Modeling typhoon wind power spectra near sea surface based on measurements in the South China sea

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Abstract

This study focuses on enhancing our understanding of the spectral features of typhoon winds with critical implications on the mitigation of disproportionate damage experienced in typhoons-prone coastal regions. Examination of data suggests that generally used empirical models of wind power spectrum for extratropical storms may not adequately represent the tropical cyclone winds. In this paper, a data-driven model is proposed for wind power spectrum in tropical cyclone winds over the sea surface. Rather than fitting data to a universal spectral description, first the physical meaning of parameters in such a model is carefully examined and the contribution of each parameter is delineated. With these backgrounds, field measurements in typhoon Hagupit are used to model these spectral parameters in terms of the Monin–Obukhov length, mean wind speed and roughness length. Finally, the proposed spectral model is validated using arbitrarily selected four hours of data in different sectors of typhoon Hagupit wind field. The model shows a good agreement with the measurements.

Highlights

► An analytical model is proposed to determine typhoon wind spectra over sea surface. ► Empirical models of spectral parameters were presented. ► Wind spectral characteristics were analyzed for typhoon Hagupit winds. ► Non-classical, elevator-like energy cascade was noted in eye wall regions of typhoon Hagupit.

Introduction

In recent years, many high rise buildings and long span bridges have been built in southern China, where typhoons frequently make landfall each year exposing dynamically sensitive structures to typhoon wind field. The fluctuations in typhoon winds are critical in establishing buffeting and other flow induced loads on these structures, which emphasizes the need to accurately describe typhoon wind characteristics and power spectrum density. Current codes and standards have instituted the premise that wind field characteristics in tropical cyclones are similar to those observed in the boundary layer winds of extratropical storms, which is formed based on careful analysis of the commonly used gust factors (ratio of peak wind speed and mean wind speed over a defined averaging interval) in a number of landfalling hurricanes in the Atlantic and Gulf coasts. Despite these apparent similarities in the nature of typhoon/hurricane wind fields, there have been questions raised regarding the role of convective features in the wind field. While these aberrations may magnify wind speeds and velocity spectra, they are also known to be transient, sporadic, and spatially patchy in the typhoon/hurricane wind field.

The wind power spectrum statistically represents the energy distribution in a turbulent flow field, which can be viewed as a superposition of eddies ranging spatially from millimeters to kilometers and temporally from a fraction of a second to hours. The behavior of turbulence spectrum within the atmospheric boundary layer follows the Kolmogorov hypotheses in the inertial sub-range, which ensures spectral description to have a universal shape when scaled appropriately in a certain range of frequencies or wave-numbers. Based on homogeneous, isotropic turbulence and field measurements, a number of spectral descriptions have been advanced primarily in strong extratropical winds (Karman, 1948, Davenport, 1961, Fichtl and McVehil, 1970, Miyake et al., 1970, Kaimal et al., 1972, Simiu, 1974, Kareem, 1985a, Kareem, 1985b, Solari, 1993, Tieleman, 1995). However in tropical cyclones, the downward transport of convective cells from aloft modulates the typhoon/hurricane near sea surface, and convective turbulence and mesoscale motion may play a more prominent role in energy transport at different scales, so that the turbulent energy distribution may not exactly mirror features observed in neutral, homogeneous, and isotropic turbulence flow. Such a conjecture was made by the third author following hurricane Alicia while examining radar data, wind observations at ground level and damage patterns. It is recently being discussed in wind engineering field (e.g., Florida Coastal Monitoring Program, NatHaz Modeling Laboratory).

To better understand tropical cyclone wind characteristics and their power spectra, a number of measurements have been conducted near top of structures or over open flat smooth land in typhoon or hurricane conditions (Xu and Zhan, 2001, Fu et al., 2008, Cao et al., 2009, Schroeder et al., 2009, Hui et al., 2009a, Hui et al., 2009b, Masters et al., 2010, Wang et al., 2011). A majority of these measurements found that tropical wind spectra matched von Karman spectrum (Karman, 1948). However, some measured results noted that the energy distribution did not exactly follow the empirical spectra and the frequency associated with the peak value of the normalized spectrum nSu(z,n)/σu2 either shifted to a low frequency or a high frequency range (Schroeder and Smith, 2003, Yu et al., 2008, Caracoglia and Jones, 2009, Zhang, 2010). The variance of fluctuations in tropical cyclones also exceeds those observed in extratropical storm boundary layer flows modeled in terms of the surface shear wind speeds. This may answer the role of energetic convective cells and their contribution to variance in fluctuations.

This paper first summarizes the theoretical background of turbulence energy spectra from a micrometeorological perspective. This is followed by an examination of the physical meaning of parameters in the universal wind spectral model and the number of parameters needed to define the spectral model is reduced from six to four. Subsequently, typhoon wind data and its turbulence wind characteristics are detailed and spectral parameters are expressed in terms of salient flow features. Finally, a data-driven model for determining power spectra for typhoon winds over the sea surface is proposed and the validation of the proposed model is examined with four hours of data in different locations of typhoon Hagupit wind field and concluding remarks are given.

Section snippets

Theoretical background of turbulence in the atmospheric boundary layer

One of the critical features of the atmospheric turbulence in the definition of structural loads is the spectral description of wind velocity fluctuations. The turbulent energy spectrum is often divided into three main ranges of frequency (Kaimal and Finnigan, 1994): (1) the energy-containing range with the bulk of the turbulent energy produced by buoyancy and shear; (2) the inertial sub-range, where energy is neither produced nor dissipated but transferred down to smaller scales; (3) the

Parameter sensitivity analysis

Typically, parameters for the most currently used spectral models were obtained by fitting the spectral model to satisfy the inertial sub-range and the low frequency range. Instinctively, one could expect that each parameter in the universal model would have its own physical meaning and influence on the energy distribution. In order to investigate the physical meaning of each parameter in Eq. (5), a sensitivity analysis was conducted. The range of values considered for each parameter is listed

Zhizai tower and instrumentations

Zhizai typhoon observation tower is a 100 m meteorological observation tower located at the top of Zhizai Island in the South China Sea. Zhizai Island is a very small island, with length about 120 m, width about 50 m, and the highest spot above the sea level is about 11 m. The geographical coordinates of the tower are 111°22′47.30″E longitude and 21°27′04.12″N latitude. The shortest straight-line distance from Zhizai tower to the mainland is about 4.5 km. Dazhuzhou Island is located on the south

Atmospheric stability in typhoon Hagupit

The parameter z/L is recognized as the measure of atmospheric stability and is expressed as (Kaimal and Finnigan, 1994):zL=(g/θ¯)(wθ¯)0u3/kzwhere (wθ¯)0 denotes temperature flux at the surface, k is the von Karman constant, L is the Obukhov length, and θ′ is the fluctuating virtual potential temperature. For neutral atmosphere, z/L tends to approach 0, for stable z/L>0, and for unstable condition z/L<0. Strictly neutral stratification does not always exist, so the near neutral

Concluding remarks

In this paper, a data-driven model for typhoon wind power spectrum is proposed based on analytical considerations and the field measurements in typhoon Hagupit in the South China Sea. The role of parameters in defining the universal turbulence energy spectrum was delineated. These parameters were evaluated using typhoon Hagupit data in terms of atmospheric stability, mean wind speed and roughness length. Accordingly, the wind spectral model was determined by introducing the empirical

Acknowledgments

The supports provided by the National Natural Science Foundation of China (Project no. 90715031) and the U.S. National Science Foundation (Grant no. CMMI0601143) are gratefully acknowledged. The authors are thankful for the reviews' helpful comments and suggestions.

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