TY - JOUR

T1 - Nonlinear internal wave packets in shelf zone

AU - Makarenko Nikolay, I.

AU - Liapidevskii Valery, Yu

AU - Denisenko Danila, S.

AU - Kukushkin Dmitri, E.

N1 - Макаренко Н.И., Ляпидевский В.Ю., Денисенко Д.С., Кукушкин Д.Е. Пакеты нелинейных внутренних волн в шельфовой зоне // Вычислительные технологии. - 2019. - Т. 24. - № 2. - С. 90-98

PY - 2019/2/1

Y1 - 2019/2/1

N2 - The problem on nonlinear internal waves propagating permanently in shallow fluid is studied semi-analytically in comparison with the field data measured on the sea shelf. At present, the most studied in this context are nonlinear solitary-type waves generated due to the tidal activity over continental slope. This paper deals with periodic cnoidaltype wave packets considered in the framework of mathematical model of continuously stratified fluid. Basic model involves the Dubreil-Jacotin-Long equation for a stream function that results from stationary fully non-linear 2D Euler equations. The longwave approximate equation describing periodic non-harmonic waves is derived by means of scaling procedure using small Boussinesq parameter. This parameter characterizes slight stratification of the fluid layer with the density profile being close to the linear stratification. The fine-scale density plays important role here because it determines the non-linearity rate of model equation, so it permits to consider strongly non-linear dispersive waves of large amplitude. As a result, constructed asymptotic solutions can simulate periodic wave-trains of sub-surface depression coupled with near-bottom wavetrains of isopycnal elevation. It is demonstrated that calculated wave profiles are in good qualitative agreement with internal wave structures observed by the authors in the field experiments performed annually during 2011-2018 in expeditions on the shelf of the Japanese sea.

AB - The problem on nonlinear internal waves propagating permanently in shallow fluid is studied semi-analytically in comparison with the field data measured on the sea shelf. At present, the most studied in this context are nonlinear solitary-type waves generated due to the tidal activity over continental slope. This paper deals with periodic cnoidaltype wave packets considered in the framework of mathematical model of continuously stratified fluid. Basic model involves the Dubreil-Jacotin-Long equation for a stream function that results from stationary fully non-linear 2D Euler equations. The longwave approximate equation describing periodic non-harmonic waves is derived by means of scaling procedure using small Boussinesq parameter. This parameter characterizes slight stratification of the fluid layer with the density profile being close to the linear stratification. The fine-scale density plays important role here because it determines the non-linearity rate of model equation, so it permits to consider strongly non-linear dispersive waves of large amplitude. As a result, constructed asymptotic solutions can simulate periodic wave-trains of sub-surface depression coupled with near-bottom wavetrains of isopycnal elevation. It is demonstrated that calculated wave profiles are in good qualitative agreement with internal wave structures observed by the authors in the field experiments performed annually during 2011-2018 in expeditions on the shelf of the Japanese sea.

KW - Asymptotic modelling

KW - Field experiment

KW - Periodic and solitary waves

KW - Weak stratification

UR - http://www.scopus.com/inward/record.url?scp=85080072266&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=37245797

U2 - 10.25743/ICT.2019.24.2.008

DO - 10.25743/ICT.2019.24.2.008

M3 - Article

AN - SCOPUS:85080072266

VL - 24

SP - 90

EP - 98

JO - Вычислительные технологии

JF - Вычислительные технологии

SN - 1560-7534

IS - 2

ER -