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JMSE
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Nonlinear Wave Dynamics and Wake Structure
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Nonlinear Wave Dynamics and Wake Structure

A special issue of Journal of Marine Science and Engineering (ISSN 2077-1312). This special issue belongs to the section "Physical Oceanography".

Deadline for manuscript submissions: closed (15 September 2022) | Viewed by 7143

Special Issue Editor

Prof. Igor Shugan

E-Mail Website1 Website2
Guest Editor
1. P.P. Shirshov Institute of Oceanology RAS, 117991 Moscow, Russia
2. Department of Marine Environment and Engineering, National Sun Yat-Sen University, Kaoshiung 80424, Taiwan
Interests: fully nonlinear waves; frequency downshift; breaking waves; vorticity waves; nonlinear dispersion; waves on current; ship wake

Special Issue Information

Dear Colleagues,

The nonlinear dynamics of water surface waves demonstrates a great variety of manifestations and reveals many unexpected properties that do not fit into the framework of existing ideas. Experimental studies of the last two decades have revealed a number of new effects in the behavior of waves, which urgently require their proper theoretical study.

Nonlinear dispersion of waves, well studied in weakly nonlinear models, still remains the object of active research in completely nonlinear wave models. The specific task of this issue is the study of highly nonlinear and dissipative processes, the transformation of breaking waves, and the evolution of the wave spectrum in the deep-water and coastal zones of the sea.

The propagation of surface waves is usually accompanied by the influence of wind, coastal currents, tides, etc. Another theme of the issue is a radical change in the behavior of waves in the presence of the indicated “external” influences.

The ship’s wake is one of the most striking examples of sea waves observed directly in natural conditions. One of the topics of the issue is the study of the structure of the ship’s wave wake under the influence of currents and wind in the coastal zone and in the open ocean.

Prof. Igor Shugan
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Journal of Marine Science and Engineering is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Fully nonlinear waves
  • Frequency downshift
  • Breaking waves
  • Vorticity waves
  • Nonlinear dispersion
  • Waves on current
  • Ship wake

Published Papers (4 papers)

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Research

12 pages, 2362 KiB  
Article
Ship’s Wake on a Finite Water Depth in the Presence of a Shear Flow
by Igor Shugan and Yang-Yih Chen
J. Mar. Sci. Eng. 2022, 10(7), 926; https://doi.org/10.3390/jmse10070926 - 4 Jul 2022
Viewed by 1096
Abstract
The ship’s wake in the presence of a shear flow of constant vorticity at a finite water depth is investigated by expanding the Whitham-Lighthill kinematic theory. It has been established that the structure of a wave ship wake radically depends on Froude number [...] Read more.
The ship’s wake in the presence of a shear flow of constant vorticity at a finite water depth is investigated by expanding the Whitham-Lighthill kinematic theory. It has been established that the structure of a wave ship wake radically depends on Froude number Fr (in terms of water depth) and especially on the critical Froude number Frcr, which depends on the magnitude and direction of the shear flow. At its subcritical values Fr<Frcr two types of waves are presented: long transverse and short divergent waves inside the wedge area with an angle depending on Fr For the supercritical range Fr>Frcr only divergent waves are presented inside the wake region. Critical Froude number Frcr is variable and mostly depends on collinear with the ship path component of the shear flow: it decreases with the unidirectional shear flow and increases on the counter shear current. The wedge angle of the ship wake expands with an increase in the unidirectional shear flow and narrows in the oncoming flow in the subcritical mode of the ship’s motion Fr<Frcr. Wake angle decreased with Froude number for Fr>Frcr and only divergent waves with the crests almost collinear with ship path are finally presented in the narrow ship wake. For a critical value of the Froude number Fr=Frcr, the ship’s wake has a total wedge angle of 180° with waves directed parallel to the ship’s motion. The presence of a shear flow crossing the path of the ship gives a strong asymmetry to the wake. An increase in the perpendicular shear flow leads to an increase in the difference between the angles of the wake arms. Full article
(This article belongs to the Special Issue Nonlinear Wave Dynamics and Wake Structure)
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25 pages, 9791 KiB  
Article
A 2D Model for 3D Periodic Deep-Water Waves
by Dmitry Chalikov
J. Mar. Sci. Eng. 2022, 10(3), 410; https://doi.org/10.3390/jmse10030410 - 11 Mar 2022
Cited by 4 | Viewed by 1783
Abstract
The paper is devoted to further development of an accelerated method for simulation of the two-dimensional surface waves at infinite depth with the use of a two-dimensional model derived with simplifications of the three-dimensional equations for potential periodic deep-water waves. A 3D full [...] Read more.
The paper is devoted to further development of an accelerated method for simulation of the two-dimensional surface waves at infinite depth with the use of a two-dimensional model derived with simplifications of the three-dimensional equations for potential periodic deep-water waves. A 3D full wave model (FWM) is based on a numerical solution of a 3D Poisson equation written in the surface-fitted coordinates for a nonlinear component of the velocity potential. For sufficient vertical resolution used for the Poisson equation, the 3D model provides very high accuracy. The simplified model is based on the 2D Poisson equation written for a free surface. This exact equation contains both the first and second derivatives of the velocity potential, i.e., it is unclosed. The analysis of the accurate solutions for the 3D velocity potential obtained with the 3D model shows that those variables are linearly connected to each other. This property allows us to obtain a 2D equation for the first derivative of the velocity potential (i.e., vertical velocity on surface), which gives the closed 2D formulation for a 3D problem of two-dimensional waves. The previously developed scheme was not universal since the parameters of the closure scheme had to be adjusted to the specific setting. The current paper offers a new formulation of a closing scheme based on the integral parameters of wave field. The method of closing the equations, as well as the numerical parameters, were chosen on the basis of the multiple numerical experiments with the full nonlinear wave model (FWM) and selection of a suitable closing scheme. That is why the given model can be called Heuristic Wave Model (HWM). The connection between the first and second variables is not precise; hence, the method as a whole cannot be exact. However, the derived 2D model is able to reproduce different statistical characteristics of the 2D wave field with good accuracy. The main advantage of the model developed is its high performance exceeding that of 3D model by about two decimal orders. Full article
(This article belongs to the Special Issue Nonlinear Wave Dynamics and Wake Structure)
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14 pages, 1402 KiB  
Article
Wave Energy Dissipation of Spilling and Plunging Breaking Waves in Spectral Models
by Yana Saprykina, Burak Aydogan and Berna Ayat
J. Mar. Sci. Eng. 2022, 10(2), 200; https://doi.org/10.3390/jmse10020200 - 1 Feb 2022
Viewed by 1610
Abstract
On the basis of field experiments and modeling, the dependence of the dissipation of the energy of waves breaking by plunging and spilling on the frequency of wave spectra was investigated. It was shown that the modeling of wave breaking should take into [...] Read more.
On the basis of field experiments and modeling, the dependence of the dissipation of the energy of waves breaking by plunging and spilling on the frequency of wave spectra was investigated. It was shown that the modeling of wave breaking should take into account the compensation of the nonlinear growth of higher wave harmonics, which occurs in different ways for waves breaking with different types and for different methods of modeling a nonlinear source term. The study revealed that spilling breaking waves have a frequency selectivity of energy dissipation at frequencies of second and third harmonics for the Boussinesq and SWAN models for any method of modeling a nonlinear source term. Plunging breaking waves have a quadratic dependence of the dissipation coefficient on frequency in the Boussinesq model and SWAN model with the SPB approximation for a nonlinear source term. The SWAN model with default LTA approximation for plunging breaking waves also assumes frequency-selective energy dissipation. The discrepancy between the LTA default method and others can be explained by the overestimation of the contribution of the second nonlinear harmonic and by inaccurate approximation for the biphase. It is possible to improve the accuracy of LTA and SPB methods by tuning SWAN model coefficients. Full article
(This article belongs to the Special Issue Nonlinear Wave Dynamics and Wake Structure)
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11 pages, 2194 KiB  
Article
Energy Spectra of Ensemble of Nonlinear Capillary Waves on a Fluid
by Elena Tobisch and Alexey Kartashov
J. Mar. Sci. Eng. 2021, 9(12), 1422; https://doi.org/10.3390/jmse9121422 - 12 Dec 2021
Cited by 1 | Viewed by 1858
Abstract
The problem of spectral description of the nonlinear capillary waves on the fluid surface is discussed. Usually, three-wave nonlinear interactions are considered as a major factor determined by the energy spectrum of these waves in the kinetic wave turbulent regime. We demonstrate that [...] Read more.
The problem of spectral description of the nonlinear capillary waves on the fluid surface is discussed. Usually, three-wave nonlinear interactions are considered as a major factor determined by the energy spectrum of these waves in the kinetic wave turbulent regime. We demonstrate that four-wave interactions should be taken into account. In this case, there are two possible scenarios for the transfer of energy over the wave spectrum: kinetic and dynamic. The first is described by the averaged stochastic interaction of waves using the kinetic equation, while the second is described by dynamic equations written for discrete modes. In this article, we compare the time scales, spectral shapes, and other properties of both energy cascades, allowing them to be identified in an experiment. Full article
(This article belongs to the Special Issue Nonlinear Wave Dynamics and Wake Structure)
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