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Transition to Turbulence and Mixing in a Quasi-two-dimensional Lorentz Force-driven Kolmogorov Flow

Transition to Turbulence and Mixing in a Quasi-two-dimensional Lorentz Force-driven Kolmogorov Flow
Author: Radford Mitchell
Publisher:
Total Pages:
Release: 2013
Genre: Fluid dynamics
ISBN:

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The research in this thesis was motivated by a desire to understand the mixing properties of quasi-two-dimensional flows whose time-dependence arises naturally as a result of fluid-dynamic instabilities. Additionally, we wished to study how flows such as these transition from the laminar into the turbulent regime. This thesis presents a numerical and theoretical investigation of a particular fluid dynamical system introduced by Kolmogorov. It consists of a thin layer of electrolytic fluid that is driven by the interaction of a steady current with a magnetic field produced by an array of bar magnets. First, we derive a theoretical model for the system by depth-averaging the Navier-Stokes equation, reducing it to a two-dimensional scalar evolution equation for the vertical component of vorticity. A code was then developed in order to both numerically simulate the fluid flow as well as to compute invariant solutions. As the strength of the driving force is increased, we find a number of steady, time-periodic, quasiperiodic, and chaotic flows as the fluid transitions into the turbulent regime. Through long-time advection of a large number of passive tracers, the mixing properties of the various flows that we found were studied. Specifically, the mixing was quantified by computing the relative size of the mixed region as well as the mixing rate. We found the mixing efficiency of the flow to be a non-monotonic function of the driving current and that significant changes in the flow did not always lead to comparable changes in its transport properties. However, some very subtle changes in the flow dramatically altered the degree of mixing. Using the theory of chaos as it applies to Hamiltonian systems, we were able to explain many of our results.


Mixing

Mixing
Author: H. Chaté
Publisher: Springer Science & Business Media
Total Pages: 416
Release: 1999
Genre: Mathematics
ISBN:

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A host of international scholars gathered for the NATO Advanced Studies Institute to discuss questions arising from the study of mixing. Although mixing does not have a reputation for being very scientific, the articles in this book analyze it in a scientific manner from the approaches of geometry, kinetics, and structure, addressing questions involving the characterization of the geometry of complex patterns, the time-scale of a process, and the structures involved in the flow. Annotation copyrighted by Book News, Inc., Portland, OR.


Turbulence

Turbulence
Author: Uriel Frisch
Publisher: Cambridge University Press
Total Pages: 318
Release: 1995-11-30
Genre: Science
ISBN: 1139935976

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This textbook presents a modern account of turbulence, one of the greatest challenges in physics. The state-of-the-art is put into historical perspective five centuries after the first studies of Leonardo and half a century after the first attempt by A. N. Kolmogorov to predict the properties of flow at very high Reynolds numbers. Such 'fully developed turbulence' is ubiquitous in both cosmical and natural environments, in engineering applications and in everyday life. The intended readership for the book ranges from first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, to professional scientists and engineers. Elementary presentations of dynamical systems ideas, of probabilistic methods (including the theory of large deviations) and of fractal geometry make this a self-contained textbook.


Turbulence in the Solar Wind

Turbulence in the Solar Wind
Author: Roberto Bruno
Publisher: Springer
Total Pages: 270
Release: 2016-10-07
Genre: Science
ISBN: 3319434403

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This book provides an overview of solar wind turbulence from both the theoretical and observational perspective. It argues that the interplanetary medium offers the best opportunity to directly study turbulent fluctuations in collisionless plasmas. In fact, during expansion, the solar wind evolves towards a state characterized by large-amplitude fluctuations in all observed parameters, which resembles, at least at large scales, the well-known hydrodynamic turbulence. This text starts with historical references to past observations and experiments on turbulent flows. It then introduces the Navier-Stokes equations for a magnetized plasma whose low-frequency turbulence evolution is described within the framework of the MHD approximation. It also considers the scaling of plasma and magnetic field fluctuations and the study of nonlinear energy cascades within the same framework. It reports observations of turbulence in the ecliptic and at high latitude, treating Alfvénic and compressive fluctuations separately in order to explain the transport of mass, momentum and energy during the expansion. Further, existing models are compared with direct observations in the heliosphere. The problem of self-similar and anomalous fluctuations in the solar wind is then addressed using tools provided by dynamical system theory and discussed on the basis of available models and observations. The book highlights observations of Yaglom’s law in solar wind turbulence, which is one of the most important findings in fully developed turbulence and directly related to the long-lasting and still unsolved problem of solar wind plasma heating. Lastly, it includes a short chapter dedicated to the kinetic range of fluctuations, which has recently been receiving more attention from the space plasma community, since this is inherently related to turbulent energy dissipation and consequent plasma heating. It particularly focuses on the nature and role of the fluctuations populating this frequency range, and discusses several model predictions and recent observational findings in this context.


Scale Invariance

Scale Invariance
Author: Annick LESNE
Publisher: Springer Science & Business Media
Total Pages: 406
Release: 2011-11-04
Genre: Science
ISBN: 364215123X

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During a century, from the Van der Waals mean field description (1874) of gases to the introduction of renormalization group (RG techniques 1970), thermodynamics and statistical physics were just unable to account for the incredible universality which was observed in numerous critical phenomena. The great success of RG techniques is not only to solve perfectly this challenge of critical behaviour in thermal transitions but to introduce extremely useful tools in a wide field of daily situations where a system exhibits scale invariance. The introduction of scaling, scale invariance and universality concepts has been a significant turn in modern physics and more generally in natural sciences. Since then, a new "physics of scaling laws and critical exponents", rooted in scaling approaches, allows quantitative descriptions of numerous phenomena, ranging from phase transitions to earthquakes, polymer conformations, heartbeat rhythm, diffusion, interface growth and roughening, DNA sequence, dynamical systems, chaos and turbulence. The chapters are jointly written by an experimentalist and a theorist. This book aims at a pedagogical overview, offering to the students and researchers a thorough conceptual background and a simple account of a wide range of applications. It presents a complete tour of both the formal advances and experimental results associated with the notion of scaling, in physics, chemistry and biology.


The Interaction of Ocean Waves and Wind

The Interaction of Ocean Waves and Wind
Author: Peter Janssen
Publisher: Cambridge University Press
Total Pages: 310
Release: 2004-10-28
Genre: Science
ISBN: 0521465400

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This book was published in 2004. The Interaction of Ocean Waves and Wind describes in detail the two-way interaction between wind and ocean waves and shows how ocean waves affect weather forecasting on timescales of 5 to 90 days. Winds generate ocean waves, but at the same time airflow is modified due to the loss of energy and momentum to the waves; thus, momentum loss from the atmosphere to the ocean depends on the state of the waves. This volume discusses ocean wave evolution according to the energy balance equation. An extensive overview of nonlinear transfer is given, and as a by-product the role of four-wave interactions in the generation of extreme events, such as freak waves, is discussed. Effects on ocean circulation are described. Coupled ocean-wave, atmosphere modelling gives improved weather and wave forecasts. This volume will interest ocean wave modellers, physicists and applied mathematicians, and engineers interested in shipping and coastal protection.


Turbulence in Rotating, Stratified and Electrically Conducting Fluids

Turbulence in Rotating, Stratified and Electrically Conducting Fluids
Author: P. A. Davidson
Publisher: Cambridge University Press
Total Pages: 701
Release: 2013-09-12
Genre: Science
ISBN: 1107434343

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There are two recurring themes in astrophysical and geophysical fluid mechanics: waves and turbulence. This book investigates how turbulence responds to rotation, stratification or magnetic fields, identifying common themes, where they exist, as well as the essential differences which inevitably arise between different classes of flow. The discussion is developed from first principles, making the book suitable for graduate students as well as professional researchers. The author focuses first on the fundamentals and then progresses to such topics as the atmospheric boundary layer, turbulence in the upper atmosphere, turbulence in the core of the earth, zonal winds in the giant planets, turbulence within the interior of the sun, the solar wind, and turbulent flows in accretion discs. The book will appeal to engineers, geophysicists, astrophysicists and applied mathematicians who are interested in naturally occurring turbulent flows.


Magnetohydrodynamic Turbulence

Magnetohydrodynamic Turbulence
Author: Dieter Biskamp
Publisher: Cambridge University Press
Total Pages: 313
Release: 2003-07-31
Genre: Science
ISBN: 1139441671

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This book presents an introduction to, and modern account of, magnetohydrodynamic (MHD) turbulence, an active field both in general turbulence theory and in various areas of astrophysics. The book starts by introducing the MHD equations, certain useful approximations and the transition to turbulence. The second part of the book covers incompressible MHD turbulence, the macroscopic aspects connected with the different self-organization processes, the phenomenology of the turbulence spectra, two-point closure theory, and intermittency. The third considers two-dimensional turbulence and compressible (in particular, supersonic) turbulence. Because of the similarities in the theoretical approach, these chapters start with a brief account of the corresponding methods developed in hydrodynamic turbulence. The final part of the book is devoted to astrophysical applications: turbulence in the solar wind, in accretion disks, and in the interstellar medium. This book is suitable for graduate students and researchers working in turbulence theory, plasma physics and astrophysics.


Introduction to Modern Magnetohydrodynamics

Introduction to Modern Magnetohydrodynamics
Author: Sébastien Galtier
Publisher: Cambridge University Press
Total Pages: 285
Release: 2016-10-06
Genre: Science
ISBN: 1107158656

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An introductory text on magnetohydrodynamics for advanced students, covering its broad range of applications in nature and in the laboratory.