Текст диссертации выложен на сайте ИТФ им. Л.Д.Ландау РАН 25 июня 2026г.
Назначить ведущей организацией - Федеральное государственное бюджетное учреждение науки «Институт океанологии им. П.П. Ширшова Российской академии наук»; Назначить официальных оппонентов: Балакина Алексея Антониевича, доктора физико-математических наук, ведущего научного сотрудника (Институт прикладной физики Российской академии наук); Зубарева Николая Михайловича, доктора физико-математических наук, член-корреспондента РАН, главного научного сотрудника (Институт электрофизики Уральского отделения Российской академии наук); Розанова Николая Николаевича, доктора физико-математических наук, академика РАН, главного научного сотрудника (Физико-технический институт им. А.Ф. Иоффе Российской академии наук)

As a follow up of the talk given last Friday, the solution of the problem of the limiting transition to the infinite domain for the capillary waves resonant merging process is shown. The problem of the large factor at the scaling dependence is solved simultaneously.

A new nonlocal spectrum of the weakly turbulent direct energy cascade for capillary waves has been derived analytically and confirmed numerically. In contrast to the well‑known Kolmogorov-Zakharov (Zakharov-Filonenko) solution, which has been known for 60 years, this spectrum is based on nonlocal interaction in the wave‑vector space and manifests itself in the range of scales where the dynamic range of the Kolmogorov-Zakharov spectrum ends. The spectrum is observed both in numerical experiments on isotropic turbulence with forcing and in simulations of decay turbulence.

In a framework of a simplified analytical model, it has been demonstrated that the Kolmogorov-Zakharov spectrum corresponding to the direct energy cascade for capillary waves has a finite dynamic range (the ratio of the minimum and maximum wave vectors). The scaling of this dynamic range as a function of the mean surface steepness has been derived. As a result of the analysis of data from numerous simulations of isotropic wave turbulence with forcing, it has been shown that the analytical scaling is in good agreement with the data from numerical experiments.

Ссылка на объявление о защите на сайте ВАКа.

Текст диссертации выложен на сайте ИТФ им. Л.Д.Ландау РАН 27 мая 2026г.

Назначить ведущей организацией - Математический институт им. В.А. Стеклова Российской академии наук
Назначить официальных оппонентов: Кривонос Сергей Олегович - доктор физико-математических наук, Международная межправительственная организация Объединенный институт ядерных исследовани; Алкалаев Константин Борисович - доктор физико-математических наук, ФГБУН Физический институт им. П.Н. Лебедева РАН

We investigate the correlation function of the intensity of a light beam with a very broad initial profile (in the plane wave limit) as it propagates through a turbulent atmosphere. We explicitly compute, to leading order, the irreducible part of the correlation function for various propagation distances and separations between observation points. The result for large separations exhibits universal power-law behavior, decaying in a power-law fashion for all propagation lengths. For small separations, the correction is independent of the distance between the points. For small distances (weak scintillation regime) it is small and grows according to a power law with increasing z; for large distances (strong scintillation regime) it is small and decreases according to a power law with increasing z; however, in the intermediate regime of moderate scintillations it becomes of order unity, and our expression for the first correction becomes inapplicable.

The report will present a study on a model of columnar coherent vortex in rotating fluid, which flow is maintained by absorption of inertial waves coming from the periphery of the system. Concerning the large-scale vortex flow in a fast-rotating frame, the quasi-linear approximation is justified for such inhomogeneous turbulence theory, when inertial waves have a cumulative effect on the mean flow via Reynolds stress [1], and advection with the vortex flow of waves prevails over wave-wave interaction in their evolution. We study the maintaining of axisymmetric vortex by random incident inertial waves with short-wave statistics, also assuming that viscosity effects are weak. Under such conditions, the dominant mechanism of energy and angular momentum transfer to mean flow is resonant absorption of wave in the vicinity of its critical layer, which was studied in previous work [2]. Considering Reynolds shear stress averaged over the ensemble, we found analytical results for the vortex mean velocity profile, which were compared with experimental evidence [3].

[1] I.V. Kolokolov, L.L. Ogorodnikov, S.S. Vergeles, Phys. Rev. Fluids, 5, 034604 (2020).
[2] N.A. Ivchenko, S.S. Vergeles, Physics of Fluids 37, 126605 (2025).
[3] D.D. Tumachev, S.V. Filatov, S.S. Vergeles, and A.A. Levchenko. JETP Letters, 118: 426–432 (2023).