dorsal/arxiv
View SchemaNumerical Proof of Self-Similarity in Burgers' Turbulence
| Authors | Erik Aurell, Sergey N. Gurbatov, Sergey I. Simdyankin |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9602005 |
| URL | https://arxiv.org/abs/patt-sol/9602005 |
Abstract
We study the statistical properties of solutions to Burgers' equation, $v_t + vv_x = \nu v_{xx}$, for large times, when the initial velocity and its potential are stationary Gaussian processes. The initial power spectral density at small wave numbers follows a steep power-law $E_0(k) \sim |k|^n$ where the exponent $n$ is greater than two. We compare results of numerical simulations with dimensional predictions, and with asymptotic analytical theory. The theory predicts self-similarity of statistical characteristics of the turbulence, and also leads to a logarithmic correction to the law of energy decay in comparison with dimensional analysis. We confirm numerically the existence of self-similarity for the power spectral density, and the existence of a logarithmic correction to the dimensional predictions.
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"abstract": "We study the statistical properties of solutions to Burgers\u0027 equation, $v_t +\nvv_x = \\nu v_{xx}$, for large times, when the initial velocity and its\npotential are stationary Gaussian processes. The initial power spectral density\nat small wave numbers follows a steep power-law $E_0(k) \\sim |k|^n$ where the\nexponent $n$ is greater than two. We compare results of numerical simulations\nwith dimensional predictions, and with asymptotic analytical theory. The theory\npredicts self-similarity of statistical characteristics of the turbulence, and\nalso leads to a logarithmic correction to the law of energy decay in comparison\nwith dimensional analysis. We confirm numerically the existence of\nself-similarity for the power spectral density, and the existence of a\nlogarithmic correction to the dimensional predictions.",
"arxiv_id": "patt-sol/9602005",
"authors": [
"Erik Aurell",
"Sergey N. Gurbatov",
"Sergey I. Simdyankin"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"title": "Numerical Proof of Self-Similarity in Burgers\u0027 Turbulence",
"url": "https://arxiv.org/abs/patt-sol/9602005"
},
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