Establishment and evaluation of a Velocity-Gaussian Function Model for internal solitary waves

doi:10.3969/j.issn.1001-909X.2024.02.005

Abstract

Abstract:

The one-dimensional theoretical model of internal solitary waves has been widely used in their prediction. However, on one hand, these theoretical models usually rely heavily on temperature and salinity data when calculating wave functions, which requires the use of moorings equipped with temperature and salinity observation instruments, resulting in high observation costs. On the other hand, they tend to have large prediction errors in complex current environments, such as lower accuracy in calculating the nonlinear phase speed and wave function of internal solitary waves. In this study, a Velocity-Gaussian Function Model was proposed, which reversed the amplitude and wave function of internal solitary waves based on the measured current velocity of the upper layer of the South China Sea from a single mooring. Furthermore, key parameters such as wave-induced current and nonlinear phase speed of internal solitary waves were calculated using a one-dimensional theoretical model. By comparing the measured data from the moorings with the results calculated by the Velocity-Gaussian Function Model, it was found that the model can simulate the wave-induced current throughout the entire water depth by inputting only the measured current velocity from the upper 150 meters of the ocean. Additionally, the error in the nonlinear phase speed can be controlled within 10% compared to the measured value. The application of the Velocity-Gaussian Function Model enables accurate prediction of internal solitary waves in the complex South China Sea, without the need for moorings equipped with temperature and salinity observation instruments, thus significantly reducing the cost of internal solitary wave observation.

Key words: internal solitary wave, Velocity-Gaussian Function Model, mooring observation

CLC Number:

P731.24

JIN Chenxin, CUI Zijian, LIANG Chujin, LIN Feilong, CHEN Zhentao. Establishment and evaluation of a Velocity-Gaussian Function Model for internal solitary waves[J]. Journal of Marine Sciences, 2024, 42(2): 55-61.

Figures/Tables 7

Fig.1 Distribution map of submersible buoy stations (Q) and anchored buoy stations (F1, F2)

Fig.2 Schematic diagram of c1 and Dmean changing with parameters i and j

Fig.3 Schematic diagram of the buoyancy frequency profile (a), the wave function calculated based on the buoyancy frequency profile (b) and the wave function output by the Velocity-Gaussian Function Model (c)

Fig.4 The measured horizontal and vertical wave-induced flow profile of the entire water depth measured by the submersible mark(a,c), horizontal and vertical wave-induced flow profile output by the Velocity-Gaussian Function Model in the entire water depth(b,d) (The red line shows the amplitude of the internal solitary wave at 260 m recorded by the ADCP, while the black line corresponds to the full-water-depth amplitude output by the Velocity-Gaussian Function Model.)

Fig.5 The horizontal and vertical wave-induced flow profile measured above 350 m by the submersible mark (a,c), horizontal and vertical wave-induced flow profile output by the Velocity-Gaussian Function Model in the entire water depth(b,d) (The red line shows the amplitude of the internal solitary wave at 260 m recorded by the ADCP, while the black line corresponds to the full-water-depth amplitude output by theVelocity-Gaussian Function Model.)

Fig.6 The horizontal and the vertical wave-induced flow profile measured above 150 m by the submersible mark (a,c), horizontal and vertical wave-induced flow profile output by the Velocity-Gaussian Function Model in the entire water depth (b,d) (The red line shows the amplitude of the internal solitary wave at 260 m recorded by the ADCP, while the black line corresponds to the full-water-depth amplitude output by the Velocity-Gaussian Function Model.)

Tab.1 Comparison of the nonlinear phase velocity of internal solitary waves calculated by the finite depth theoretical model and the Velocity-Gaussian Function Model and measured by the anchored buoy

时间(内孤立波到达F2)		非线性相速度/(m·s^-1)
日期	时刻	根据有限深度理论计算	根据速度-高斯函数模型模拟	实测值
2021-06-25	22:19	2.97	2.46	2.42
2021-07-08	23:16	2.80	2.78	2.65
2021-07-09	22:58	2.88	2.76	2.66
2021-07-10	22:49	2.88	2.54	2.60
2021-07-11	23:49	2.96	2.96	2.83
2021-07-13	00:40	3.50	2.38	2.62

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