], and correlated their results satisfactorily with the Grashof number of Eq. (37). 

The measurements of Rouse, Yih and Humphries (1952) [1] helped to generalize the temperature and velocity relationships for turbulent plumes from small sources, and established the Gaussian profile approximation as adequate descriptions for normalized vertical velocity (w) and temperature (7), e.g. 

The technique requires simultaneous fast and accurate measurements of both the vertical velocity and the trace species in question. Fortunately the technology for the measurement of turbulence with the necessary resolution is available. Sonic anemometers can readily yield air motion data with the required resolution (10). Likewise, the ability to handle the air motion and chemical concentration data with modern computer data systems is well in hand (II). Thus these aspects can be ignored, and the major limitation can be dealt with the availability of appropriate chemical sensors with sufficient time and chemical resolution. 

To clarify the mutual interactions between the gas bubbles and its surrounding liquid flow (mostly turbulent) in a bubbly flow, information of bubble s shape and motion is one of the key issues as well as the surrounding liquid velocity distribution. Tokuhiro et al. (1998, 1999) enhanced the PIV/LIF combination technique proposed by Philip et al. (1994) with supplementation of SIT to simultaneously measure the turbulent flow velocity distribution in liquid phase around the gas bubble(s) and the bubble s shape and motion in a downward flow in a vertical square channel. The typical experimental setup of the combination of PIV, LIF, and SIT is shown in Figure 14. The hybrid measurement system consists of two CCD cameras one for PIV/LIF (rear camera) and the other for SIT (front). The fluorescent particles are Rhodamine-B impregnated, nominally 1-10 pm in diameter with specific density of 1.02, and illuminated in a light sheet of approximately 1 mm thickness (Tokuhiro et al., 1998,1999). The fluorescence is recorded through a color filter (to cut reflections) by the rear camera. A shadow of the gas bubble is produced from infrared LEDs located behind the gas bubble. A square "window" set within the array of LEDs provides optical access for... 

The derivation of Eq (19-24) assumes that the coefficient of eddy viscosity, nef for momentum and matter are the same (see Chapter 8). It further assumes that the distribution of vertical velocity and concentration varies logarithmically with height from the ground surface. Actually this is not the case, because near the ground surface turbulence does not operate, and the variation begins from the source point as we have shown earlier in the present chapter. 

Given an approximate estimate for the rate of growth of crz in terms of the vertical turbulence crw = (Uc)/10) and the spatial average of the variation of the mean vertical velocity 1 /3(U lr/d2 leads to (by considering detrainment from their wakes)... 

Plant canopies exhibit remarkable turbulence statistics, which makes canopy aerodynamics a topic of substantial scientific interest. Of particular note are the degree to which vertical and streamwise velocities are correlated, and the high degree of skewness in these two velocity components. The correlation coefficient that relates stream-wise and vertical velocities, defined as... 

The distributed array of drag elements in vegetation canopies creates a mean wind profile that contains an elevated shear layer centred near the canopy top that more closely approximates a plane mixing layer than a wall layer. This velocity stmcture is responsible for turbulence characteristics that differ substantially from those over a smooth surface. Velocity spectra are sharply peaked, streamwise and vertical velocities have probability densities that are strongly skewed, streamwise and vertical velocities are correlated more strongly that would be expected over a smoother surface, and transport is dominated by coherent flow structures with sweeps more important than ejections. 

Here it is the vector of the horizontal velocity, U the vertically integrated horizontal velocity, w is the vertical velocity, r is the sea-level elevation, V/, the horizontal nabla operator, q a source term of water flux, T the temperature, S the salinity, p the pressure, and p is the density. Moreover,/is the inertial frequency,/= 2 1 sin 0, where 1 Zn (1 I 1/365.2425)724 h is the earth s angular velocity and 0 is the latitude. Turbulent viscosity is indicated by the term D, . Wind forcing enters the scheme as a vertical boundary condition. The equations are solved usually in spherical coordinates, but are written here for simplicity in Cartesian form. 

Conceptual models aimed at explaining the dominant processes associated with gas transfer can be generalized as being either turbulent eddy dif-fusivity or surface renewal models others are based on similarity considerations with reference to experimental data. Irrespective of the model type, it may be assumed that the vertical velocity fluctuations near the sur-... 

Flux-resolving, fluctuation-based methods In these methods the vertical turbulent eddy flux F is measured as pw c, where overbars and primes denote time means and fluctuations, respectively, and w is the vertical velocity component. They include eddy-covariance and eddy-accumulation methods for measuring fluxes from towers and aircraft. They are not normally regarded as atmospheric inverse methods, since that term usually refers to methods which relate a mean concentration field to a source density or surface flux distribution. 

These equations provide a complete solution to the forward problem of calculating c(z) from a given (f> z) in a uniform canopy. The rec [uired turbulence properties are canopy profiles of the standard deviation time scale Tiiz) for vertical velocity. 

Figure 16.1 shows a typical record of one wind component that might be obtained by an anemometer. From such a record a mean velocity u, can be obtained. Wind turbulence refers to the properties of the fluctuations about the mean in a record such as the one shown in Figure 16.1. These fluctuations are primarily responsible for the spreading of a cloud of pollutants in the atmosphere. It is important to measure all three components of the wind velocity, since the vertical fluctuations are often the most important in transporting pollutants. The vertical velocity fluctuations provide a direct measure of the stability of the atmosphere. In order to obtain a record such as the one shown in Figure 16.1 a sensitive, rapidly responding wind vane and anemometer are required. Vertical fluctuations can be measured by ...

The second term at the right-hand side of Eq. (2) is known as the turbulent covariance. Similarly, the turbulence variance of a quantity is given by C -C (which is the square of the standard deviation). If in Eq. (2) A represents one of the velocity components, then AC is the total flux of C, and the second term at the right-hand side of Eq. (2) represents a turbulent flux of C. For instance, uc and wc are the horizontal and vertical turbulent fluxes of the variable C, respectively. Here, u and w are the turbulent fluctuations of the horizontal and vertical velocities. Near the surface, the mean vertical wind W is usually small, and, thus, the total vertical fluxes are normally domirrated by the trrrbulent contributions. 

In the surface layer over homogeneous terrain, so-called surface-layer (or Monin-Obukhov) similarity theory can be used to study the combined effects of convective and mechanical turbulence on the profiles and distributions of mean and turbulence characteristics. For instance, if at r variable with the dimensions of velocity is normahzed by the friction velocity m+o, the resultant dimensionless qirantity then only depends on z/Z. As an example of the application of this type of similarity or scaling, consider the standard deviation of vertical velocity Surface-layer similarity theory requires... 

There is a significant difference between spectra of the horizontal and vertical velocity components. Because the atmosphere is quasi-two-dimensional, very large eddies are quasi-two-dimensional that is, at low frequencies, horizontal eddies have much more energy than vertical eddies. In contrast, high-frequency turbulence has more nearly equal energy for all components. This is why the variances of the horizontal components are generally much larger than those of the vertical component. 

In this section, a description is provided of the use of water-air two-phase jet to model steel-Ar two-phase system. The horizontal and vertical velocity components are measured with a two-channel laser Doppler velocimeter [17]. Empirical relations are given for the mean values and the root-mean-square values of the turbulence components. Predictions of the trajectory of the two-phase jet are also discussed. 

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