An Introduction to Gravity Currents and Intrusions

An Introduction to Gravity Currents and Intrusions

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Gravity currents and intrusions are the ubiquitous phenomena where a fluid of one density flows horizontally into a fluid of a different density. For researchers and engineers, the ability to understand and predict these flow fields is essential in wide-ranging applications including those involved with atmospheric and ocean dynamics, the propagation of pollutants, and the dispersion of volcanic clouds. Although many new theories, experimental data, simulation results, and insights have surfaced recently, most of these developments remain scattered in journals and conference papers. A systematic and unified introduction to the field, which incorporates the new results and developments, is bound to facilitate the application of the available knowledge to both practical problems and further investigations. Written by a recognized authority active in recent developments in gravity current research, An Introduction to Gravity Currents and Intrusions provides an up-to-date, self-contained, and systematic introduction to the study, interpretation, and prediction of gravity current flows. The author uses a simple mathematical framework to provide an accessible and comprehensive introduction to the mathematical and physical aspects of this important topic. The text supplies researchers and practitioners with the foundation required to formulate problems, interpret experimental results and measurements data, obtain simple and insightful analytical estimates and solutions, and develop or implement numerical codes for related problems. The book also points out gaps of knowledge in the current understanding that require further research. This accessible reference requires only a basic background in fluid mechanics and applied mathematics, making it an ideal starting place for researchers and engineers new to the field. It can also serve as a textbook for upper-level undergraduate and graduate level courses in fluid more

Product details

  • Electronic book text | 512 pages
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • London, United Kingdom
  • 2 Tables, black and white; 182 Illustrations, black and white
  • 1584889047
  • 9781584889045

Table of contents

IntroductionClassificationThe Navier-Stokes equationsNon-stratified ambient currentsShallow-water (SW) formulation for high-Re flowsMotion of the interface and the continuity equationOne-layer modelA useful transformationThe full behavior by numerical solutionDam-break stageSimilarity solutionThe validity of the inviscid approximationThe steady-state current and nose jump conditionsBenjamin's analysisJump conditionBox models for 2D geometryFixed volume current with inertial-buoyancy balanceInflow volume changeTwo-layer SW modelIntroductionThe governing equationsBoussinesq system in dimensionless formJumps of interface for H < 2Energy and work in a two-layer modelAxisymmetric currents, SW formulationGoverning equationsA useful transformationThe full behavior by numerical solutionDam-break stageSimilarity solutionThe validity of the inviscid approximationSome comparisonsBox models for axisymmetric geometryFixed volume current with inertial-buoyancy balanceInflow volume changeEffects of rotationAxisymmetric case Rotating channelBuoyancy decays: particle-driven, porous boundary, and entrainmentParticle-driven currentsAxisymmetric particle-driven currentExtensions of particle-driven solutionsCurrent over a porous bottomAxisymmetric current over a porous bottomEntrainmentNon-Boussinesq systemsIntroductionFormulationDam-break and initial slumping motionThe transition and self-similar stagesSummaryLubrication theory formulation for viscous currents2D geometryAxisymmetric currentCurrent in a porous mediumII Stratified ambient currents and intrusionsContinuous density transitionIntroduction The SW formulation SW results and comparisons with experiments and simulationsDam breakCritical speed and nose-wave interactionSimilarity solutionThe validity of the inviscid approximationAxisymmetric and rotating casesSW formulationSW and NS finite-difference resultsThe validity of the inviscid approximationThe steady-state currentSteady-state flow patternResultsComparisons and conclusionsIntrusions in 2D geometryIntroductionTwo-layer stratificationLinear transition layerRectangular lock configurationsCylindrical lock in a fully linearly-stratified tankSimilarity solution Non-symmetric intrusionsIntrusions in axisymmetric geometryIntroductionTwo-layer stratificationFully linearly-stratified tank, part-depth locksBox models for 2D geometryFixed volume and inertial-buoyancy balanceS = 1, inflow volume changeBox models for axisymmetric geometryFixed volume and inertial-buoyancy balanceS = 1, inflow volume changeLubrication theory for viscous currents with S = 12D geometryAxisymmetric geometryEnergyIntroduction2D geometryAxisymmetric geometrySW equations: characteristics and finite-difference schemesCharacteristicsNumerical solution of the SW equationsNavier-Stokes numerical simulationsFormulationA finite-difference codeOther codesSome useful formulasLeibniz's TheoremVectors and coordinate systemsshow more

Review quote

The whole book is well written in a clear and pedagogical general style. ... the author has, in my opinion, produced the first comprehensive book entirely devoted to the modeling of gravity currents and intrusions. This book will be particularly useful to graduate and PhD students, as well as to academics and research engineers working in this field. It may be used as a self-consistent document to get a detailed idea of the state of knowledge about a given problem or a guide toward more specialized papers. It is rich with ideas regarding the direction in which further research is warranted. This book is ideal to get a first, and yet deep, understanding of the dynamics of gravity currents and intrusions. -International Journal of Multiphase Flow, 37, 2011 ... Noteworthy previous reviews have been written by Simpson (1987) and Huppert (2006). ... In spite of the profound analytical contributions made by these authors, neither review is especially heavy on equations. Stepping into this void is M. Ungarish whose recent monograph devotes most of its pages to the development of a unified theoretical description of gravity current flow in a wide variety of incarnations. ... Ungarish provides a useful summary of the requisite mathematical tools in the appendices and does not shy away from putting these to purposeful employ. On the other hand, each chapter is largely self-contained; for experienced readers, the monograph can be used as a helpful reference in guiding future research. ... Ungarish's consideration of different geometries, flow regimes, etc. is broad, making his book of potential interest to researchers from disparate fields, including oceanography, atmospheric science, hydraulic engineering, and others.-M.R. Flynn, Journal of Fluid Mechanics, 2010show more