Quantitative description of turbulence using simple physical/mathematical models remains a challenge in classical physics and hydrologic dynamics. This study monitored the turbulence velocity field at the surface and ...Quantitative description of turbulence using simple physical/mathematical models remains a challenge in classical physics and hydrologic dynamics. This study monitored the turbulence velocity field at the surface and bottom of Taihu Lake, in China, a large shallow lake with a heterogeneous complex system, and conducted a statistical analysis of the data for the local turbulent structure. Results show that the measured turbulent flows with finite Reynolds numbers exhibit properties of non-Gaussian distribution. Compared with the normal distribution, the Levy distribution with meaningful parameters can better characterize the tailing behavior of the measured turbulence. Exit-distance statistics and multiscaling extended self-similarity(ESS) were used to interpret turbulence dynamics with different scale structures. Results show that the probability density function of the reverse structure distance and the multiscaling ESS can effectively capture the turbulent flow dynamics varying with water depth. These results provide an approach for quantitatively analyzing multiscale turbulence in large natural lakes.展开更多
1 Introduction The Lévy Laplacian was first introduced by P. Lévy in studying functionals on L^2 [0, 1] and has been investigated by many authors. In the white noise analysis setting Hida first defined L...1 Introduction The Lévy Laplacian was first introduced by P. Lévy in studying functionals on L^2 [0, 1] and has been investigated by many authors. In the white noise analysis setting Hida first defined Lévy Laplacian Δ_L via the second variation of a U-functional and proved that Δ_L annihilates functionals of square integrable (cf. Refs. [3, 4]). InRef. [3], Hida and Sait proved the following formula: Δ_L(?)=-(?)- (Δ_LF)~^, where F is Kuo’s Fourier transform of F. In Ref. [4], according to the original idea of P. Lévy a definition of the Lévy Laplacian was proposed. In the present note we will give a new ex-展开更多
基金supported by the National Key R&D Program of China(Grant No.2017YFC0405203)the National Natural Science Foundation of China(Grants No.11572112,41628202,and 41330632)
文摘Quantitative description of turbulence using simple physical/mathematical models remains a challenge in classical physics and hydrologic dynamics. This study monitored the turbulence velocity field at the surface and bottom of Taihu Lake, in China, a large shallow lake with a heterogeneous complex system, and conducted a statistical analysis of the data for the local turbulent structure. Results show that the measured turbulent flows with finite Reynolds numbers exhibit properties of non-Gaussian distribution. Compared with the normal distribution, the Levy distribution with meaningful parameters can better characterize the tailing behavior of the measured turbulence. Exit-distance statistics and multiscaling extended self-similarity(ESS) were used to interpret turbulence dynamics with different scale structures. Results show that the probability density function of the reverse structure distance and the multiscaling ESS can effectively capture the turbulent flow dynamics varying with water depth. These results provide an approach for quantitatively analyzing multiscale turbulence in large natural lakes.
基金Research supported by the National Natural Science Foundation of China
文摘1 Introduction The Lévy Laplacian was first introduced by P. Lévy in studying functionals on L^2 [0, 1] and has been investigated by many authors. In the white noise analysis setting Hida first defined Lévy Laplacian Δ_L via the second variation of a U-functional and proved that Δ_L annihilates functionals of square integrable (cf. Refs. [3, 4]). InRef. [3], Hida and Sait proved the following formula: Δ_L(?)=-(?)- (Δ_LF)~^, where F is Kuo’s Fourier transform of F. In Ref. [4], according to the original idea of P. Lévy a definition of the Lévy Laplacian was proposed. In the present note we will give a new ex-
