Statistical Characteristics of the Ensemble of Internal Wave Solitons
- PDF / 1,108,023 Bytes
- 8 Pages / 612 x 792 pts (letter) Page_size
- 19 Downloads / 155 Views
istical Characteristics of the Ensemble of Internal Wave Solitons E. G. Didenkulovaa, *, E. N. Pelinovskya, b, c, and T. G. Talipovab, c aNational
Research University Higher School of Economics, Moscow, 101000 Russia Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, 603155 Russia c Alekseev State Technical University, Nizhny Novgorod, 603155 Russia *e-mail: [email protected]
b
Received March 19, 2020; revised July 29, 2020; accepted August 5, 2020
Abstract—Numerical simulation is used to study the statistical characteristics of an ensemble of internal wave solitons propagating under conditions close to those of the Australian shelf. The distribution of the pulse amplitude depending on the traveled distance, as well as statistical moments such as skewness and kurtosis, are constructed. It is shown that both moments decrease by about 20% with distance. Keywords: internal waves, solitons, soliton turbulence, Gardner equation, numerical simulation, statistical moments DOI: 10.1134/S0001433820060031
INTRODUCTION Internal waves on ocean shelves are present almost everywhere, from the far north and south to the equator and from the Atlantic to the Pacific [1–11]. It is noted that internal waves on shelves are of nonlinear character and are often represented as an ensemble of soliton-like waves, mainly of the first mode, as well as second and sometimes higher modes [2, 6, 12–17]. Surface solibores (undular bores) are also ubiquitous [18, 19]. One example of recorded soliton-like internal waves [2] is presented in Fig. 1. This record was taken from two buoys on the Australian North West Shelf in the coastal zone; the water depth reached 80 m and the buoys were distanced from one another by about 2 km. Here, a pronounced density stratification took place;
the characteristic form of the Brunt–Väisälä frequency (buoyancy) is presented in Fig. 2. Nonlinear internal waves are often described using Korteweg–de Vries type equations [20–22]. In doing this, almost all calculations are performed within the framework of the dynamic model, when one or several solitons are specified in one place of the space and the properties of the wavefield are determined somewhere else [17, 23]. In the meantime, the number of observed solitons in groups is rather large and, to describe them, one needs statistical approaches. Naturally, the vast database of oceanographic data on recorded internal waves is treated by statistical analysis. The integrated spectrum of internal waves in the open ocean was constructed by Garrett and Munk as early as in 1979 [24]. Then, it was adapted to different coastal regions of the World Ocean [25]. The repeatability frequency of
Isotherm Displacements 80
Shelf 26°C
C2
40
E
40 0 80
E
C1
Break 25°C
C1
C2
D2
D3
40 0 80
E
E
Shelf 25°C
Isotherm Displacements 80 D1
D1 Break 26°C
D2
D3
40 0
0
Fig. 1. Records of soliton ensembles of internal waves for 24 h on the Australian North West Shelf at two different points along the wave propagation path. The Shelf wave recorder
Data Loading...
