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Bottleneck effect in three-dimensional turbulence simulations.

Wolfgang Dobler¹, Nils Erland L Haugen, Tarek A Yousef

¹Kiepenheuer-Institut für Sonnenphysik, Schöneckstrasse 6, D-79104 Freiburg, Germany. Wolfgang.Dobler@kis.uni-freiburg.de

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|October 4, 2003

Summary

This summary is machine-generated.

Turbulence simulations reveal a "bottleneck effect" in 3D energy spectra, which is less pronounced in 1D spectra. Second-order structure functions offer a more reliable method for analyzing turbulence scaling exponents.

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Area of Science:

Fluid dynamics
Computational physics
Turbulence research

Background:

Numerical simulations of turbulence at high resolutions (e.g., 512^3) exhibit deviations from theoretical energy spectra.
A phenomenon known as the "bottleneck effect" causes shallower energy spectra (less than k^-5/3) near the dissipation range.

Purpose of the Study:

To investigate the "bottleneck effect" in three-dimensional (3D) turbulence simulations.
To compare the 3D bottleneck effect with its manifestation in one-dimensional (1D) spectra.
To evaluate the suitability of different spectral analyses for inferring turbulence scaling exponents.

Main Methods:

Performing three-dimensional turbulence simulations at high numerical resolutions.
Analyzing three-dimensional energy spectra and comparing them with one-dimensional spectra.
Examining the relationship between 1D and 3D spectra under isotropy assumptions.
Calculating and comparing transversal, longitudinal, and second-order structure functions.

Main Results:

The bottleneck effect is significantly weaker in one-dimensional spectra compared to three-dimensional spectra.
The observed differences between 1D and 3D spectra can be explained by the transformation between them, assuming an isotropic turbulent velocity field.
Transversal and longitudinal spectra are similar and can be accurately derived from 3D spectra.
Second-order structure functions are less affected by the bottleneck effect.

Conclusions:

The bottleneck effect in turbulence simulations is resolution-dependent and more prominent in 3D spectra.
One-dimensional spectra and second-order structure functions provide more robust insights into turbulence scaling than 3D spectra near the dissipation range.
Computational analysis of turbulence requires careful consideration of spectral dimensionality and analysis methods.