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Applicability Analysis of Gradient Wind Field Model

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Applicability Analysis of Gradient Wind Field Model 2016 International Conference on Applied Mechanics, Mechanical and Materials Engineering (AMMME 2016) ISBN: 978-1-60595-409-7 Applicability Analysis of Gradient Wind Field Model Qing QI*, Hai-ying NIU, Guo-yi LI and Lin-ping YU College of Ocean and Civil Engineering, Dalian Ocean University, Dalian, 116024, China *Corresponding author Keywords: Typhoon, Gradient wind field model, Applicability, Holland. Abstract. The typhoon wind field model is an important part of the typhoon risk methods. And the accuracy of typhoon wind field model is one of the key factors influencing typhoon risk assessment. In this paper, the applicability of different gradient wind field models are analyzed. At first, the reasonability of gradient wind field model is brief discussed. Then different gradient wind field models are used to calculate two typhoons. By comparing with the measured wind speed, several kinds of gradient wind field models show better simulation results. The comparison indicates that Holland gradient wind field model matches well with the measurements and has better applicability than other models. Introduction Extreme winds and waves in a typhoon can cause severe damage to coastal structures, including the loss of property and human life. Also, typhoon disaster would affect the sustainable development of regional economy. In order to reduce economic loss, an effective approach to the risk assessment is to simulate the typhoon wind field using limited information, such as the typhoon’s position, central pressure drop and radius to maximum winds. Many scholars have proposed empirical and analytical models for calculating the wind speed distribution of a typhoon. The parametric typhoon model using the gradient wind equation is considered to be applied universally. In order to verify the applicability of different gradient wind field model, it is necessary to discuss the reasonability of gradient wind assumption of a typhoon. In this paper, eight gradient wind field models, including the V.Bjerknes [1] model, Takahashi [2] model, Fujita [3] model, Myers [4] model, Jelesnianski [5] model, inner domain Fujita and outer Takahashi [6,7] model, modified Fujita [8]model and Holland [9]model, are used to simulate the typhoon wind field. The wind speed distribution and the extreme wind speeds of various wind field models are very different, so it is necessary to analyze the applicability of each wind field model. Through comparisons between the simulated and observed results, the applicability of the gradient wind field model are analyzed and results indicated that the Holland typhoon wind field model has better applicability than other models. Gradient Wind Field Model Generally, the typhoon pressure distribution formula is as follows: P− P f (r) = c (1) Pn− P c Where P is the pressure at distance r from the center of the typhoon, Pn is the ambient pressure, and Pc is the central pressure. By the assumption of f(r), we can get different pressure distributions. By the derivation of Eq.(1), pressure gradient force distribution expression as follows: ∂P = ∆P ⋅ f ′(r) (2) ∂r where ∆P is the central pressure drop, which equals Pn- Pc . Based on the gradient wind balance (Figure 1), the radial distribution of typhoon field profile equation could be build: r∂ P r2 f 2 rf V = ⋅+ − (3) g ρ ∂r 4 2 Where f is Coriolis force, and ρ is the air density. Figure 1. Gradient equilibrium along the radial direction. νg is the gradient wind speed, ∂P/∂r is the pressure gradient at 2 distance r from the typhoon center, fvg is Coriolis force, and vg /r is the centrifugal force. As the gradient wind field model simply supposed that the trajectory of the air particle was circled (as shown in Figure 1), it could not correctly describe the spiral flows of a typhoon and also could not properly consider the frictional drag. Ignoring the asymmetry of typhoon wind field induced by typhoon movement, the typhoon wind field is symmetric, which is mentioned by Jakobsen[10]. The radial distribution of wind speed is deduced as followed: 1/2 r∂ P r2 f 2 rf v =⋅+ − (4) ρ∂r 4⋅ cos 2 α 2 ⋅ cos α When the deflection angle is zero, the Eq. (4) can be simplified to the gradient wind Eq. (3), and the wind speed deviation will not exceed 10%. This also shows that the gradient wind model is established on a solid theoretical basis and is widely used. In this paper, the following eight kinds of gradient wind field model are mainly analyzed. V.Bjerknes Wind Field [1] V. Bjerknes pressure distribution is expressed by 2 R max f (r)= 1 − 2 2 (5) R max +r Where Rmax is the radius to maximum winds, which is based on empirical formulas or satellite observations. Takahashi Wind Field [2] Takahashi pressure distribution is expressed by R f (r)= 1 − max (6) Rmax + r Fujita Wind Field [3] Fujita pressure distribution is expressed by 1 − r 2 f (r)=− 1 1 +⋅ 2 ( ) 2 (7) Rmax Myers Wind Field [4] Myers pressure distribution is expressed by R f (r)= exp − max (8) r Jelesnianski Wind Field [5] Jelesnianski pressure distribution is expressed by 1 r 3 ⋅( ),0 ≤r ≤ R max 4 R f() r = max (9) 3⋅ R 1−max ,r ≥ 2 R 4r max Inner Domain Fujita and Outer Takahashi Wind Field [6,7] Inner domain Fujita and outer Takahashi pressure distribution is expressed by 2 −1/2 r 11+2− ,0 ≤r ≤ 2 R max R f() r = max (10) r ,r≥ 2 R max Rmax + r Modified Fujita Wind Field [8] Modified Fujita wind field pressure distribution is expressed by 1 2 − 2 r 2 r f (r)=−+⋅ 1 1 2 ⋅− 1 (11) R R max ∞ Where R∞ is environment radius. Holland Wind Field [9] Holland pressure distribution is expressed by R b f (r)= exp − max (12) r Where b is the Holland radial pressure profile parameter, which is commonly defined from about 0.5 to 2.5. According to above review of the gradient wind field models, the radial pressure profile and wind speed profile are given in Figure 2 and Figure 3. When the pressure drop and the maximum wind speed radius are constant, the range of the pressure distribution profile is 0≤f (r) ≤ 1 (Fig 2.). The Holland pressure profile and wind speed profile are in the middle. Figure 2. Pressure distribution profile along the radial direction for different wind field models. Figure 3. Wind profiles along the radial direction for different wind field models. From Figure 3, the wind speed profiles of different wind field model are very different, and the extreme wind speeds do not occur in the same location. So it is important to verify the applicability of the eight kinds of gradient wind model. Application Examples In this paper, Typhoon "Koppu"(0915) and Typhoon "Nesat"(1117) are calculated. And according to the eight kinds of gradient wind field model, the simulation results are compared with the observed results. Typhoon tracks are given in Figure 4. Figure 4. Typhoon track about Typhoon "Koppu" (left) and Typhoon "Nesat" (right) (Typhoon network in South China Sea). The measure point of Typhoon Koppu is located at latitude E112.3°and longitude N16.8°. Through the calculation of eight kinds of wind field model, the simulated wind speeds is compared with the measured wind speeds, that is showed in Figure 5. It is clearly that Holland gradient wind field model is fitting well. Figure 5. Comparison between simulated and measured wind speed of different wind models of typhoon Koppu. Figure 6. Comparison between simulated and measured wind speed of different wind models of typhoon Nesat at measure point 1. The measure point of Typhoon Nesat is located at latitude E112.3°and longitude N16.8°. Through the calculation of eight kinds of wind field model, the simulated wind speeds is compared with the measured wind speeds, that is showed in Figure 6. It is clearly that Holland gradient wind field model is fitting well. From Figs.5 and 6, the Holland gradient wind model is the best fitted one in the eight gradient typhoon wind field models. Summary In this paper, the reasonability of the gradient wind field model is discussed and the applicability of the eight kinds of gradient wind field model is analyzed. By comparisons of the simulated wind speeds and measured wind speeds, the Holland gradient wind field model matches well with the measurements, and it shows better applicability than other wind field models. Acknowledgment The work is financially supported by the State key laboratory open fund of Dalian University of Technology(LP1302). References [1] China Meteorological Administration. Yearbook of Tropical Cyclones. Shanghai: China Meteorological Press, 2007. [2] K Takahashi, Distribution of pressure and wind in a typhoon. Meteor. Soc. Japan, 1932(17):417-421. [3] T Fujita. Pressure distribution in typhoon. Geophys . Mag, 1952, 23:437. [4] V. A. Myers, Maximum hurricane winds.Bul1. Amer. Metero. Sco, 1957, 38 (4):227. [5] P Chester., Jelesnianski, A numerical computation of storm tides by a tropical storm impinging on a continental shelf. Monthly Weather Review, 1965, 93(6): 643-358. [6] K Takahashi, Distribution of pressure and wind in a typhoon[J]. Meteor. Soc. Japan, 1939, 2(17):417-421. [7] J B Huang, X Zhao , Z Y Li, On Numerical Simulation Method of Wind Wave in North Bay of South China Sea [J] .Transport Engineering of Water Resources, 2008 (1): 7- 10. [8] Z H Chen, Y K Tan, L Li .Improvement of Fujita Formula and Its Application in Typhoon Forecasting. Meteorological Science and Technology, 2011, 39 (1): 1-8. [9]G J Holland., An analytic model of the wind and pressure profiles in hurricanes.
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