Aldo Giorgini

The validity of the boussinesq approximation for liquids and gases

Abstract A new method for obtaining approximate equations for natural convection flows is presented. The systematic application of this method leads to explicit conditions for the neglect of various terms. It is shown that this method allows the specification of the conditions under which the traditional Boussinesq approximation applies to a given Newtonian liquid or gas. The method is applied to room temperature water and air.

Nonlinear perturbation of the vortex shedding from a circular cylinder

The influence of finite-amplitude perturbations on the unsteady vortex shedding past an impulsively started circular cylinder is investigated by means of a numerical model. The computational scheme is a mixed spectral–finite analytic technique, in which the fast-Fourier-transform algorithm is used for the evaluation of the nonlinear terms in the two-dimensional time-dependent Navier–Stokes equations in their stream function–vorticity transport form (the Helmholtz formulation) at Re = 1000. The vortex shedding is promoted by imposing at t = 0 a small rotational field to the initially irrotational flow. Attention is focused on the strength of the perturbation vortex, which affects the way in which the vortex shedding develops in time. The results of the simulations are presented by means of computer-generated drawings of absolute streamlines, relative streamlines and vorticity fields; it appears that, when the strength of the initial perturbation assumes the minimum value that has been tested, the vortex shedding phenomenon develops in a way different from that resulting from other numerical experiments of the same kind.

Temporal evolution of high-order vortices in the nonsymmetric wake past a circular cylinder

The nonsymmetric, nonsteady flow of a viscous incompressible fluid around an impulsively started circular cylinder at Reynolds number Re = 3000 (based on the free stream velocity and cylinder diameter) is numerically simulated to explore the evolution in time of high-order vortices developing in the cylinder near wake. The two-dimensional Navier–Stokes equations in the streamfunction-vorticity transport form are numerically integrated with the use of a computational technique in which the flow fields are expanded in Fourier series along the azimuthal direction and the convolutions arising from the convective term of the vorticity transport equation are evaluated by means of fast Fourier transform algorithms; the time marching is executed with a fourth-order Runge–Kutta algorithm (first four iterations) and a predictor–corrector scheme for the subsequent iterations. The evolution in time of primary, secondary and tertiary vortices developing in the early stages of development of the nonsymmetric wake of the cylindrical body clearly emerges from the numerical simulations and is accurately described; the results are presented in terms of computer generated images of streamline fields and vorticity fields. The mutual interaction of vortical structures of different order in the near wake of the cylinder appears in the results of the calculations.

Direct transversal integration of the Navier-Stokes equations

Abstract This work concerns the numerical integration of the vorticity-streamfunction formulation of the Navier-Stokes equations in their Fourier Space form. The expansion is done with respect to the direction along which the flow is periodic (the expansion direction), and the direct integration is performed along the direction normal to that (transversal direction). In this paper, the Navier-Stokes equations are expanded in Fourier series along the axial direction for plane Couette flow, along the azimuthal coordinate θ for the case of plane flow around a circular cylinder1, and along the longitudinal coordinate z for the case of axisymmetric flow between concentric rotating cylinders2. The resulting vorticity transport equations contain convolution terms which can be efficiently calculated by the use of the Fast Fourier Transform (FFT) algorithm3. The streamfunction-vorticity equation becomes an ordinary differential equation in Fourier space. Its numerical integration is performed by means of a scheme introduced here for the first time4. Another important feature of the scheme concerns the determination of the vorticity at the boundaries through integral relations which involve the values of the vorticity within the flow domain and the values of the streamfunction at the boundaries5.

Lateral Movements of Vadose Water in Layered Soils

Abstract Since groundwater contamination is becoming recognized as a serious problem both in the United States and abroad, and since the contamination processes involve the vadose zone below the soil surface, the question on whether Infiltration may occur in directions other than vertical acquires a place of utmost importance. In this paper it is shown that, under particular conditions, which are chosen so as to emphasize the importance of the problem, lateral Infiltration occurs and it can be more predominant than vertical Infiltration.

Computergraphical Description of the Dynamics of a Turbulence Model

In the recent years, the numerical simulation of fluid flows has been extensively undertaken by several investigators. The limited number of exact solutions to the Navier-Stokes equations, which describe the motion of a viscous incompressible fluid, can be readily expanded by means of numerical experiments. The major difficulties inherent in the numerical simulation of highly intricate unsteady flows are constituted by facility problems. A full-fledged numerical study of the three-dimensional turbulent field described by the Navier-Stokes equations, while simple in principle, would require computers with speeds and memories of some orders of magnitude larger than those of presently available computers.

Pressure calculations by direct transversal integration

Abstract This article concerns the numerical integration of the Poisson equation of the pressure field once the velocity field is given. The pressure equation is integrated in its Fourier space form. The expansion is done with respect to the direction along which the flow is assumed to be periodical, and the direct integration is performed along the transversal direction. In this paper the direct transversal integration technique 1 , is applied to the plane Couette flow, to the plane flow past a circular cyclinder, and to the axisymmetric flow between two concentric cylinders. In all the above cases the convolution sums appearing in the pressure equation are solved by the use of the FFT algorithm.

Mode interaction segregation for non-linear differential equations

The periodic solutions of the Van der Pol equation x − α(1 − x2) x + x = 0 are investigated for α < 1 by means of a method that preserves the non-linearity of the equation but that takes into account the order of infinitesimal in α of the Fourier amplitudes of x. A successive approximation scheme can be applied and the zero-th approximation is shown compared to the results of a numerical experiment covering, virtually, all values of α. The method yields all Fourier amplitudes at any given approximation stage.