A novel parallel technique for Fourier-Galerkin pseudo-spectral methods with applications to two-dimensional Navier-Stokes equations and inviscid Boussinesq approximation equations is presented. It takes the advantage of the programming structure of the phase-shift de-aliased scheme for pseudo-spectral codes, and combines the task-distribution strategy [Yin, Clercx and Montgomery, Comput. Fluid...

Boussinesq systems of nonlinear partial differential equations are fundamental equations in geophysical fluid dynamics. In this paper, we use asymmetric ideas and moving frames to solve the two-dimensional Boussinesq equations with partial viscosity terms studied by Chae (Adv. Math. 203 (2006), 497-513) and the three-dimensional stratified rotating Boussinesq equations studied by Hsia, Ma and W...

In this paper, we study various dissipative mechanics associated with the Boussinesq systems which model two-dimensional small amplitude long wavelength water waves. We will show that the decay rate for the damped one-directional model equations, such as the KdV and BBM equations, holds for some of the damped Boussinesq systems.

We consider the numerical simulation of a three-dimensional two-phase incompressible flow with a viscous interface. The simulation is based on a sharp interface Navier-Stokes model and the Boussinesq-Scriven constitutive law for the interface viscous stress tensor. In the recent paper [Soft Matter 7, 7797–7804, 2011] a model problem with a spherical droplet in a Stokes Poiseuille flow with a Bo...

The primitive equations are derived from the Boussinesq system of incompressible flow under the hydrostatic balance assumption, by taking the zero singular perturbation limit of the small aspect ratio. This singular perturbation limit of small aspect ratio can be rigorously justified, see, Azérad–Guillén [1] and Li–Titi [26]. The primitive equations play a fundamental role for weather predictio...

We consider the abstract initial value problem for evolution equations which describe heat convection of incompressible viscous fluids. It is difficulty that we do not neglect the dissipation function in contrast to the Boussinesq approximation. This problem has uniquely a mild solution. Moreover, a mild solution of this problem can be a strong or classical solution under appropriate assumption...

In this report, generalized wave breaking equations are developed using three dimensional fully nonlinear extended Boussinesq equations to encompass rotational dynamics in wave breaking zone. The derivation for vorticity distributions are developed from Reynold based stress equations.

We consider the three-dimensional Boussinesq equations, and obtain an Osgood type regularity criterion in terms of the velocity gradient.

A mathematical model for turbulent gas-liquid flows is presented. It is shown that bubble-induced buoyancy resembles natural convection and can be readily incorporated into an incompressible flow solver by using an analog of the Boussinesq approximation. Extra transport equations are introduced to describe the evolution of the gas holdup and compute the turbulent eddy viscosity in the framework...

The stabilized Gauge-Uzawa method (SGUM), which is a 2nd-order projection type algorithm used to solve Navier-Stokes equations, has been newly constructed in the work of Pyo, 2013. In this paper, we apply the SGUM to the evolution Boussinesq equations, which model the thermal driven motion of incompressible fluids. We prove that SGUM is unconditionally stable, and we perform error estimations o...