Statistical and dynamical analyses of propagation mechanisms of solitary internal waves in a two-layer stratification

The blocking effect of submarine ridges on the propagation of internal solitary waves (ISWs) over the topography of the seabed results in the fission of the solitary waves that accompany the generation of reflected and transmitted waves. In this study, multivariate analysis of variance (MANOVA) is used to investigate the inseparable relationship between the transmission and reflection. An examination of the error sums of squares and cross-products (SSCP) matrix and the correction matrix shows that the correlation between the transmission (at/ai) and reflection coefficients (ar/ai) is quite low (0.284). Moreover, from multivariate testing, including Pillai’s trace, Wilks’ lambda, Hotelling’s trace and Roy’s largest root, we conclude that the ridge height has a large effect (η = 0.456) on both the amplitude of the transmitted and reflected waves, as well as large (η = 0.411) and very large (η = 0.469) effects on the amplitudes of the transmitted and reflected waves, respectively. In conclusion, the results in the present study highlight the importance of the role played by ridge height in coherent ISW transmission and reflection during oceanic wave–ridge interactions.