Anomalous transport of a passive scalar at the transition to dynamical chaos in a barotropic shear layer

Реутов, В. П.; Rybushkina, G. V.

doi:10.1016/j.euromechflu.2018.11.017

Cited by 6 publications

(24 citation statements)

References 28 publications

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“…[ [17,20], введем параметр надкритичности течения  U U c / . Отметим, что изменение γ приводит к изменению безразмерных параметров, входящих в (4),…”

Section: основные уравнения и граничные условияunclassified

“…АНОМАЛьНый ПЕРЕНОС ПРИМЕСИ Система уравнений (4)-(6) решалась численно с помощью псевдоспектрального метода в трактовке работ [26,27]. Решение для осциллирующих по координате x полей представлялось в виде усеченных комплексных рядов Фурье [17]. Производные по координате y аппроксимировались конечными разностями второго порядка точности.…”

Section: основные уравнения и граничные условияunclassified

“…Неопределенность в выборе дополнительных нейтральных мод, которая является поводом для критики кинематических моделей [13], исключается в динамически согласованных моделях, основанных на решении полной нелинейной сис темы уравнений движения жидкости, которая позволяет изучать движение частиц-трассеров в режиме насыщения баротропной неустойчивости [13][14][15][16][17][18]. В работе [14] рассмотрена динамическая модель аномального переноса в баротропной меандрирующей струе.…”

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“…Однако условия малой толщины критического слоя и малой диссипации, необходимые для реализации данной модели, зачастую трудновыполнимы. В работах [16,17] разрабатывались динамические модели аномального переноса в слоях сдвига с модифицированным профилем скорости. В [16] показано, что течение в виде вязкого слоя сдвига с двумя максимумами на профиле завихренности имеет две неустойчивые моды, фазовые скорости которых различны.…”

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“…Обнаружен лагранжев хаос (перемешивание жидких частиц) при регулярном и хаотическом эйлеровом поле скорости. В [17] построена динамическая модель аномального переноса для течения типа слоя сдвига с немонотонным равновесным профилем скорости. В отличие от [16] рассмотрено возбуждение цепочки, содержащей семь структур на периоде c учетом вязкости, бета-эффекта и внешнего (донного) трения, что в большей степени соответствует геофизическим приложениям.…”

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Unsteady chains of wave structures and anomalous transport of а passive scalar in a barotropic jet flow

Reutov¹,

Rybushkina²

2019

Известия Российской академии наук. Физика атмосферы и океана

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The onset of anomalous transport of a passive scalar at the excitation of unsteady chains of wave structures with closed streamlines in a barotropic jet flow modeling zonal flows in the Earths atmosphere and ocean and in laboratory experiments is investigated. The analysis is performed within a dynamical model describing saturation of the barotropic instability in a plane-parallel channel flow with allowance for the beta-effect and external friction. The equations of a quasi-two-dimensional flow are solved numerically with the aid of a pseudospectral method. It is found that the generation of high modes in a jet with a two-hump velocity profile leads to accelerated transition to the complex dynamics, at which an increase in supercriticality first gives rise to а multiharmonic regime with a discrete spectrum. The exponents of the power dependence on the time of the averaged (over the ensemble) tracer particle displacement and its variance are computed for the basic generation regimes, which confirms the occurrence of anomalous diffusion of the scalar. A self-similar probability density function of tracer displacements is obtained and the dependence of the transition to complex dynamics on the number of vortices in the chain and on the strength of the beta-effect is elucidated. Numerical estimates are presented, which confirm the possibility of generation of unsteady vortex chains and the related anomalous transport of the scalar.barotropic flow; chains of wave structures; dynamical chaos; anomalous advection and diffusion

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Section: основные уравнения и граничные условияunclassified

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Unsteady chains of wave structures and anomalous transport of а passive scalar in a barotropic jet flow

Reutov¹,

Rybushkina²

2019

Известия Российской академии наук. Физика атмосферы и океана

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Transition to the dynamical chaos and anomalous transport of a passive scalar in the annular Kolmogorov flow

Реутов

Rybushkina

2020

Physics of Fluids

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In this paper, we are concerned with the transition to dynamical chaos and related anomalous transport of a passive scalar in the annular Kolmogorov flow, which is considered as a model of the barotropic zonal flows in the Earth’s atmosphere and ocean or their laboratory analogs. The investigation of the anomalous transport is conducted within a dynamically consistent flow model describing the saturation of barotropic instability. The analysis is based on the numerical solution of equations of a quasi-two-dimensional flow in an annular channel with rigid walls taking into account the beta-effect and external (bottom) friction. It is supposed that the sinusoidal velocity profile of the Kolmogorov flow has three periods inside a channel and the sticking condition on the channel walls is satisfied. Four basic regimes arising with increasing flow supercriticality, the last of which corresponds to dynamical chaos, are distinguished. It is found that five modulated chains of wave-vortex structures with closed streamlines are formed in the channel and their temporal behavior is studied by making videos. The frequency–wavenumber spectra of the longitudinal velocity at certain values of radial coordinates are drawn and the largest Lyapunov exponent is determined in the regime of dynamical chaos. The relationship between the streamlines behavior and the discrete peaks of frequency–wavenumber spectra is elucidated. The occurrence of anomalous transport of a passive scalar is confirmed by drawing trajectories of tracer particles, as well as by determining exponents of the time dependence of mean particle displacement and its variance.

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Unsteady Chains of Wave Structures and Anomalous Transport of Passive Admixture in a Barotropic Jet Flow

Реутов

Rybushkina

2019

Izv. Atmos. Ocean. Phys.

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Anomalous transport of a passive scalar at the transition to dynamical chaos in a barotropic shear layer

Cited by 6 publications

References 28 publications

Unsteady chains of wave structures and anomalous transport of а passive scalar in a barotropic jet flow

Unsteady chains of wave structures and anomalous transport of а passive scalar in a barotropic jet flow

Transition to the dynamical chaos and anomalous transport of a passive scalar in the annular Kolmogorov flow

Unsteady Chains of Wave Structures and Anomalous Transport of Passive Admixture in a Barotropic Jet Flow

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