We report the experimental observation of Richardson dispersion and a double cascade in a thin horizontal fluid flow induced by Faraday waves. The energy spectra and the mean spectral energy flux obtained from particle image velocimetry data suggest an inverse energy cascade with Kolmogorov type scaling E(k) ∝ k(γ), γ ≈ -5/3 and an E(k) ∝ k(γ), γ ≈ -3 enstrophy cascade. Particle transport is studied analyzing absolute and relative dispersion as well as the finite size Lyapunov exponent (FSLE) via the direct tracking of real particles and numerical advection of virtual particles. Richardson dispersion with <ΔR(2)(t)> ∝ t(3) is observed and is also reflected in the slopes of the FSLE (Λ ∝ ΔR(-2/3)) for virtual and real particles.
We describe a two-dimensional CNN array of resistively coupled Chua's circuits which can be designed to implement some elementary aspects of spatial recognition, namely, recognizing open curves from closed ones and locating the shortest path between two locations. In the latter, two situations are analyzed: flat and wrinkled surfaces. The two-dimensional CNN array of Chua's circuits is shown, for the first time, to be capable of finding the shortest path between two points on a wrinkled labyrinth. The performance of this parallel processing approach was examined using computer simulations although this method can be implemented in real time via VLSI technology.
Based on ten years (1998–2007) of satellite ocean color data we analyze the spatiotemporal patterns in the seasonal Madagascar plankton bloom with respect to the advection of the recently discovered Southern Indian Ocean Countercurrent (SICC). In maps of Finite‐time Lyapunov Exponents (FTLE) and Finite‐Time Zonal Drift (FTZD) computed from altimetry derived velocities we observe a narrow zonal jet that starts at ∼25°S at the southern tip of Madagascar, an important upwelling region, and extends to the east further than the largest plankton blooms (∼2500 km). In bloom years, the jet coincides with large parts of the northern boundary of the plankton bloom, acting as a barrier to meridional transport. Our findings suggest that advection is an important and so far underestimated mechanism for the eastward propagation and the extent of the plankton bloom. This supports the hypothesis of a single nutrient source south of Madagascar.
Sprial breakup in the Belousov-Zhabotinsky reaction has been observed under the influence of an externally applied alternating electric current. The dynamic mechanism of this breakup is explained in the framework of this reaction. The dependence of the critical electric current amplitude on the period of the wave and on the excitability of the medium is analyzed. Spiral breakup is shown to provide a limit of validity of electric-field-induced drift of vortices in excitable media. Experimental results are complemented with numerical simulations provided by two- and three-variable Oregonator models.
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