希尔伯特-黄变换技术及在边界层湍流研究中的应用

The Hilbert-Huang transform technique and its applications to the study of the turbulence boundary layer.

大气边界层中的湍流运动可以视为由许多不同时空尺度的湍涡叠加形成的,谱分析方法可以将这些不同尺度的涡旋分离开来。在介绍希尔伯特-黄变换(HHT)的基础上,选取2011年4月16日00—01时(北京时)、05-06时、12—13时不同时段的大气湍流观测数据,采用希尔伯特-黄变换技术分析了内蒙古科尔沁沙地地区的谱分布特征,得到的各内在模函数对应的中心瞬时频率可以表现出不同尺度上的湍流波动,其中,包含周期为3—5和10-13 min的阵风和重力内波,并在希尔伯特边际谱中体现。三维希尔伯特谱分布表明湍流能量多集中在频率小于0.5 Hz的低频段;大气湍流脉动较强的时段,其内在模函数和希尔伯特谱也对应着较大的能量。对比传统的快速傅里叶变换(FFT)方法,希尔伯特-黄变换可以更清晰地表现出湍流的频谱分布。

The turbulence movement can be treated as consisting of many eddies of different time-spatial scales, and spectrum analysis can separate these eddies. On the basis of the introduction to the Hilbert-Huang transform （HHT）, HHT is applied into a series of the turbulence data in the Horqin Sandy Land during the periods of 00 ： 00 - 01： 00, 05 ： 00 - 06 ： 00 and 12 ： 00 - 13 ：00 BT on 16 April 2011. It is shown that the central instantaneous frequencies of Intrinsic Mode Functions （IMFs） are able to show the turbulence fluctu- ations at the different scales which include the gust in 3 - 5 min and the internal gravity wave in 10 - 13 rain as in the Hilbert marginal spectrums. The 3D Hilbert spectrums denote that turbulence energy concentrates in the bands lower than 0.5 Hz. Corresponding with the strong turbulence periods, IMFs and the Hilbert spectrums contain more power as well. Compared with the traditional technique （Fast Fourier Transform, FFT）, HHT can perform the distribution of spectrum more clearly.