Search results for "Boussinesq"

One-dimensional Mixed MHD Convection

2006

The parallel, fully developed flow of an electrically conducting fluid between plane parallel walls under the simultaneous influence of a driving pressure head, buoyancy, and magnetohydrodynamic (MHD) forces is studied. The fluid is assumed to be internally heated and the flow is modeled as one-dimensional and incompressible, while the Boussinesq approximation is adopted for the buoyancy terms. Analytical solutions are obtained for temperature, velocity and electrical potential under different electrical boundary conditions, forced to natural convection intensity ratios and values of the magnetic induction. Generalized working charts are presented which synthetically describe the system''s …

Route to chaos in the weakly stratified Kolmogorov flow

2019

We consider a two-dimensional fluid exposed to Kolmogorov’s forcing cos(ny) and heated from above. The stabilizing effects of temperature are taken into account using the Boussinesq approximation. The fluid with no temperature stratification has been widely studied and, although relying on strong simplifications, it is considered an important tool for the theoretical and experimental study of transition to turbulence. In this paper, we are interested in the set of transitions leading the temperature stratified fluid from the laminar solution [U∝cos(ny),0, T ∝ y] to more complex states until the onset of chaotic states. We will consider Reynolds numbers 0 < Re ≤ 30, while the Richardson numb…

A NEW SOLVER FOR NON-ISOTHERMAL FLOWS IN NATURAL AND MIXED CONVECTION

2022

Most thermal fluid flow of real-life practical problems fall in the category of low Mach-number or incompressible flow (e.g., industrial flows inside ducts, or around stationary/moving objects, flows in biological/biomedical problems, or atmospheric flows). Several numerical techniques have been proposed for simulation of thermal flows, Finite Difference (FDM), Finite Element (FEM), Finite Volume (FVM) and Lattice Boltzmann (LBM) methods. Unlike the FVMs and FEMs, the classical FDMs show some difficulties in handling irregular geometries. Conventional formulation of FEMs (e.g., Galerkin FEMs) suffers from the lack of local mass balance, recovered by modified formulations (Narasimhan &amp; W…

Exact Solutions of the Two Dimensional Boussinesq and Dispersive Water Waves Equations

2010

In this paper two-dimensional Boussinesq and dispersive water waves equations are investigated in exact solutions. The Exp-function method is used for seeking exact solutions of the equations through symbolic computation.

Oscillazioni della linea di riva in presenza di frangimento

2009

Oscillazioni della linea di riva in modelli alla Boussinesq

2008

Random wave run-up with a physically-based Lagrangian shoreline model

2014

Abstract In the present paper the run-up of random waves was calculated by means of a numerical method. In situ measurements based on a video imaging technique have been used for the validation of the present numerical model. The on-site run-up measurements have been carried out at Lido Signorino beach, near Marsala, Italy,along a transect, normal to the shore. A video camera and a linear array of rods have been used to obtain field data. Numerical simulations with a 1DH Boussinesq-type of model for breaking waves which takes into account the wave run-up by means of a Lagrangian shoreline model have been carried out. In such simulations random waves of given spectrum have been propagated in…

A Shoreline model for breaking waves

2011

In order to simulate the wave motion and, in turn, the flow, within the nearshore region, in the last decades the derivation and the application of depth-integrated type of models have been widely investigated and developed. However, in such models, the problems of facing wave breaking and the moving shoreline are not trivial and therefore several approaches have been proposed. About wave breaking, approaches both based on the adoption of an artificial eddy viscosity Zelt (1991) and on the concept of roller Veeramony (2000), Karambas (2003), Musumeci (2005) have been implemented. As regards the shoreline boundary condition, a couple of numerical techniques have been mainly adopted, namely t…

ON THE BOUSSINESQ HIERARCHY

2002

A new sequence of nonlinear evolution systems satisfying the zero curvature property is constructed, by using the invariant singularity analysis. All these systems are completely integrable and a pseudo-potential (linearization) is explicitly determined for each of them. The second system of the sequence is the Broer-Kaup system, which, as is well known, corresponds to the higher order Boussinesq approximation in describing shallow water waves.

From first to fourth order rational solutions to the Boussinesq equation

2020

Rational solutions to the Boussinesq equation are constructed as a quotient of two polynomials in x and t. For each positive integer N , the numerator is a polynomial of degree N (N + 1) − 2 in x and t, while the denominator is a polynomial of degree N (N + 1) in x and t. So we obtain a hierarchy of rational solutions depending on an integer N called the order of the solution. We construct explicit expressions of these rational solutions for N = 1 to 4.