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Data from: 2D, 2Layer, interfacial waves due to one vortex pair

Citation

Liu, Di (2021), Data from: 2D, 2Layer, interfacial waves due to one vortex pair, Dryad, Dataset, https://doi.org/10.5061/dryad.qnk98sfhj

Abstract

This data set contains the results of the downstream wave heights of the interfacial waves in the 2D, 2Layer fluids flows considered in the article Interference of Internal waves due to two point vortices: linear analytical solution and nonlinear interaction". This work considered the interaction/interference between two vortices int the background of the 2D, 2-Layer fluids flows to simulate the ocean internal waves. More details about the research can be seen in the draft. Besides, MATLAB files that were used to calculate numerical fully nonlinear solutions and linearized solutions, to evalutate the downstream wave heights/lengths, and to generates figures located in the article are contained.

The Folder jfnk contains the functions that evaluate the nonlinear solutions via JFNK method. The Folder linear contains the functions that can be used to evaluate the linearized solutions. And the folder reusltsAnalysis consists of the tools that evaluate the wave height/length of the nonlinear solutions.

The results in the data provide the nonlinear downstream wave heights which vary with the distance between two vortices. Four cases based on different signs of these two vortices are considered: both positive (denoted as PP), both negative (denoted as NN), one positive one negative (denoted as PN), and one negative one positive (denoted as NP). More analysis and results are presented in the article.

Methods

The results data are evaluated from the nonlinear solutions, which are obtained by the following functions.

The functions in the folder jfnk implement the calculations of the interfacial waves via JFNK method with a preconditioner.

The functions in the folder linear implements the evaluations of the linearized solutions in the form of the Cauchy integral.

The functions in the folder reusltsAnalysis return the wave height/ wave length/ amplitude of the steady downstream waves via searching the local minimum/maximum of the nonlinear wave profiles.

Usage Notes

The function mytest_JFNK in the folder jfnk is the main function.

Meanwhile, the function interfaceEta_vp and linearizedHeight_vp can be used directly.