Based on the measurement of one-dimensional(1D) optical path difference(OPD) of the supersonic turbulent boundary layer, an analytical form for the power spectrum of the two-dimensional(2D) OPD is obtained with its st...Based on the measurement of one-dimensional(1D) optical path difference(OPD) of the supersonic turbulent boundary layer, an analytical form for the power spectrum of the two-dimensional(2D) OPD is obtained with its structure function and under the locally homogeneous isotropic assumption. The universality of this spectrum is argued, and its validity is checked by the comparison with experimental result. The potential applications of this model in theoretical and numerical studies are emphasized. Another contribution of this work is around the application of correlation function to analyzing the statistics of OPD. Based on our results and other results published elsewhere, we show that the OPD is often not stationary,and one should be cautious about using this tool.展开更多
The density distribution of a supersonic turbulent boundary layer is measured with the nanoparticle-based planar laser scattering technique, and the temporal evolution of its optical path difference (OPD) in a short t...The density distribution of a supersonic turbulent boundary layer is measured with the nanoparticle-based planar laser scattering technique, and the temporal evolution of its optical path difference (OPD) in a short time interval is characterized by proper orthogonal decomposition (POD). Based on the advantage of POD in capturing the energy of a signal, a temporal evolution model is suggested for the POD coefficients of the OPD. In this model, the first few coefficients vary linearly with time, and the others are modeled by Gaussian statistics. As an application, this method is used to compute the shortexposure optical transfer function.展开更多
The nano-particle-based planar laser scattering(NPLS) technique is used to measure the density distribution in the supersonic mixing layer of the convective Mach number 0.12,and the optical path difference(OPL),which ...The nano-particle-based planar laser scattering(NPLS) technique is used to measure the density distribution in the supersonic mixing layer of the convective Mach number 0.12,and the optical path difference(OPL),which is quite crucial for the study of aero-optics,is obtained by post processing.Based on the high spatiotemporal resolutions of the NPLS,the structure of the OPL is analysed using wavelet methods.The coherent structures of the OPL are extracted using three methods,including the methods of thresholding the coefficients of the orthogonal wavelet transform and the wavelet packet transform,and preserving a number of wavelet packet coefficients with the largest amplitudes determined by the entropy dimension.Their performances are compared,and the method using the wavelet packet is the best.Based on the viewpoint of multifractals,we study the OPL by the wavelet transform maxima method(WTMM),and the result indicates that its scaling behaviour is evident.展开更多
This paper is a further work of the authors' paper published previously (Liao T H and Gao Q 2005 Chin. Phys. Lett. 22 2316). The amplitudes of fractional Fourier transform of Cantor sets are analysed from the view...This paper is a further work of the authors' paper published previously (Liao T H and Gao Q 2005 Chin. Phys. Lett. 22 2316). The amplitudes of fractional Fourier transform of Cantor sets are analysed from the viewpoint of multifractal by wavelet transform maxima method (WTMM). An integral operation is carried out before the application of WTMM, such that the function obtained can be considered as the perturbed devil staircase. Also, wavelets with large number of vanishing moments are used, which makes the complete singularity spectrum more accessible. The validity of multifractal formalism is guaranteed by restricting parameter q to a proper range, so that the phenomenon of multifractal phase transition can be explained reasonably. Particularly, the method of determining the range of parameter q in the above paper is developed to be more operational and rigorous.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.61008037)the National Basic Research Program of China(Grant No.2009CB724100)
文摘Based on the measurement of one-dimensional(1D) optical path difference(OPD) of the supersonic turbulent boundary layer, an analytical form for the power spectrum of the two-dimensional(2D) OPD is obtained with its structure function and under the locally homogeneous isotropic assumption. The universality of this spectrum is argued, and its validity is checked by the comparison with experimental result. The potential applications of this model in theoretical and numerical studies are emphasized. Another contribution of this work is around the application of correlation function to analyzing the statistics of OPD. Based on our results and other results published elsewhere, we show that the OPD is often not stationary,and one should be cautious about using this tool.
基金Project supported by the Innovation Research Foundations for Postgraduates of National University of Defense Technology and Hunan Province, Chinathe National Natural Science Foundation of China (Grant No. 61008037)
文摘The density distribution of a supersonic turbulent boundary layer is measured with the nanoparticle-based planar laser scattering technique, and the temporal evolution of its optical path difference (OPD) in a short time interval is characterized by proper orthogonal decomposition (POD). Based on the advantage of POD in capturing the energy of a signal, a temporal evolution model is suggested for the POD coefficients of the OPD. In this model, the first few coefficients vary linearly with time, and the others are modeled by Gaussian statistics. As an application, this method is used to compute the shortexposure optical transfer function.
基金Projected supported by the Innovation Research Foundations for Postgraduates of National University of Defense Technology and Hunan Provincethe National Natural Science Foundation of China (Grant No. 61008037)
文摘The nano-particle-based planar laser scattering(NPLS) technique is used to measure the density distribution in the supersonic mixing layer of the convective Mach number 0.12,and the optical path difference(OPL),which is quite crucial for the study of aero-optics,is obtained by post processing.Based on the high spatiotemporal resolutions of the NPLS,the structure of the OPL is analysed using wavelet methods.The coherent structures of the OPL are extracted using three methods,including the methods of thresholding the coefficients of the orthogonal wavelet transform and the wavelet packet transform,and preserving a number of wavelet packet coefficients with the largest amplitudes determined by the entropy dimension.Their performances are compared,and the method using the wavelet packet is the best.Based on the viewpoint of multifractals,we study the OPL by the wavelet transform maxima method(WTMM),and the result indicates that its scaling behaviour is evident.
文摘This paper is a further work of the authors' paper published previously (Liao T H and Gao Q 2005 Chin. Phys. Lett. 22 2316). The amplitudes of fractional Fourier transform of Cantor sets are analysed from the viewpoint of multifractal by wavelet transform maxima method (WTMM). An integral operation is carried out before the application of WTMM, such that the function obtained can be considered as the perturbed devil staircase. Also, wavelets with large number of vanishing moments are used, which makes the complete singularity spectrum more accessible. The validity of multifractal formalism is guaranteed by restricting parameter q to a proper range, so that the phenomenon of multifractal phase transition can be explained reasonably. Particularly, the method of determining the range of parameter q in the above paper is developed to be more operational and rigorous.
