This paper introduces an energy-preserving stochastic model for studying wave effects on currents in the ocean mixing layer. The is called forcing by Lie transport (SFLT). SFLT derived here from a constrained variational principle, so it has Kelvin circulation theorem. examples of given treat 3D Euler fluid flow, rotating shallow water dynamics and Euler-Boussinesq equations. In each example, o...

Abstract This paper presents the results of applying a new iterative method to linear and nonlinear fractional partial differential equations in fluid mechanics. A numerical analysis was performed find an exact solution wave equation Burgers’ equation, as well approximate KdV Boussinesq equation. Fractional derivatives order α are described using Caputo's definition with 0 < ≤ 1 or 2 . compa...

We study the Navier-Stokes-Darcy-Boussinesq system that models thermal convection of a fluid overlying saturated porous medium in general decomposed domain. In both two and three spatial dimensions, we first prove existence global weak solutions to initial boundary value problem subject Lions Beavers-Joseph-Saffman-Jones interface conditions. The proof is based on proper time-implicit discretiz...

In this paper we further improve the modified extended tanh-function method to obtain new exact solutions for nonlinear partial differential equations. Numerical applications of the proposed method are verified by solving the improved Boussinesq equation and the system of variant Boussinesq equations. The new exact solutions for these equations include Jacobi elliptic doubly periodic type, Weie...

A family of Boussinesq systems has been proposed in [8] to describe the bi-directional propagation of small amplitude long waves on the surface of shallow water. In this paper, we investigate the boundary stabilization of the generalized higher order Boussinesq systems of KdV–type posed on a interval. We design a two-parameter family of feedback laws for which the solutions are globally defined...

Non-Oberbeck-Boussinesq (NOB) effects are measured experimentally and calculated theoretically for strongly turbulent Rayleigh-Bénard convection of ethane gas under pressure where the material properties strongly depend on the temperature. Relative to the Oberbeck-Boussinesq case we find a decrease of the central temperature as compared to the arithmetic mean of the top- and bottom-plate temper...

In this article, we derive a viscous Boussinesq system for surface water waves from Navier-Stokes equations. So, we use neither the irrotationality assumption, nor the Zakharov-Craig-Sulem formulation. During the derivation, we find the bottom shear stress, and also the decay rate for shallow (and not deep) water. In order to justify our derivation, we check it by deriving the viscous Korteweg-...

We show that stationary statistical properties for uniformly dissipative dynamical systems are upper semi-continuous under regular perturbation and a special type of singular perturbation in time of relaxation type. The results presented are applicable to many physical systems such as the singular limit of infinite Prandtl-Darcy number in the Darcy-Boussinesq system for convection in porous med...

We study the Boussinesq equation from the point of view of a multipletime reductive perturbation method. As a consequence of the elimination of the secular producing terms through the use of the Korteweg–de Vries hierarchy, we show that the solitary–wave of the Boussinesq equation is a solitary–wave satisfying simultaneously all equations of the Korteweg–de Vries hierarchy, each one in an appro...