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University of Texas Rio Grande Valley
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
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Full-Text Articles in Physical Sciences and Mathematics
Dissipation Scales And Anomalous Sinks In Steady Two-Dimensional Turbulence, Eleftherios Gkioulekas
Dissipation Scales And Anomalous Sinks In Steady Two-Dimensional Turbulence, Eleftherios Gkioulekas
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
In previous papers I have argued that the fusion rules hypothesis, which was originally introduced by L’vov and Procaccia in the context of the problem of three-dimensional turbulence, can be used to gain a deeper insight in understanding the enstrophy cascade and inverse energy cascade of two-dimensional turbulence. In the present paper, we show that the fusion rules hypothesis, combined with nonperturbative locality, itself a consequence of the fusion rules hypothesis, dictates the location of the boundary separating the inertial range from the dissipation range. In so doing, the hypothesis that there may be an anomalous enstrophy sink …
Bifurcations Of Traveling Wave Solutions For An Integrable Equation, Jibin Li, Zhijun Qiao
Bifurcations Of Traveling Wave Solutions For An Integrable Equation, Jibin Li, Zhijun Qiao
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
This paper deals with the following equation mt= 1/2 1/mk xxx− 1/2 1/mk x, which is proposed by Z. J. Qiao J. Math. Phys. 48, 082701 2007 and Qiao and Liu Chaos, Solitons Fractals 41, 587 2009. By adopting the phase analysis method of planar dynamical systems and the theory of the singular traveling wave systems to the traveling wave solutions of the equation, it is shown that for different k, the equation may have infinitely many solitary wave solutions, periodic wave solutions, kink/antikink wave solutions, cusped solitary wave solutions, and breaking loop solutions. We discuss in a detail the …