Some specific features of chaotization of the pulsating barotropic flow over elliptic and axisymmetric sea-mounts

Abstract

A comparison of the chaotic advection in the barotropic inviscid unidirectional pulsating flow over a sea-mount of axisymmetric and elliptic form is presented. The process of passive markers' transport from vortical region into the flow-through region is studied. In particular the evolution of the corresponding Poincaré sections with the change of frequency and amplitude of oscillations is presented. An approach to study the mechanism and parameters of chaotic advection in the open systems with finite lifetime trajectories is presented, which is based on the study of the distribution of time necessary to carry markers into the flow-through region. The optimal for chaotic mixing frequency of external excitation is calculated. The results show that in the case of elliptic sea-mount chaotic transport of markers can be more efficient than in the axisymmetric case, and the corresponding phase portraits have significantly different structures.

Determination of the optimal excitation frequency range in background flows

“…3, [16][17][18] The paper concludes with a discussion in Sec. II, we formulate a model for the stream function ͑2͒.…”

“…3, [15][16][17] It has been found that there exists, at least, a range of perturbation frequencies for which the chaotic transport is maximal. ͑1͒ and ͑2͒ is the problem of dependence of chaotic transport and mixing on perturbation parameters.…”

“…5,16 Hence, if we uniformly distribute a certain number of markers inside VR and determine which fraction of them will leave this area after a sufficiently long period of time, we will determine the ratio of the number of chaotic trajectories to the total number of trajectories. Using numerical simulation, we analyze the dependence of chaotization degree on perturbation frequency.…”

“…4,5,16 Here is a brief description of these models. 4,5,16 Here is a brief description of these models.…”

Interaction of a monopole vortex with an isolated topographic feature in a three-layer geophysical flow

“…As it has been mentioned above, we are interested only in the singular perturbations of form (4) (without losing any generality, we put the background flow value to be zero, i.e. q * i = 0 (Kozlov, 175 1995;Izrailsky et al, 2004)). Hence, by setting boundary conditions Φ i | r→∞ = 0, and ∂Φ i /∂r| r→∞ = 0 to Laplace and Helmholtz equations (9), we obtain two sets of Green's function superpositions satisfying system (9) for the upper (m = 1) and middle (m = 2) layer monopole propagation 180 cases,…”