Sergei Badulin | Ocean County College (original) (raw)

Papers by Sergei Badulin

arXiv (Cornell University), Jul 11, 2022

The asymptotic solutions for linear waves generated by oscillating source of elliptic shape in th... more The asymptotic solutions for linear waves generated by oscillating source of elliptic shape in the motionless media is constructed with the recently developed Reference Solution Approach (RSA). Pronounced anisotropy of the solutions is found for elongated sources both for amplitudes and phases of the resulting wave pattern. The classic Kelvin angles of the ship wave patterns determine specific directions of this anisotropy, thus, demonstrating the role of wave dispersion. The analytical results within the RSA are shown to agree remarkably well with exact solutions of the linear wave problem.

Journal of Oceanological Research

In the early morning of August 20, 2023, at the age of 85, the outstanding Soviet and Russian sci... more In the early morning of August 20, 2023, at the age of 85, the outstanding Soviet and Russian scientist, poet and public figure, Academician, Doctor of Physical and Mathematical sciences Vladimir Evgenievich Zakharov passed away. On August 1, he celebrated his 84th birthday. For many years, Academician Zakharov headed the Laboratory of Nonlinear Wave Processes at the Shirshov Institute of Oceanology of RAS and actively participated in the development of the Institute as a center of advanced fundamental research. Based on the memories of colleagues, the author examines the role of Vladimir Evgenievich in the life of the Institute and the place of the Institute in the life of Vladimir Evgenievich himself. A brief summary of the main stages of his eventful life as a world-famous scientist, talented poet and concerned citizen is given at the end of the article. A large selection of materials about the life of Vladimir Evgenievich can be found on the memorial page (http://kao.itp.ac.ru/Z...

The authors appreciate efforts of the reviewer and his/her valuable comments. The paper is signif... more The authors appreciate efforts of the reviewer and his/her valuable comments. The paper is significantly updated: almost all the figures have been re-drawn, additional numerical runs have been carried out as recommended by one of referee for longer duration and with higher directional resolution. Ten new references appeared in the paper bibliography. A native speaker who checked the text has made very few suggestions in English style and grammar. Our answers follow the reviewer's report.

Теоретическая и математическая физика, Feb 27, 2020

Рассматривается обобщение кинетического уравнения Хассельманна, предложенное Ньюэллом и Захаровым... more Рассматривается обобщение кинетического уравнения Хассельманна, предложенное Ньюэллом и Захаровым в 2008 г. Новое уравнение учитывает не только резонансные четырехволновые взаимодействия, но и диссипацию, связанную с обрушением волн. В уравнение вводится функция диссипации, зависящая от потока энергии по спектру. Эта функция определена с точностью до функционального параметра, оптимальный выбор которого должен быть сделан по результатам сравнения с экспериментом. Кинетическое уравнение, снабженное такой функцией диссипации, должно описывать обычно наблюдаемый в экспериментах переход от спектра Колмогорова-Захарова E(omega)simomega−4E(\omega)\sim\omega^{-4}E(omega)simomega−4 к спектру Филлипса E(omega)simomega−5E(\omega)\sim\omega^{-5}E(omega)simomega−5. Версию функции диссипации, выраженную в терминах спектра энергии, можно использовать в задачах численного моделирования и прогноза морского волнения.

Remote Sensing of Environment, Nov 1, 2021

Abstract As an extension of wave period inversion models based on altimetry data by an artificial... more Abstract As an extension of wave period inversion models based on altimetry data by an artificial neural network approach, a Deep Neural Network approach (DNN) mean wave period model is developed by introducing new parameters as DNN inputs. In addition to conventional altimeter-derived parameters such as significant wave height (SWH) and the normalized radar cross-section (NRCS) sigma0, the spatial (along-track) SWH gradient and SWH standard deviation (STD) for standard 1-s altimetry data are assumed to be responsible for random wave field dynamics and, thus, for the observed characteristic mean wave period. A comparison with in situ measurements of wave buoys shows higher accuracy of the novel DNN models by using these new parameters. The wave period estimation from DNN model is also consistent with the latest wave reanalysis and indicates less bias when compared to the buoys. The global mean wave steepness distribution from the DNN model shows good agreement with those provided by the wave reanalysis. The sensitivity of input variables sigma0, SWH, SWH gradient, and SWH STD on the results of the DNN model are also investigated. Perspectives on the DNN method for developing universal mission-independent wave period models are discussed. Objectives of the work The mean wave period is an important parameter for characterizing wave properties and can be retrieved from altimeter observations. Considering random wave field dynamics, we present a deep neural network (DNN) model for mean wave period retrieval by introducing the SWH gradient and standard deviation as the inputs. The mean wave period estimation of the DNN model shows good agreement with the latest wave reanalysis and less bias compared to buoys. In an attempt to make the DNN mean wave period retrieval model universal, a method of applying DNN model cross-altimetry missions is presented.

Nonlinear Processes in Geophysics, Jun 6, 2017

Moscow University Physics Bulletin, Jul 1, 2017

The classic problem of linear wave-packet propagation in a dispersive medium is considered. Asymp... more The classic problem of linear wave-packet propagation in a dispersive medium is considered. Asymptotic equations of the Cauchy problem for two-dimensional Gaussian wave packets are constructed in terms of Fourier integrals. These asymptotic solutions are regular at the caustics and describe new physical features of wave-packet propagation: rotation in space and formation of a wave front with anomalously slow dispersion (quasi-dispersive).

Authors are grateful to the referee for attentive reading of the manuscript and valuable comments... more Authors are grateful to the referee for attentive reading of the manuscript and valuable comments and suggestions. The authors took all these comments into account when preparing the revised version. Many changes are made in the text, almost all the figures have been re-drawn, additional numerical runs have been carried out as recommended by the referee for longer duration and with higher directional resolution. Ten new references appeared in the paper bibliography. Finally, the paper becomes three pages longer. A native speaker who checked the text has made very few suggestions in English style and grammar.

Proceedings of the First International Conference on Ocean Thermohydromechanics-2017, Nov 30, 2017

Earth and Space Science, Mar 1, 2022

The article presents a joint analysis of wind and wave characteristics derived from Voluntary Obs... more The article presents a joint analysis of wind and wave characteristics derived from Voluntary Observing Ship (VOS) data and measurements of the innovative Ku‐band radar SWIM (Surface Waves Investigation and Monitoring) carried by Chinese‐French Ocean SATellite (CFOSAT). Global distributions of significant wave height and wind speed in both data sets demonstrate good qualitative and quantitative agreement, especially in regions with a high spatio‐temporal density of visual observations. A particular focus is made on discriminating wave systems by joint analysis of separately observed wind sea and swell characteristics in VOS and the partitions of wave spectra measured by SWIM. It is shown that three wave partitions from SWIM cannot be clearly attributed to wind sea, first, and secondary swell systems. The first partition aggregates both wind sea and swell in the operational wavelength range of the SWIM radar, while the second and third partitions fit neither wind sea, nor swell. A comparison of VOS and SWIM data within a 50 km radius and a 30 min time lag shows a very close match for most parameters in terms of mean values, yet with relatively high dispersion of individual measurements.

Pure and Applied Geophysics, 2021

This paper considers the interaction of Rossby waves with large-scale flows. We focus on the case... more This paper considers the interaction of Rossby waves with large-scale flows. We focus on the case of a non-zonal baroclinic plane-parallel flow with vertical shear. We develop short-wave asymptotics for linear waves in the vicinity of the critical layer. Vertical wave modes (eigenfunctions) of the corresponding boundary problem are presented in terms of Hermite polynomials. In addition to the classical case, when the wave modes are focused on the absolute minimum of the vertical profile of the baroclinic flow velocity, we show that there is another option when a mode is formed with focusing not on the minimum, but the absolute maximum of the vertical profile of the background flow velocity. The new option makes it possible to implement new dynamical regimes that are considered in the paper. We obtain a new criterion that limits the number of vertical modes and, thus, determines regimes of the mode localization in depth or its de-localization. Theoretical criteria of different regimes of Rossby wave dynamics in the non-zonal baroclinic are presented in terms of two dimensionless variables: B associated with "an effective β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document} -parameter" and S=N2/f2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S=N^2/f^2$$\end{document} (N is the Brunt–Väisälä frequency, and f is the Coriolis parameter). The analysis of experimental data shows the relevance of theoretically predicted effects.

The role of nonlinear transfer in dynamics of wind-driven waves is a subject of heated discussion... more The role of nonlinear transfer in dynamics of wind-driven waves is a subject of heated discussion for last years. The result of this discussion gives a key to burning problems of wave modelling: what constituents of wind wave balance should be attacked first both theoretically and experimentally? Recent studies (Resio et al., 2004; Zakharov, 2005; Badulin et al., 2005b) shows definitely the leading role of nonlinear transfer for growing wind seas. Effective asymptotic models of wind-driven seas can be proposed in this case. The asymptotic model of growing wind sea has been presented recently as the split balance model (Badulin et al., 2005a, 2006, 2007). Within the model the spectral evolution is described by conservative kinetic equation (Hasselmann, 1962) for wave action spectral density N(k, t)

Modern day studies of wind-driven sea waves are usually focused on wind forcing rather than on th... more Modern day studies of wind-driven sea waves are usually focused on wind forcing rather than on the effect of resonant nonlinear wave interactions. The authors assume that these effects are dominating and propose a simple relationship between instant wave steepness and time or fetch of wave development expressed in wave periods or lengths. This law does not contain wind speed explicitly and relies upon this asymptotic theory. The validity of this law is illustrated by results of numerical simulations, in situ measurements of growing wind seas and wind wave tank experiments. The impact of the new vision of sea wave physics is discussed in the context of conventional approaches to wave modeling and forecasting.

Theoretical and Mathematical Physics, 2020

We consider an extension of the kinetic equation developed by Newell & Zakharov [1]. The new equa... more We consider an extension of the kinetic equation developed by Newell & Zakharov [1]. The new equation takes into account not only the resonant four-wave interactions but also the dissipation associated with the wave breaking. A dissipation function that depends on the spectral energy flux is introduced into the equation. This function is determined up to a functional parameter, which optimal choice should be made based on comparison with experiment. A kinetic equation with this dissipation function describes the transition from the Kolmogorov-Zakharov spectrum E(ω) ∼ ω −4 to the Phillips spectrum E(ω) ∼ ω −5 usually observed experimentally. The version of the dissipation function expressed in terms of the energy spectrum can be used for wave modelling and prediction of sea waves.