Environmental Hazards: The Fluid Dynamics and Geophysics of Extreme Events (Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore)

One of the priority areas of ICSU (The International Council for Science) is Natural and Human-Induced Environmental Hazards and Disasters. The School - held at the Institute for Mathematical Sciences, Singapore from 20 April to 2 May 2009 - on which this volume is based on was sponsored by ICSU and by its members from IUTAM (the International Union of Theoretical and Applied Mechanics) and IUGG (the International Union of Geodesy and Geophysics). This volume provides an indepth graduate-level introduction to the fluid dynamics and geophysics of hazards such as tropical cyclones, flooding, atmospheric pollution and tsunamis. It also includes discussion of the possible effects of climate change on these phenomena. Indeed, the current importance of this area is of great public concern. Preface......Page 6 1. Introduction......Page 12 2. Vorticity and the Biot-Savart law......Page 14 3. The Euler equation and its invariants......Page 17 4. The stretched vortex of Burgers (1948)......Page 20 5. Kelvin-Helmholtz instability......Page 22 6. Transient instability and streamwise vortices......Page 26 7. Turbulence, viewed as a random field of vorticity......Page 30 8. The Kolmogorov-Obukhov energy-cascade theory......Page 31 References......Page 36 1. Introduction......Page 40 2.1.1. Dimensional analysis......Page 41 2.1.2. Exact dispersion relation......Page 42 2.2. Froude Number......Page 43 2.3. Stratification and buoyancy frequency......Page 44 2.4. Internal Gravity Waves......Page 47 2.5. Mountain Waves......Page 49 2.6. Mass, momentum and energy fluxes......Page 51 3.2. Parcel argument......Page 52 3.3. Dimensional analysis......Page 53 3.3.1. Rayleigh number......Page 54 3.5. High Rayleigh number......Page 55 3.6. Very High Rayleigh number......Page 57 4.1. Plumes - dimensional analysis......Page 58 4.2.1. Entrainment assumption......Page 60 4.4.1. Dimensional analysis......Page 61 4.5. Fires......Page 63 5.2.1. Dimensional analysis......Page 64 5.2.2. Laboratory verification......Page 66 6.1. Rotating frame and the Coriolis force......Page 67 6.2. Inertial oscillations......Page 69 6.3. Rossby radius of deformation and eddies......Page 70 6.4. Buoyancy-driven coastal currents......Page 72 References......Page 73 1. Introduction......Page 74 2.1. Atmospheric properties......Page 75 2.2. Solar forcing......Page 77 2.3. Greenhouse effect......Page 78 2.4. Radiative transfer......Page 80 2.5. Climate change......Page 82 2.6. Further atmospheric properties......Page 84 2.7. Oceanic properties......Page 86 2.8. Ocean forcing......Page 87 3.1. Role of dynamics......Page 88 3.2. Rotating fluids......Page 89 3.3. Weather and climate models......Page 92 3.4. Dynamical processes......Page 93 3.5. General circulation of the atmosphere......Page 97 3.6. Ocean circulation......Page 99 3.7. Tropical Ocean-Atmosphere Coupling......Page 103 References......Page 107 1. Introduction......Page 110 2.1. The ENSO......Page 114 2.2. The ENSO Modoki......Page 117 2.2.1. Ocean-atmosphere coupling......Page 120 2.2.2. ENSO Modoki vs. ENSO Impacts......Page 121 2.3. The Indian Ocean Dipole......Page 125 2.3.1. Ocean-atmosphere coupling......Page 127 2.3.2. Triggering and termination processes......Page 128 2.3.3. IOD impacts......Page 130 2.3.4. IOD predictions......Page 132 3. IOD, ENSO and ENSO Modoki Interactions......Page 134 4. Discussions......Page 137 References......Page 138 1. Introduction......Page 144 2. Tropical cyclone variability in the instrumental record......Page 146 3. Paleotempestology......Page 149 4. Attribution......Page 150 5. Simulating global warming effects on tropical cyclones......Page 153 6. Effect of tropical cyclones on climate......Page 156 7. Summary......Page 160 References......Page 161 1. Motivation......Page 168 2. Transport and mixing in the atmosphere......Page 170 3.2. Evolution equations......Page 174 3.3. Stretching in linear flows......Page 176 3.4. The relation between stretching and mixing......Page 179 3.5. ‘Type I’ and ‘Type II’ flows......Page 180 3.6. Stirring and transport in quasi-two-dimensional flows......Page 183 4. Modelling approaches......Page 187 5.1. The 2000 ACTO campaign – combining chemical measurements and backward trajectory calculations......Page 189 5.2. ‘Around the world in 17 days’ – transport of smoke from Russian forest fires......Page 195 5.3. ‘Observational and modeling analysis of a severe air pollution episode in western Hong Kong’......Page 198 6. Conclusion......Page 201 References......Page 203 1. Motivation......Page 206 2. Climatic Setting......Page 207 3. Horizontal Energy Transport in the Atmosphere......Page 209 4. Rain Making......Page 211 5. Baroclinic Instability and the Synoptic Scale......Page 214 7. Propagation Speed of Synoptic Weather Systems......Page 216 8. Conceptual Results for Rain......Page 218 9. Three Historical Mid-Latitude Extreme Rain Events......Page 219 9.1. Central Europe: Elbe 2002......Page 220 9.3. Mississippi 1993......Page 222 10. Orographic Precipitation Modeling......Page 223 10.1. Non-Hydrostatic Numerical Modeling: the Meso-Scale Numerical Weather Prediction Model COSMO......Page 225 10.1.1. Basic Equations......Page 226 10.1.3. Microphysics......Page 227 10.1.5. Turbulence......Page 229 10.2. Sensitivity Studies of Orographic Precipitation using the COSMO Model......Page 230 10.3. Estimating Maximum Orographic Precipitation......Page 233 11. Convective Precipitation......Page 236 11.1. Mesoscale Convective Systems......Page 238 12. Conclusion......Page 239 References......Page 240 1. Introduction......Page 244 2.1.1. Weather charts......Page 247 2.1.2. Atmospheric properties......Page 248 2.1.3. Energy in the atmosphere......Page 250 2.1.4. Water vapour in the atmosphere......Page 252 2.2.2. Equations of motion......Page 254 2.2.3. Synoptic scales of motion......Page 255 2.2.4. Small scale motion......Page 256 2.3.1. Scales of meteorological phenomena......Page 257 2.3.2. Monsoons......Page 258 2.4.1. Cyclones......Page 259 2.4.3. Thunderstorms......Page 260 3. Hydrology......Page 261 4.1. Dynamics of well-mixed waterbodies......Page 266 4.1.2. Periodic input function......Page 268 4.1.3. Impulse input......Page 269 4.2. Dissolved oxygen systems......Page 270 4.3. Water quality in rivers and streams......Page 273 4.3.1. Point sources......Page 274 4.3.3. Unsteady state dispersive systems......Page 276 4.4.1. Enhanced Stream Water Quality Model (QUAL2E)......Page 278 4.4.3. One Dimensional Riverine Hydrodynamic and Water Quality Model (EPD-RIV1)......Page 279 References......Page 280 1. Introduction......Page 284 2.1. The first scientific encounter of solitons......Page 286 2.2. Behavior of solitons......Page 288 2.3. Derivation of Boussinesq-type and KdV Equations......Page 291 2.4. Importance of various phenomena for tsunami propagation, a sensitivity analysis......Page 297 3. Tsunami Forecasting......Page 300 3.1. Tsunami source estimation......Page 301 3.2. Quick Tsunami Forecasting Techniques......Page 304 References......Page 307 Rogue Waves......Page 312 1. Introduction......Page 313 2. The NLS equation......Page 316 3. Absolute and convective instabilities......Page 318 4. The case with only second-order dispersion......Page 319 5. Classifying the instabilities in the presence of third-order dispersion......Page 320 6. Summary and conclusions......Page 321 References......Page 322 Index......Page 326 1. A brief introduction to vortex dynamics and turbulence / H. Keith Moffatt -- 2. Geophysical and environmental fluid dynamics / Tieh-Yong Koh and Paul F. Linden -- 3. Weather and climate / Emily Shuckburgh -- 4. Dynamics of the Indian and Pacific oceans / Swadhin Behera and Toshio Yamagata -- 5. The hurricane-climate connection / Kerry Emanuel -- 6. Transport and mixing of atmospheric pollutants / Peter H. Haynes -- 7. Extreme rain events in mid-latitudes / Gerd Tetzlaff, Janek Zimmer, and Robin Faulwetter -- 8. Dynamics of hydro-meteorological and environmental hazards / A.W. Jayawardena -- 9. Tsunami modeling and forecasting techniques / Pavel Tkalich and Dao My Ha -- 10. Rouge waves / F. Dias, T.J. Bridges, and J.M. Dudley The Institute for Mathematical Sciences at the National University of Singapore hosted a Spring School on Fluid Dynamics and Geophysics of Environmental Hazards from 19 April to 2 May 2009. This volume contains the content of the nine short lecture courses given at this School, with a focus mainly on tropical cyclones, tsunamis, monsoon flooding and atmospheric pollution, all within the context of climate variability and change.The book provides an introduction to these topics from both mathematical and geophysical points of view, and will be invaluable for graduate students in applied mathematics, geophysics and engineering with an interest in this broad field of study, as well as for seasoned researchers in adjacent fields. The Institute for Mathematical Sciences at the National University of Singapore hosted a Spring School on Fluid Dynamics and Geophysics of Environmental Hazards from 19 April to 2 May 2009. This volume contains the content of the nine short lecture courses given at this School, with a focus mainly on tropical cyclones, tsunamis, monsoon flooding and atmospheric pollution, all within the context of climate variability and change. The book provides an introduction to these topics from both mathematical and geophysical points of view, and will be invaluable for graduate students in applied mathematics, geophysics and engineering with an interest in this broad field of study, as well as for seasoned researchers in adjacent fields