Structure functions in two-dimensional turbulence

1992 ◽  
Vol 88 (1) ◽  
pp. 105-116 ◽  
Author(s):  
Siegfried Grossmann ◽  
Peter Mertens
Keyword(s):  
Structure Functions ◽  
Two Dimensional

scholarly journals Characterizing sand ripples at equilibrium phases

2013 ◽  
Vol 61 (4) ◽  
pp. 293-298 ◽  
Author(s):  
Jie Qin ◽  
Deyu Zhong ◽  
Guangqian Wang
Keyword(s):  
Time Series ◽  
Random Fields ◽  
Morphological Characteristics ◽  
Structure Functions ◽  
Second Order ◽  
Order Structure ◽  
Two Dimensional ◽  
Sand Ripples ◽  
Digital Elevation ◽  
Equilibrium Phases

Abstract Morphological characteristics of ripples are analyzed considering bed surfaces as two dimensional random fields of bed elevations. Two equilibrium phases are analyzed with respect to successive development of ripples based on digital elevation models. The key findings relate to the shape of the two dimensional second-order structure functions and multiscaling behavior revealed by higher-order structure functions. Our results suggest that (1) the two dimensional second-order structure functions can be used to differentiate the two equilibrium phases of ripples; and (2) in contrast to the elevational time series of ripples that exhibit significant multiscaling behavior, the DEMs of ripples at both equilibrium phases do not exhibit multiscaling behavior.

Exact third-order structure functions for two-dimensional turbulence

2018 ◽  
Vol 851 ◽  
pp. 672-686 ◽  
Author(s):  
Jin-Han Xie ◽  
Oliver Bühler
Keyword(s):  
Structure Functions ◽  
Spectral Energy ◽  
Order Structure ◽  
Two Dimensional ◽  
Third Order ◽  
Transfer Rates ◽  
The Third ◽  
Random Forcing ◽  
Asymptotic Expressions ◽  
Special Case

We derive and investigate exact expressions for third-order structure functions in stationary isotropic two-dimensional turbulence, assuming a statistical balance between random forcing and dissipation both at small and large scales. Our results extend previously derived asymptotic expressions in the enstrophy and energy inertial ranges by providing uniformly valid expressions that apply across the entire non-dissipative range, which, importantly, includes the forcing scales. In the special case of white noise in time forcing this leads to explicit predictions for the third-order structure functions, which are successfully tested against previously published high-resolution numerical simulations. We also consider spectral energy transfer rates and suggest and test a simple robust diagnostic formula that is useful when forcing is applied at more than one scale.

Structure functions of quasi-two-dimensional turbulence in a laboratory experiment

2011 ◽  
Vol 113 (3) ◽  
pp. 516-529 ◽  
Author(s):  
A. E. Gledzer ◽  
E. B. Gledzer ◽  
A. A. Khapaev ◽  
O. G. Chkhetiani
Keyword(s):  
Laboratory Experiment ◽  
Structure Functions ◽  
Two Dimensional

Two-dimensional isotropic inertia–gravity wave turbulence

2019 ◽  
Vol 872 ◽  
pp. 752-783 ◽  
Author(s):  
Jin-Han Xie ◽  
Oliver Bühler
Keyword(s):  
Total Energy ◽  
Isotropic Turbulence ◽  
Vertical Plane ◽  
Boussinesq Equations ◽  
Structure Functions ◽  
Wave Turbulence ◽  
Spectral Energy ◽  
Order Structure ◽  
Two Dimensional ◽  
Third Order

We present an idealized study of rotating stratified wave turbulence in a two-dimensional vertical slice model of the Boussinesq equations, focusing on the peculiar case of equal Coriolis and buoyancy frequencies. In this case the fully nonlinear fluid dynamics can be shown to be isotropic in the vertical plane, which allows the classical methods of isotropic turbulence to be applied. Contrary to ordinary two-dimensional turbulence, here a robust downscale flux of total energy is observed in numerical simulations that span the full parameter regime between Ozmidov and forcing scales. Notably, this robust downscale flux of the total energy does not hold separately for its various kinetic and potential components, which can exhibit both upscale and downscale fluxes, depending on the parameter regime. Using a suitable extension of the classical Kármán–Howarth–Monin equation, exact expressions that link third-order structure functions and the spectral energy flux are derived and tested against numerical results. These expressions make obvious that even though the total energy is robustly transferred downscale, the third-order structure functions are sign indefinite, which illustrates that the sign and the form of measured third-order structure functions are both crucially important in determining the direction of the spectral energy transfer.

Advective structure functions in anisotropic two-dimensional turbulence

2021 ◽  
Vol 916 ◽  
Author(s):  
Brodie C. Pearson ◽  
Jenna L. Pearson ◽  
Baylor Fox-Kemper
Keyword(s):  
Structure Functions ◽  
Two Dimensional

Abstract

scholarly journals Stratified Kelvin-Helmholtz turbulence of compressible shear flows

2018 ◽  
Author(s):  
Romit Maulik ◽  
Omer San
Keyword(s):  
Power Density ◽  
Spatial Resolution ◽  
Shear Flows ◽  
Incompressible Flows ◽  
Three Dimensional ◽  
Structure Functions ◽  
Compressible Turbulence ◽  
Power Density Spectrum ◽  
Two Dimensional ◽  
Density Spectrum

Abstract. We study the scaling laws and structure functions of stratified shear flows by performing high-resolution numerical simulations of inviscid compressible turbulence induced by Kelvin-Helmholtz instability. An implicit large eddy simulation approach is adapted to solve our conservation laws for both two-dimensional (with a spatial resolution of 16,3842) and three-dimensional (with a spatial resolution of 5123) configurations utilizing different compressibility characteristics such as shocks. For three-dimensional turbulence, we find that both kinetic energy and density-weighted energy spectra follow the classical Kolmogorov k−5/3 inertial scaling. This phenomenon is observed due to the fact that the power density spectrum of three-dimensional turbulence yields the same k−5/3 scaling. However, we demonstrate that there is a significant difference between these two spectra in two-dimensional turbulence since the power density spectrum flattens to k−1/4. This flattening may be assumed to be a reason for the k−7/3 scaling observed in the two-dimensional density-weight kinetic every spectra for high compressibility as compared to the k−3 scaling traditionally assumed with incompressible flows. Further inquiries are made to validate the statistical behavior of the various configurations studied through the use of second and third order velocity structure functions where it is noticed that scaling behavior differs between the two- and three-dimensional cases wherein only the latter is seen to follow trends from K41 theory.

Structure Functions and Dispersion Laws in Two-Dimensional Turbulence

1985 ◽  
Vol 42 (9) ◽  
pp. 941-949 ◽  
Author(s):  
Armando Babiano ◽  
Claude Basdevant ◽  
Robert Sadourny
Keyword(s):  
Structure Functions ◽  
Two Dimensional
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