The method of dynamic mode decomposition in shallow water and a swirling flow problem

In this paper, a new vector‐filtering criterion for dynamic modes selection is proposed that is able to extract dynamically relevant flow features from dynamic mode decomposition of time‐resolved experimental or numerical data. We employ a novel modes selection criterion in parallel with the classic selection based on modes amplitudes, in order to analyze which of these procedures better highlight the coherent structures of the flow dynamics. Numerical tests are performed on two distinct problems. The efficiency of the proposed criterion is proved in retaining the most influential modes and reducing the size of the dynamic mode decomposition model. By applying the proposed filtering mode technique, the flow reconstruction error is shown to be significantly reduced. Copyright © 2016 John Wiley & Sons, Ltd.     

The Analysis of Some Characteristic Equations Arising in Population and Epidemic Models

Epidemic models with a general infective period distribution are formulated as functional differential equations, as are population models with a general life span distribution. The analysis of the local stability properties of equilibria of such models leads to a characteristic equation involving the Laplace transform of the infective period (or life span) distribution. We obtain conditions under which all roots of the characteristic equation are in the left half plane, implying asymptotic stability of equilibrium, for every infective period distribution. We also consider the converse problem of describing when instability can occur for specific infective period distributions.     

Quadratically Nonlinear Cylindrical Hyperelastic Waves: Derivation of Wave Equations for Axisymmetric and Other States

A rigorous approach of nonlinear continuum mechanics is used to derive nonlinear wave equations that describe the propagation and interaction of hyperelastic cylindrical waves. Nonlinearity is introduced by means of metric coefficients, the Cauchy—Green strain tensor, and the Murnaghan potential and corresponds to the quadratic nonlinearity of all basic relationships. Quadratically nonlinear wave equations are derived for three states (configurations): (i) axisymmetric configuration dependent on the radial and axial coordinates and independent of the angular coordinate, (ii) configuration dependent on the angular coordinate, and (iii) axisymmetric configuration dependent on the radial coordinate. Four ways of introducing physical and geometrical nonlinearities to the wave equations are analyzed. Six different systems of wave equations are written __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 72–84, June 2005.     

Effects of atmospheric pressure and air concentration in the fluid on the motion of a rigid sphere along a wall (experiment)

The effects of the dissolved air concentration and atmospheric pressure on the motion of a rigid sphere along a wall in a fluid are studied experimentally. These effects are the result of the occurrence of a gas bubble in the lubrication layer between the moving sphere’s and the wall. It is found that, depending on the air concentration in the fluid and the atmospheric pressure, during the sphere motion the bubble volume may either increase or remain constant. From the observations, it is clear that the variation of the bubble volume is associated with the unsteady motion of the sphere.     

On the nature of the boundary layers instabilities in a flow between a rotating and a stationary discSur la nature des instabilités de couche limite dans un écoulement entre un disque fixe et un disque tournant

Both theoretical linear stability analysis and direct numerical simulation are performed to study the transition flow between a stationary and a rotating disc. This paper concerns three-dimensional spiral and annular patterns computed with a high-order (spectral) numerical method and related to Bödewadt layer instabilities. The characteristic parameters of these boundary layer patterns are compared to the theoretical results and interpreted in terms of type I and type II generic instabilities. Moreover, the absolute instability regions are also theoretically identified and the critical Reynolds numbers of the convective/absolute transition in both layers are given. To cite this article: E. Tuliska-Sznitko et al., C. R. Mecanique 330 (2002) 91–99.