Experimental investigation on the propagation characteristics of internal solitary waves based on a developed piecewise dynamic mode decomposition method

Abstract

The propagation of internal solitary waves (ISWs) flowing over the submerged topography is a strongly nonlinear process. To extract the dynamic characteristics of this process, an improved dynamic mode decomposition method is proposed in this paper, which is named piecewise dynamic mode decomposition (PDMD). The innovation of this method is to split the entire evolution process into several quasi-linear segments before modal analyzing to reduce the requirements on the spatial and temporal resolutions of input measured data. A feasible criterion for linearity is introduced by combining the proper orthogonal decomposition method, which is an important basis of PDMD. The data used in the analysis are provided by the experiments conducted in a stratified wave tank. The experimental conditions are set as ISWs flowing over two typical bottom topographies. The interfacial displacement and flow field information are analyzed as the measured data. Through reconstruction and modal analysis of experimental data, the effectiveness and flexibility of PDMD are verified for the ISW problem. The physical meaning of segmentation points can be explained. Based on the results of model decomposition, the main propagation characteristics of ISWs under different conditions are discussed. The evolution of the waveform or local flow phenomena can be simplified to the superposition of linear modes with frequency information.