| Title |
Phase and precession evolution in the Burgers equation
|
|---|---|
| Published in |
The European Physical Journal E, March 2016
|
| DOI | 10.1140/epje/i2016-16034-5 |
| Pubmed ID | |
| Authors |
Michele Buzzicotti, Brendan P. Murray, Luca Biferale, Miguel D. Bustamante |
| Abstract |
We present a phenomenological study of the phase dynamics of the one-dimensional stochastically forced Burgers equation, and of the same equation under a Fourier mode reduction on a fractal set. We study the connection between coherent structures in real space and the evolution of triads in Fourier space. Concerning the one-dimensional case, we find that triad phases show alignments and synchronisations that favour energy fluxes towards small scales --a direct cascade. In addition, strongly dissipative real-space structures are associated with entangled correlations amongst the phase precession frequencies and the amplitude evolution of Fourier triads. As a result, triad precession frequencies show a non-Gaussian distribution with multiple peaks and fat tails, and there is a significant correlation between triad precession frequencies and amplitude growth. Links with dynamical systems approach are briefly discussed, such as the role of unstable critical points in state space. On the other hand, by reducing the fractal dimension D of the underlying Fourier set, we observe: i) a tendency toward a more Gaussian statistics, ii) a loss of alignment of triad phases leading to a depletion of the energy flux, and iii) the simultaneous reduction of the correlation between the growth of Fourier mode amplitudes and the precession frequencies of triad phases. |
X Demographics
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Geographical breakdown
| Country | Count | As % |
|---|---|---|
| Unknown | 1 | 100% |
Demographic breakdown
| Type | Count | As % |
|---|---|---|
| Scientists | 1 | 100% |
Mendeley readers
The data shown below were compiled from readership statistics for 13 Mendeley readers of this research output. Click here to see the associated Mendeley record.
Geographical breakdown
| Country | Count | As % |
|---|---|---|
| Unknown | 13 | 100% |
Demographic breakdown
| Readers by professional status | Count | As % |
|---|---|---|
| Student > Ph. D. Student | 6 | 46% |
| Researcher | 2 | 15% |
| Student > Bachelor | 1 | 8% |
| Professor | 1 | 8% |
| Unknown | 3 | 23% |
| Readers by discipline | Count | As % |
|---|---|---|
| Mathematics | 5 | 38% |
| Psychology | 1 | 8% |
| Physics and Astronomy | 1 | 8% |
| Engineering | 1 | 8% |
| Unknown | 5 | 38% |
Attention Score in Context
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#21,270,045
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#585
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Outputs of similar age from The European Physical Journal E
#16
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