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.
The chaotization of a vortical flow caused by a nonstationary incident flow is studied by the examples of several dynamically consistent models. It is shown that for relatively small values of excitation amplitude, the chaotization of such flows and, correspondingly, chaotic transport of passive scalars is determined by a small number of nonlinear resonances with frequencies close to the excitation frequency. Hence, the analysis of locations and overlaps of these resonances in the considered models makes it possible to derive fairly good estimates of excitation frequencies that are optimal for the chaotic transport.
Ключевые слова: математическая модель, популяция, размер особи, флуктуации среды обитания, оптимальный сбор урожая, рыболовство, промысловое усилие, доход Работа выполнена при частичной финансовой поддержке комплексной программы фундаментальных исследований Дальневосточного отделения РАН «Дальний Восток», проект № 15-I-4-006 o (0262-2015-0067).
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