in this paper, a boussinesq equation is solved by using the adomian's decomposition method, modified adomian's decomposition method and homotopy analysis method. the approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. the existence and uniqueness of the solution and the convergence of the propose...

Two physical parameters are introduced into the basic ocean equations to generalize numerical ocean models for various vertical coordinate systems and their hybrid features. The two parameters are formulated by combining three techniques: the arbitrary vertical coordinate system of Kasahara [Kasahara, A., 1974. Various vertical coordinate systems used for numerical weather prediction. Mon. Weat...

This paper is concerned with the local well-posedness of Oberbeck Boussinesq approximation for unsteady motion a drop in another fluid separated by closed interface surface tension. We are devoted to obtaining linearized Oberbeck-Boussinesq fixed domain using Hanzawa transformation, and maximal $ L^{p} $-$ L^{q} regularities two-phase system obtained authors [10] establish existence uniqueness ...

Through the use of Boussinesq scaling we develop and test a model for resolving non-hydrostatic pressure profiles in nonlinear wave systems over varying bathymetry. A Green–Nagdhi type polynomial expansion is used to resolve the pressure profile along the vertical axis, this is then inserted into the pressure-Poisson equation, retaining terms up to a prescribed order and solved using a weighted...

A coupled Boussinesq-boundary integral method is developed to simulate nonlinear water wave interaction with structures consisting of multiple layers with different physical and hydraulic characteristics. The flow field in the water region is modeled with a modified set of Boussinesq-type equations, with additional terms to account for the flow of water into/out of the porous region. The equati...

Two-dimensional shallow water systems are frequently used in engineering practice to model environmental flows. The benefit of these systems are that, by integration over the water depth, a two-dimensional system is obtained which approximates the full three-dimensional problem. Nevertheless, for most applications the need to propagate waves over many wavelengths means that the numerical soluti...

We establish local and global existence results for Boussinesq type equations on a circle, employing Fourier series and a fixed point argument. 0. Introduction and Main Results. In the present work, we want to consider the question of existence and uniqueness of solutions for Boussinesq type equations (0.1) utt − uxx + uxxxx + ∂ xf(u) = 0, x ∈ T, t ∈ R, where T is the unit circle and f(u) is a ...

This paper studies solutions of the two-dimensional incompressible Boussinesq equations with fractional dissipation. The spatial domain is a periodic box. The Boussinesq equations concerned here govern the coupled evolution of the fluid velocity and the temperature and have applications in fluid mechanics and geophysics. When the dissipation is in the supercritical regime (the sum of the fracti...

[1] The method of recession analysis proposed by Brutsaert and Nieber (1977) remains one of the few analytical tools for estimating aquifer hydraulic parameters at the field scale and beyond. In the method, the recession hydrograph is examined as dQ/dt = f(Q), where Q is aquifer discharge and f is an arbitrary function. The observed function f is parameterized through analytical solutions to th...

The two-dimensional incompressible Boussinesq equations with partial or fractional dissipation have recently attracted considerable attention and the global regularity issue has been extensively investigated. This paper aims at the global regularity in the case when the dissipation is critical. The critical dissipation refers to α + β = 1 when Λα ≡ (−Δ)α2 and Λβ represent the fractional Laplaci...