Experimental and Theoretical Analyses of Internal Waves of Finite Amplitude

Abstract

Experimental and theoretical investigations are conducted in order to understand the propagation of internal waves in a density-stratified water layer. In a laboratory, the internal waves were artificially generated by two different systems—an oil-pressure-type wave-generating pump, and a horizontal flap-type wavemaker. An electronic apparatus was used to measure the temporal displacements of the free surface and the density interface. An image processing technique was also undertaken to illustrate the spatial variations of the density interface. These test data are compared with the calculated results by the third-order finite-amplitude approximation. The theoretical solution yields a depression of the density interface at the wave trough, and slightly lower rise at the wave crest against the small-amplitude wave solution, when the thickness of the lower layer is larger than that of the upper layer. On the contrary, the internal wave profile is more peaked at the wave crest and flatter at the wave trough for the case of a larger upper-layer thickness. The difference in absolute height between the two points increases significantly with an increasing ratio of the thickness of the upper layer to that of the lower layer.