Introduction
According to Glickman (2000), the turbulence intensity is defined as the ratio of the root-mean-square of the eddy velocity to the mean wind speed; in general, it is a quantity that characterizes the intensity of gusts in the airflow. Mathematically, the turbulent intensities in horizontal and vertical directions are σu/U, συ/U, and σw/U, where σu, συ, and σw are the standard deviations of velocity fluctuations in the x, y, and z directions, respectively, and U is the mean wind speed. Note that the mean wind speed, rather than the particular component mean velocity, is used in the definition of turbulence intensities (Arya 1999). In air pollution meteorology and dispersion, these turbulence intensities are related to the particle dispersion parameters in the y and z directions (i.e., σy and σz), respectively (see e.g., Panofsky and Dutton 1984; Zannetti 1990; Arya 1999).
For neutral and stable conditions
For unstable conditions
The self-correlation problem between (σu,υ/u∗) and (h/L)
For unstable conditions when Tsea > Tair, Eq. (4) has been used extensively in air pollution meteorology (see, e.g., Panofsky and Dutton 1984; Zannetti 1990; Arya 1999). However, this equation suffers from self-correlation as discussed below.
An alternative relationship between (σu,υ/Uz) and (z/L)
Equation (24) is further verified by another independent dataset. In order to obtain as large a variance of |z/L| as possible, data from the 1975 Air-Mass Transformation Experiment (AMTEX '75) (see Fujitani and Hayashi 1975) are employed. This dataset includes overwater measurements of σu, συ, and σw in addition to wind speed and air and sea temperatures. Note that AMTEX '75 was conducted over the open East China Sea in February 1975 and that values of |z/L| extended to nearly 7. [For the computation of |z/L|, see Hsu and Blanchard (2003).] Figure 2 is our result. Note that the vertical axis is the estimated (σu/Uz), based on Eq. (24), and the horizontal axis represents the measured (σu/Uz). Because the rmse is small in comparison with the data range, we conclude that Eq. (24) is a useful approximation between the longitudinal turbulence intensity (σu/Uz) and the stability parameter (z/L).
Note that during the first half of January 2002, cold air moved over the eastern Gulf of Mexico, including the freezing temperature line, which eventually draped over the northern Gulf Coast. To further verify Eq. (27), Fig. 4 is provided. If one accepts these smaller rmses as compared with the gust factor analyzed, one can say that Eq. (27) is useful operationally.
Conclusions
Several conclusions may be drawn from this study:
Under neutral and stable conditions, the turbulence intensities in the horizontal and vertical directions are linearly related to the gust factor as derived in Eqs. (9)–(11).
Under unstable conditions, the ratio of the mixing height and buoyancy length cannot be related to the horizontal turbulence intensity because of the self-correlation problem. Therefore, the popular formula shown in Eq. (4) should not be used for overwater applications.
Because of the self-correlation problem stated above, an alternative formula is proposed in Eq. (24), which relates the horizontal turbulence intensity to the surface-based stability parameter (z/L).
For practical applications the gust factor is found to be related to (z/L), which was shown statistically in Eq. (27).
Using Eq. (27), variations in horizontal and vertical turbulence intensities with the gust factor are proposed for practical applications in Eqs. (29) and (30), respectively.
In order to further verify Eqs. (9), (10), (11), (29), and (30), turbulent intensity measurements on an NDBC buoy are necessary. Because U10, G, and z/L are available at buoys 42001, 42002, and 42003, it is recommended that further experiments be conducted at these stations if logistically practical.
Acknowledgments
This study was partially supported by the Minerals Management Service (MMS), U.S. Department of the Interior, through the Coastal Marine Institute of Louisiana State University under a cooperative agreement with Louisiana State University. The contents of this paper do not necessarily reflect the views or policies of the MMS.
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