Premium
Investigation of Coriolis effect on oceanic flows and its bifurcation via geophysical Korteweg–de Vries equation
Author(s) -
Ak Turgut,
Saha Asit,
Dhawan Sharanjeet,
Kara Abdul Hamid
Publication year - 2020
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22469
Subject(s) - bifurcation , korteweg–de vries equation , nonlinear system , conservation law , mathematics , mathematical analysis , homogeneous space , gaussian , traveling wave , classical mechanics , physics , geophysics , mechanics , geometry , quantum mechanics
Abstract In this work, we have investigated Coriolis effect on oceanic flows in the equatorial region with the help of geophysical Korteweg–de Vries equation (GKdVE). First, Lie symmetries and conservation laws for the GKdVE have been studied. Later, we implement finite element method for numerical simulations. Propagation of nonlinear solitary structures, their interaction and advancement of solitons can be seen in the results so produced. Additionally, Gaussian initial condition and undular bore initial condition are also investigated. Results so obtained have been found in perfect agreement with the available results. Bifurcation analysis of the oceanic traveling wave of the GKdVE is presented depending on traveling wave velocity and Coriolis parameter. It is discerned that velocity of the traveling wave and Coriolis parameter affect significantly on the propagation of the nonlinear waves.