Asymptotic solution of a weak nonlinear model for the mid-latitude stationary wind field of a two-layer barotropic ocean

Abstract

A weak nonlinear model of a two-layer barotropic ocean with Rayleigh dissipation is built. The analytic asymptotic solution is derived in the mid-latitude stationary wind field, and the physical meaning of the corresponding problem is discussed.

Homotopic Approximate Solutions for the General Perturbed Nonlinear Schrödinger Equation

“… are very close to each other. This behaviour is coincident with that for the approximate solution of the weakly disturbed evolution equation(19).…”

“…Recently, based on the idea of HPM, Mo proposed the homotopic mapping method to handle some nonlinear problems with small perturbed term [17]. A great quantity of works about this subject have been researched by many authors, such as perturbed Kdv-Burgers equation [18], mid-latitude stationary wind field [19] etc.…”

A class of asymptotic solution for the time delay wind field model of an ocean

“…So wind stress in the meridional zone shows no uniform distribution. In order to overcome the limit of a horizontal one-dimensional model some scholars [6][7][8][9][10][11][12][13] built a two-dimensional barotropic quasi-equilibrium ocean linear model under wind forcing, considering Rayleigh friction. Recently, many scholars [14][15][16][17] have studied nonlinear problems and built many approximate methods.…”

Approximate derivative-dependent functional variable separation for quasi-linear diffusion equations with a weak source

“…[20] During the past decades, some approximate methods based on symmetry group theory and perturbation theory were presented so as to seek approximate solutions and to investigate the properties of perturbed equations, for instance, the approximate symmetry method, the approximate conditional symmetry method, the approximate potential symmetry method, the approximate generalized conditional symmetry method (AGCS), and the approximate homotopy symmetry method. [21][22][23][24][25][26][27][28][29][30] Recently, we defined a new concept of the approximate functional separable solutions (AFSSs), and presented the approximate functional variable separation approach (AFVSA) based on AGCS, which was applied to the porous medium equation with a perturbed nonlinear source. [31] Meanwhile, the approximate derivative-dependent functional variable separation approach (ADDFVSA) was established, and was applied to the generalized diffusion equations with perturbation.…”