Determination of the optimal excitation frequency range in background flows

Abstract

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.

Diffusion-affected passive scalar transport in an ellipsoidal vortex in a shear flow

“…2) starts moving irregularly, that is, two close fluid particle trajectories exponentially diverge in a finite time. Also, a certain amount of the fluid (two "islands" of regular motion astride the vortex) is involved in regular motion (a great body of literature concerning chaotic advection in geophysical hydrodynamics can be found in Koshel and Prants, 2006;Koshel et al, 2008;Izrailsky et al, 2008). It is worth mentioning that the trajectories of fluid particles, contained within the ellipsoidal vortex (grey region), cannot intersect the vortex's boundary.…”

Baroclinic multipole evolution in shear and strain

“…With such a choice of perturbation parameters, the trajectories corresponding to the 1 : 1 resonance exist only in closed domains; they are localized near elliptic points and located far enough from trajectories of 1 : 2 resonances. Therefore, we can expect only overlapping of 1 : 2 and 1 : 3 resonance domains or (if the perturbation amplitude is sufficiently small) 1 : 3 and 1 : 4 resonance domains (Izrailsky et al 2006(Izrailsky et al , 2008. In this case, there exists a probability that a narrow stochastic layer will appear in the neighborhood of separatrices; the closed domains and, more significantly, the domain between separatrices, will remain mostly regular (Izrailsky et al 2008).…”

“…Therefore, we can expect only overlapping of 1 : 2 and 1 : 3 resonance domains or (if the perturbation amplitude is sufficiently small) 1 : 3 and 1 : 4 resonance domains (Izrailsky et al 2006(Izrailsky et al , 2008. In this case, there exists a probability that a narrow stochastic layer will appear in the neighborhood of separatrices; the closed domains and, more significantly, the domain between separatrices, will remain mostly regular (Izrailsky et al 2008). In such a situation, a regular barrier should persist in this domain.…”

“…Their evaluation requires the knowledge of the rotation frequencies of vortices along the closed trajectories. This allows the determination of parameters of the unsteady external flow, which are optimal for the appearance of chaotic regimes (Izrailsky et al 2006(Izrailsky et al , 2008 or for the manifestation of some specific effects of chaotization . Figure 8 gives the dependence of rotation frequency for lower layer vortices on their initial position x 0 or y 0 on the x-or y-axis for some sets of trajectories of figure 2.…”

Complex Plankton Dynamics in a Topographic Eddy

“…Несмотря на то, что анализу перемешивания и переноса примесей в топографических вихрях посвящено много публикаций (см., например, [12]), влияние на транспорт частоты внешнего возмущения остается недостаточно изученным.…”