An Introduction to Gravity Currents and Intrusions

An Introduction to Gravity Currents and Intrusions

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Description

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 dynamics.
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Product details

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

Table of contents

Introduction
Classification
The Navier-Stokes equations

Non-stratified ambient currents
Shallow-water (SW) formulation for high-Re flows
Motion of the interface and the continuity equation
One-layer model
A useful transformation
The full behavior by numerical solution
Dam-break stage
Similarity solution
The validity of the inviscid approximation
The steady-state current and nose jump conditions
Benjamin's analysis
Jump condition
Box models for 2D geometry
Fixed volume current with inertial-buoyancy balance
Inflow volume change
Two-layer SW model
Introduction
The governing equations
Boussinesq system in dimensionless form
Jumps of interface for H < 2
Energy and work in a two-layer model
Axisymmetric currents, SW formulation
Governing equations
A useful transformation
The full behavior by numerical solution
Dam-break stage
Similarity solution
The validity of the inviscid approximation
Some comparisons
Box models for axisymmetric geometry
Fixed volume current with inertial-buoyancy balance
Inflow volume change
Effects of rotation
Axisymmetric case
Rotating channel
Buoyancy decays: particle-driven, porous boundary, and entrainment
Particle-driven currents
Axisymmetric particle-driven current
Extensions of particle-driven solutions
Current over a porous bottom
Axisymmetric current over a porous bottom
Entrainment
Non-Boussinesq systems
Introduction
Formulation
Dam-break and initial slumping motion
The transition and self-similar stages
Summary
Lubrication theory formulation for viscous currents
2D geometry
Axisymmetric current
Current in a porous medium

II Stratified ambient currents and intrusions
Continuous density transition
Introduction
The SW formulation
SW results and comparisons with experiments and simulations
Dam break
Critical speed and nose-wave interaction
Similarity solution
The validity of the inviscid approximation
Axisymmetric and rotating cases
SW formulation
SW and NS finite-difference results
The validity of the inviscid approximation
The steady-state current
Steady-state flow pattern
Results
Comparisons and conclusions
Intrusions in 2D geometry
Introduction
Two-layer stratification
Linear transition layer
Rectangular lock configurations
Cylindrical lock in a fully linearly-stratified tank
Similarity solution
Non-symmetric intrusions
Intrusions in axisymmetric geometry
Introduction
Two-layer stratification
Fully linearly-stratified tank, part-depth locks
Box models for 2D geometry
Fixed volume and inertial-buoyancy balance
S = 1, inflow volume change
Box models for axisymmetric geometry
Fixed volume and inertial-buoyancy balance
S = 1, inflow volume change
Lubrication theory for viscous currents with S = 1
2D geometry
Axisymmetric geometry
Energy
Introduction
2D geometry
Axisymmetric geometry
SW equations: characteristics and finite-difference schemes
Characteristics
Numerical solution of the SW equations
Navier-Stokes numerical simulations
Formulation
A finite-difference code
Other codes
Some useful formulas
Leibniz's Theorem
Vectors and coordinate systems
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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, 2010
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