Russian Journal of Earth Sciences Russian Journal of Earth Sciences Russian Journal of Earth Sciences 1681-1208 57832 10.2205/2023ES000853 HFFKNC ОРИГИНАЛЬНЫЕ СТАТЬИ ORIGINAL ARTICLES ОРИГИНАЛЬНЫЕ СТАТЬИ Asymptotics of Far Fields of Surface and Internal Gravitational Waves from Local and Nonlocal Perturbation Sources Асимптотики дальних полей поверхностных и внутренних гравитационных волн от локальных и нелокальных источников возмущений https://orcid.org/0000-0002-8251-2370 Владимиров Игорь Юрьевич Vladimirov Igor' Yur'evich iyuvladimirov@rambler.ru

кандидат физико-математических наук;

candidate of physical and mathematical sciences;

 Институт океанологии им. П.П. Ширшова РАН Москва Россия Shirshov Institute of Oceanology of Russian Academy of Sciences Moscow Russian Federation 10 12 2023 10 12 2023 23 4 1 13 21 03 2023 22 05 2023 https://rjes.ru/en/nauka/article/57832/view

Исследованы дальние поля внутренних гравитационных волн от радиально-симметричного начального возмущения линий равной плотности в слое стратифицированной среды конечной толщины, а также дальние поля поверхностных волн от импульсного источника в однородной жидкости конечной глубины. Получены интегральные представления волновых возмущений. Построены равномерные и неравномерные асимптотические решения, позволяющие описывать амплитудно-фазовую структуру дальних полей поверхностных и внутренних волн. Установлено, что равномерные асимптотики позволяют эффективно рассчитывать дальние волновые поля как вблизи, так и вдали от волнового фронта.

The far fields of internal gravity waves from a radially symmetric initial perturbation of lines of equal density in a layer of a stratified medium of finite thickness, as well as the far fields of surface waves from an impulse source in a homogeneous liquid of finite depth, are studied. Integral representations of wave perturbations are obtained. Uniform and non-uniform asymptotic solutions are constructed that allow describing the amplitude-phase structure of the far fields of surface and internal waves. It is established that uniform asymptotics make it possible to effectively calculate long range wave fields both near and far from the wave front.

 стратифицированная среда внутренние гравитационные волны дальние поля поверхностные волны равномерные асимптотики волновой фронт функция Эйри stratified medium internal gravitational waves far fields surface waves uniform asymptotics wave front Airy function. Работа выполнена по теме государственного задания № FMWE-2021-0002. The work was carried out on the topic of state assignment No. FMWE-2021-0002.

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