Nonlinear Dynamics Of Transcritical Flows

The German Aerospace Research Establishment (DFVLR) has initiated a new series of seminars concerning fundamental problems in applied engineering sciences. These seminars will be devoted to interdisciplinary topics related to the vast variety of DFVLR activities in the fields of fluid mechanics, flight mechanics, guidance and control, materials and struc tures, non-nuclear energetics, communication technology, and remote sensing. The purpose of the series is twofold, namely, to bring modern ideas and techniques to the attention of the DFVLR in order to stimulate internal activi ties, and secondly, to promulgate DFVLR achievements wi thin the international scientific/technical community. To this end, prominent speakers from Germany and other countries will be invited to join in a series of lectures and discussions on certain topics of mutual interest. The first colloquium of this series dealt with the dynamics of nonlinear systems, especially in relation'to its application to fluid mechanics, particularly in transcritical flows. Of special interest are questions concerning the formation of nonlinear three-dimensional structures in classical fluid mechanical stability problems, the physical process of transition to turbulence, and the appearance of chaotic solutions. The scope of lectures reaches from self-organization in physical systems to structural stability of three-dimensional vortex patterns, the treatment of dissipative and conservative systems, the formation of nonlinear structures in the region of laminar-turbulent transition, and numerical simulation of cumulus cloud convection in meteorology. The seminar should provide an insight into the extent to which theoretical findings in Non linear Dynamics apply to the comprehension of fluid-mechanical problems.

This monograph develops a generalised energy flow theory to investigate non-linear dynamical systems governed by ordinary differential equations in phase space and often met in various science and engineering fields. Important nonlinear phenomena such as, stabilities, periodical orbits, bifurcations and chaos are tack-led and the corresponding energy flow behaviors are revealed using the proposed energy flow approach. As examples, the common interested nonlinear dynamical systems, such as, Duffing’s oscillator, Van der Pol’s equation, Lorenz attractor, Rössler one and SD oscillator, etc, are discussed. This monograph lights a new energy flow research direction for nonlinear dynamics. A generalised Matlab code with User Manuel is provided for readers to conduct the energy flow analysis of their nonlinear dynamical systems. Throughout the monograph the author continuously returns to some examples in each chapter to illustrate the applications of the discussed theory and approaches. The book can be used as an undergraduate or graduate textbook or a comprehensive source for scientists, researchers and engineers, providing the statement of the art on energy flow or power flow theory and methods.

Nonlinear Dynamics: A Two-Way Trip from Physics to Math provides readers with the mathematical tools of nonlinear dynamics to tackle problems in all areas of physics. The selection of topics emphasizes bifurcation theory and topological analysis of dynamical systems. The book includes real-life problems and experiments as well as exercises and work

This volume is the collection of papers presented at the workshop on 'The Stability of Spatially Varying and Time Dependent Flows" sponsored by the Institute for Computer Applications in Science and Engineering (lCASE) and NASA Langley Research Center (LaRC) during August 19- 23, 1985. The purpose of this workshop was to bring together some of the experts in the field for an exchange of ideas to update the current status of knowledge and to help identify trends for future research. Among the invited speakers were D.M. Bushnell, M. Goldstein, P. Hall, Th. Herbert, R.E. Kelly, L. Mack, A.H. Nayfeh, F.T. Smith, and C. von Kerczek. The contributed papers were by A. Bayliss, R. Bodonyi, S. Cowley, C. Grosch, S. Lekoudis, P. Monkewitz, A. Patera, and C. Streett. In the first article, Bushnell provides a historical background on laminar flow control (LFC) research and summarizes the crucial role played by stability theory in LFC system design. He also identifies problem areas in stability theory requiring further research from the view-point of ap plications to LFC design. It is an excellent article for theoreticians looking for some down-to-earth applications of stability theory.

The past decade has seen remarkable growth in research related to petroleum reseIVoir simulation. This growth reflects several developments, not the least of which is the increased interest in oil recovery technologies requiring sophisticated engineer ing. Augmenting this interest has been the broader availability of supercomputers capable of handling the tremendous computational demands of a typical reseIVoir simulator. The field of reseIVoir simulation incorporates several major facets of applied mathematics. First, in view of the varieyt and complexity of the processes encoun tered, it is imperative that the modeler adopt a systematic approach to establishing the equations governing reseIVoir flows. Second, the mathematical structure of these flow equations needs to be carefully analyzed in order to develop appropriate and efficient numerical methods for their solution. Third, since some aspects of the discretized flow equations are typically stiff, one must develop efficient schemes for solving large sparse systems of linear equations. This monograph has three parts, each devoted to one of these three aspects of reseIVoir modeling. The text grew out of a set of lectures presented by the authors in the autumn of 1986 at the IBM Scientific Center in Bergen, Norway. We feel that it is only appropriate to caution the reader that many of the ideas that we present in this monograph do not reflect standard approaches in petroleum reseIVoir simulation. In fact, our aim is to outline promising new ways of attacking reseIVoir simulation prob lems, rather than to compile another textbook for the mainstream.

1. 1 Scope of the Study The detailed and reasonably accurate computation of large scale turbulent flows has become increasingly important in geophysical and engi neering applications in recent years. The definition of water quality management policies for reservoirs, lakes, estuaries, and coastal waters, as well as the design of cooling ponds and solar ponds, requires an ade quate quantitative description of turbulent flows. When the diffusion of some tracer (be it active, such as temperature or salinity, or passive, such as dissolved oxygen) is of relevance to a specific application, the proper determination of the effects of turbulent transport processes has paramount importance. Thus, for instance, the proper understanding of lake and reservoir dynamics requires, as a first step, the ability to simulate turbulent flows. Applications in other areas of geophysical research, such as meteorology and oceanography are easily identified and large in number. It should be stressed that, in this context, the analyst seeks predictive ability to a certain extent. Accordingly, the need for simulation models that closely resemble the natural processes to be repre sented has recently become more evident. Since the late 1960s considerable effort has been devoted to the development of models for the simulation of complex turbulent flows. This has resulted in the establishment of two approaches which have been, or 2 have the potential for being, applied to problems of engineering and geophysical interest.