Approximate solution for mechanism of thermally and wind-driven ocean circulation

Abstract

The thermally and wind-driven ocean circulation is a complicated natural phenomenon in the atmospheric physics. Hence we need to reduce it using basic models and solve the models using approximate methods. A nonlinear model of the thermally and wind-driven ocean circulation is used in this paper. The results show that the zero solution of the linear equation is a stable focus point, which is the path curve trend origin point as time (t) trend to infinity. By using the homotopic mapping perturbation method, the exact solution of the model is obtained. The homotopic mapping perturbation method is an analytic solving method, so the obtained solution can be used for analytic operating sequentially. And then we can also obtain the diversified qualitative and quantitative behaviors for corresponding physical quantities.

Approximate Analytic Solution of Solitary Wave for a Class of Nonlinear Disturbed Long-Wave System

“…and ξ = x ± √ 1 + at, C i (i = 1, 2) are arbitrary constants, a is a positive constant. Continuously, using the same method, we can also obtain the higher order approximation of the solitary wave solution for the disturbed long-wave system (18), (19).…”

“…Recently, many scholars such as Ni and Wei, [13] Bartier, [14] Libre et al, [15] and Guarguaglini et al [16] have done many work. Using the method of differential inequalities and others Mo et al considered also a class of reaction diffusion problems, [17] the shock wave, [18] the ecological environment, [19] the soliton wave, [20−22] the laser pulse, [23] the ocean science [24] and the atmospheric physics [25−30] etc. In this paper, we consider a class of nonlinear longwave system, and obtain approximate solution of the solitary wave.…”

Asymptotic solving method for sea-air coupled oscillator ENSO model

“…( 7), ( 8), (15), and ( 16) with the initial conditions T (0) = 1, h(0) = 0, we have From Eqs. ( 15), ( 16), (19), and (26), we obtain the first-order approximate solution (T 1app (t), h 1app (t)) of the sea-air coupled oscillator of the ENSO model ( 28) and ( 29)…”