Abstract
Abstract. Spatial distributions of the main properties of the mode function and kinematic and non-linear parameters of internal waves of the second mode are derived for the South China Sea for typical summer conditions in July. The calculations are based on the Generalized Digital Environmental Model (GDEM) climatology of hydrological variables, from which the local stratification is evaluated. The focus is on the phase speed of long internal waves and the coefficients at the dispersive, quadratic and cubic terms of the weakly non-linear Gardner model. Spatial distributions of these parameters, except for the coefficient at the cubic term, are qualitatively similar for waves of both modes. The dispersive term of Gardner's equation and phase speed for internal waves of the second mode are about a quarter and half, respectively, of those for waves of the first mode. Similarly to the waves of the first mode, the coefficients at the quadratic and cubic terms of Gardner's equation are practically independent of water depth. In contrast to the waves of the first mode, for waves of the second mode the quadratic term is mostly negative. The results can serve as a basis for expressing estimates of the expected parameters of internal waves for the South China Sea.
Highlights
The South China Sea is an example of shelf seas where highly energetic internal solitary waves often generate up to 100–200 m vertical displacements of water masses
This paper focuses on the construction of maps of phase speed and coefficients at various terms of Gardner’s equation
We evaluated the mode function (z) for the second mode as the normalised eigenfunction of the boundary problem (2) to the procedure employed in Kurkina et al (2017)
Summary
The South China Sea is an example of shelf seas where highly energetic internal solitary waves often generate up to 100–200 m vertical displacements of water masses. The associated variations have been thoroughly studied for internal solitary waves of the first mode using common databases of the vertical structure of temperature and salinity (Levitus, 1982; Carnes, 2009) This approach made it possible to construct climatologically valid maps of spatio-temporal variations in various coefficients of Gardner’s equation for internal waves of the first mode in different regions of the world ocean. As many regions of the world ocean support propagation of internal waves of higher modes, it is important to expand this kind of “climatology” of internal wave propagation regimes to cover, to a first approximation, the properties of large-amplitude internal waves of the second mode Such maps of the kinematic parameters (wave speed and the coefficient at the linear term) and coefficients at the non-linear terms of the relevant evolution equation make it possible to rapidly evaluate several core properties of the dynamics and Nonlin.
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