Name Index

AAmbühl, 393, 395Anderson, 340Archimed, 132, 133, 135, 136, 286ASME, 399, 400, 412

BBatchelor, 210, 222, 412, 415Beaufort, 278Berezin, 153Bernoulli, 170, 225Bessel, 352Betten, 38Bingham, 405Bjerknes, 321Block, 38Boltzmann, 113Boussinesq, 109, 110, 127, 128, 141, 145,

147–150, 153, 193, 194, 199, 205, 206,212, 222, 224, 258, 299

Bowden, 357Bowen, 38Bowman, 391, 392Bradley, 393, 394Bradshaw, 404Brown, 100, 398, 410Brunt, 150, 287, 288, 290, 294, 295, 306Bryson, 222Bührer, 393, 395Burger, 21Bye, 328

CCamp, 407Caratheodory, 69, 79Carnot, 69, 78, 79Castelli, 413, 415

Cauchy, 68, 69, 74, 91, 108, 114, 115, 117,118, 121–123, 125, 138, 139, 157, 404

Celsius, 391, 394, 405, 408Chadwick, 38Chen, 391, 394, 397Choboter, 267Clausius, 69, 79, 81Cooper, 270, 357Coriolis, 20, 21, 98, 151, 162, 165, 175, 195,

264, 267, 297, 319, 322, 323, 328, 330,349, 357

Cosserat, 113Csanady, 356, 358

Dd’Alembert, 226, 228, 258Defant, 345, 346, 404Descartes, 225Dietrich, 182Dirac, 295, 312Dorsey, 405, 409Duhem, 69, 79Dulong, 98

EEinstein, 221, 410, 411Ekman, 212, 319–321, 340–348, 350, 351,

353–358, 360, 368, 375, 394, 404Ellison, 353Ertel, 172, 177Euclid, 30, 31Euler, 68, 74, 76, 86–88, 101, 128, 159, 170,

175, 224, 225, 293, 343, 353

FFabuss, 405, 407Father Louis, 3Fatio de Duillier, 5

K. Hutter et al., Physics of Lakes, Volume 1: Foundation of the Mathematicaland Physical Background, Advances in Geophysical and Environmental Mechanicsand Mathematics, DOI 10.1007/978-3-642-15178-1,C© Springer-Verlag Berlin Heidelberg 2011

419

420 Name Index

FAVRE, 192, 193, 195Fer, 269, 271Fermat, 108Feynman, 25, 222Fick, 144, 145, 200, 212Findenegg, 16Fischer, 375Fjeldstad, 370, 375Fleming, 345Fofonoff, 404Forel, 5, 16, 19Foristall, 372Foucault, 98Fourier, 200, 212, 229, 232, 297Frisch, 210Froude, 22

GGalile, 68Gauss, 60, 103, 106, 108, 136Gedney, 320, 362, 364–368Glauert, 188Goldstein, 374Green, 62, 91, 369, 371, 375, 412Gurtin, 38

HHall, 405Hansalic, 203Heaps, 3, 328, 338, 345–347, 355–358, 363Heaviside, 370Helmholtz, 170–172, 175, 177, 179Hidaka, 370Hide, 177Hinze, 210Hollan, 3, 4Hooke, 75Hutchinson, 16, 266Hutter, 38, 153, 203, 210, 211, 266, 294, 389,

405

IImboden, 396Irish, 378Isdale, 407–409Ivanov, 270

JJackson, 405Jäger, 403Jänichen, 4Jeffrey, 410, 415Jelesnianski, 372, 376

Jöhnk, 8, 17, 38, 203, 210, 211, 266Johnson, 345Jones, 203, 357Joule, 81

KKatz, 177Kearsley, 404, 405Kelvin, 69, 79, 80, 82, 160, 161, 170, 255Kennedy, 394Kepler, 75Kielmann, 372Kirchhoff, 108Klingbeil, 38Knudsen, 394Koizumi, 406, 408, 409Kolmogorov, 212Korosi, 407Kowalik, 372Kronecker, 32Krümmel, 406Kubinski, 403, 404Kuwahara, 403

LLacomb, 350, 360Lagrang, 86Lagrange, 75Lamb, 222, 374Lanchester, 188Landau, 222Langmuir, 268Laplace, 62, 128, 234, 300Launder, 203Lautrup, 222Leaman, 270LeBlond, 222, 294Leibniz, 75, 180, 225Leibovich, 222Lesieur, 210Lick, 320, 362, 364–368Lifshitz, 222Lighthill, 222, 294Lin, 412Liouville, 302Liu, 38Löffler, 16Lumley, 210

MMadsen, 351, 353, 355Maiss, 47Marshall, 269, 270Massel, 222

Name Index 421

Maxwell, 405, 415Mayer, 69, 78, 81McComb, 210Mei, 222Miles, 339Millero, 391, 394, 397, 403, 404Mills, 405, 407Miyake, 406, 408, 409Monin, 210Montgomery, 413, 415Moore, 99Mortimer, 5, 7, 249, 254, 339Munk, 213, 214, 218, 219, 340Mysak, 222, 294

NNansen, 321Napoleon, 391Navier, 98, 188, 194, 198, 200, 212, 349Newton, 67, 68, 70, 74–77, 83, 99, 117, 123,

124, 128, 140, 166, 225, 279, 286, 319,331, 359, 394, 404, 410, 411

Nomitsu, 375

OOseen, 412

PPapin, 78Pascal, 131Pearce, 357Pedlosky, 165Phillips, 222Pickard, 345, 346Piquet, 210Planck, 79Platzman, 320, 321, 372, 374–385Poincaré, 255Pointing, 205Poiseuille, 404, 405Pond, 345, 346Popov, 399, 402, 403, 413–415Prandtl, 125, 188, 199–202, 204, 210, 328,

351, 357, 358, 380

RRao, 374REYNOLDS, 192Reynolds, 21, 103, 119, 136, 137, 185, 187,

188, 192, 195, 196, 198, 199, 201, 203,210–214, 217, 219, 356, 412

Richardson, 21, 339, 340Riemann, 108Rodi, 203

Rossby, 21, 154Rotta, 210Ruellan, 243, 244Rupin, 406

SSander, 211Sarasin, 5Schleicher, 404Schmidt, 200, 204Schoonover, 391, 392Schott, 270Schröder, 177Schulthaiss, 3Seebass, 222Send, 269, 270Shimaraev, 269Spalding, 203Spencer, 38Stein, 405, 412Steinwehr, 403Stoker, 222Stokes, 62, 64, 159, 164, 169, 188, 194, 198,

200, 212, 217, 261, 349, 405, 407, 410, 412Stommel, 99Sturm, 302Svensson, 210, 355, 356Sverdrup, 345

TTaylor, 59, 115, 197, 235, 236, 286, 348, 373,

391–393, 411Tennekes, 210Thomas, 363Tikhomirov, 20Tilton, 391–393Townsend, 210Trösch, 389, 405Treder, 177Truesdell, 69, 76, 79, 177

UUmlauf, 203

VVäisälä, 150, 287, 288, 290, 294, 295, 306Van Dyke, 222, 244Vaux, 270Venn, 225von Kármán, 351

WWüest, 274, 396Walker, 222

422 Name Index

Wallet, 243, 244Wang, 38, 212, 404Weber, 108Weis, 203Weisbach, 6Welander, 320, 363, 372White, 404, 405Whitham, 222Wilson, 393, 394

Witten, 363Wüest, 141

YYaglom, 210

ZZatsepin, 183

Lake Index

AAmadeus, 12Aral Sea, 12Athabaska, 12

BBaikal, 11, 12, 19, 20, 109, 141, 195, 266, 273,

390Balaton, 11, 12Balkhash, 12

CCaspian Sea, 10–12Chad, 11, 12Constance, 3, 5, 11, 12, 15, 18, 47, 266, 269,

275, 277–279, 307

DDead Sea, 10, 12, 18

EEdward, 12Erie, 12, 320, 363–366, 376, 382, 385Eyre, 11, 12

GGairdner, 12Geneva, 266, 269–271Great Bear, 12Great Lakes, 20Great Lakes of America, 266Great Salt, 12Great Slave, 12Green Bay, 3

HHuron, 12

IIssyk Kul, 12

KKuronian lagoon, 207

LLac Léman, 5, 7Ladoga, 12, 20, 266Lake of Geneva, 12Lake of the Four Cantons, 265Lake of Zürich, 12

MManitoba, 12Maracaibo, 12Michigan, 3, 12Mweru, 12

NNeusiedler See, 207Nicaragua, 12Nyasa, 12

OOnega, 12, 20, 266Ontario, 12, 363

QQinghai, 11, 12

RReindeer, 12Rudolf, 12

SSuperior, 12

423

424 Lake Index

TTanganyika, 11, 12, 195, 266Tianchi, 10Titicaca, 12Tonle, 12Torrens, 12Tung Ting, 12

UUrmia, 12

VVenern, 12

Victoria, 11, 12Vierwaldstätter See, 265, 266Vistula lagoon, 207Volta, 12Vostok, 11, 12

WWinnipeg, 11, 12Winnipegosis, 12Wuxi, 207

ZZürich, 294, 295, 297, 298

Subject Index

AAbsolute acceleration, 97Absolute system, 95Absolute temperature, 69Acceleration, 85, 88Acoustic waves, 110Adiabaticity assumption, 148Algebraic Reynolds stress model, 211Amictic lake, 17Amplitude, 244Angular momentum, 76Angular velocity, 136Angular velocity of the Earth, 35Anisotropic turbulence, 212Anisotropic turbulent flow state, 210Anisotropy of viscous stresses, 410Anisotropy tensor, 211Anoxia, 266Antarctica, 17Anti-nodal lines, 249Approximation

constant density layer, 311constant-density-two-layer, 313long-wave, 239, 246rigid lid, 267, 316shallow water, 234short-wave, 238, 245two-layer, 281

Archimedian buoyancy force, 132, 135Archimedian principle, 132, 133, 136, 286Aspect ratio, 20, 150, 153Associative law, 26, 27Assumption

hydrostatic pressure, 247long-wave, 247shallow-water, 247

Assumption of turbulent objectivity, 214At the bottom surface, 209At the free surface, 209

Autocorrelation, 197Average, 185Averaged density field, 197Averaging operator, 187

BBalance

of energy, 77, 136of entropy, 69of linear momentum, 74of mass, 73, 100of moment of momentum, 76of momentum, 110of momentum of momentum, 110

Balance law, 67, 72, 80for dissipation rate

of the turbulent kinetic energy, 203for the mixing length, 202for the turbulent kinetic energy, 203in a general form, 69of energy, 83, 103, 224of entropy, 103of internal energy, 140of linear momentum, 222of mass, 83, 103, 222of moment of momentum, 111, 112of momentum, 83, 103of momentum of momentum, 83

Baroclinicity, 311Barycentric velocity, 193Basal boundary condition, 208Basal condition

no-slip, 329, 332perfect sliding, 329, 332viscous linear sliding, 332

Basis, 30Bathymetric profile, 47Beats, 234Beaufort’s scale, 278

425

426 Subject Index

Bottom slip, 328Boundary condition, 207

for k and ε, 209for momentum, 207for species concentration, 209for the temperature, 208

Boundary layer, 334thickness, 243turbulent, 351

Boussinesqapproximated equation, 149approximation, 147assumption, 145fluid, 109, 127, 141, 145, 153number, 153

Boussinesq fluid, 193, 194, 199, 205, 206, 212,299

Brownian motion, 100, 398Brunt-Väisälä frequency, 287, 289, 290, 294,

295, 306Buoy, 222Buoyancy

effect, 205force, 132, 133, 193frequency, 150, 287parameter, 153period, 289, 290, 293

Burger number, 21

CCabbeling, 272Carrier medium, 221Cartesian coordinate system, 30Cauchy

lemma, 114, 117stress tensor, 125

Center of gravity (or mass), 274, 276, 278,280, 281, 316

Centigrades, 394Centrifugal force, 99Centripetal acceleration, 97Change in potential energy, 281Channel flow, 404Characteristic equation, 93Characteristic turbulent eddy, 192Circulation, 58, 264, 319

anticyclonic, 273cyclonic, 273steady, 322

wind-induced, 330wind induced, 328

Classical principle of relativity, 68Closure relation, 204

Clusters, 389Coefficient

constant drag, 332friction (drag), 329of thermal expansion, 389, 396skin friction, 380

Cold monomictic, 17Collinear, 29Commutative law, 26Complex number, 26Component, 141Compressibility, 391Compressible fluid, 193Conductivity, 396Conservation

of energy, 69of linear momentum, 69of mass, 69of moment of momentum, 69

Conservation law, 9, 68Constituent, 141, 142Constitutive theory, 83Continuity equation, 106Continuous density variation, 280Convective acceleration, 323, 330Convective chimney, 269, 270Convective derivative, 87Convergence zone, 272Coriolis

acceleration, 35, 97, 195force, 20, 99parametre, 21

Correlation, 190Counter phase, 249Cross–product, 33Curl, 57Current

drift, 354vertical structure, 353

geostrophic, 349gradient, 320, 327, 358, 360slope, 327surface, 353, 382vertical structure, 319, 328, 336, 338wind drift, 327, 346wind-driven

steady, 358wind-induced, 319

tme-dependent, 369vertical structure, 347

Current meter, 245Cyclonic, 20

Subject Index 427

DD’Alembert solution, 228De-aeration, 392Deep ocean convection, 269Deflection angle, 348Deformation gradient, 90Density, 389, 390

of pure water, 391anomaly, 131, 153measurement, 391preserving, 106, 193weighted average, 193

Density perturbation, 247Derivative, 41Deuterium, 389Differentiation, 41Diffusion, 141

coefficient, 145of momentum, 264

Diffusive mass flux of tracer, 144Diffusivity, 145Dilatant, 123

fluid, 124Dimension, 29Dimictic, 16, 266

lake, 17Dirac pulse, 295Direct Numerical Simulation, 194, 210, 212Direction of steepest descent, 47Dispersion, 232Dispersion relation, 228, 242, 245

finite-depth, 246quantised, 257

Dissipation, 140, 224, 299, 308Dissipation rate

density, 198due to the mean velocity, 198due to the mean velocity field, 198

Distance, 29Distribution of

density, 263mass, 262, 263

Distributive law, 27Diurnal circulation, 19Divergence

free, 106of tensor field, 50of vector field, 50, 54operator

for a second rank tensor field, 55solenoidal, 106theorem, 106

DNS, 194, 210, 212

Down-stroke, 338Down-welling, 338Drag coefficient, 277, 290Drift, 244Dual vector, 57Dyadic product, 39Dynamic

bulk, 127shear viscosity, 124

EEarly anisotropic closure scheme, 212Eddy, 7

diffusivity, 200viscosity, 198

Eddy viscosity, 331, 346, 351, 355, 357E-folding depth, 246E-folding time, 293Eigenfunctions, 252Eigenmodes, 252Eigenvalues, 252, 307

problem, 252Ekman

depth, 319, 342, 346, 348, 351, 360layer, 356problem, 320, 348spiral, 319, 341, 343, 346–348, 350theory, 340

Electrical conductivity, 389, 390, 396Electronic recording unit, 296Ellipses, 242Energy, 68

balance equationin conservative form, 139

Enthalpy function, 140Entropy, 69, 79, 80

production, 80Environment, 71Epilimnion, 8, 15, 275, 283, 296, 297, 308,

310, 311, 330, 333, 337Equation

acoustic, 222hydrostatic, 247Laplace, 234linear wave, 223of motion, 121

kinematic, 236of state, 107wave, 226, 228

EquationsBessel’s differential, 352Navier-Stokes, 349shallow water, 240viscous hydrodynamic, 322

428 Subject Index

Equivalent, 31Equivalent depth, 313Ergodic

property, 211Ergodic1hypothesis, 189Ergodicity, 212Euclidean space, 31Euler acceleration, 97Euler’s law

of angular momentum, 69of moment of momentum, 76

Euleriandescription, 86representation, 86

Externalforce, 76pressure, 131

Extinction coefficient, 205

FFavre average, 193Fetch, 277Fick’s

first law, 145of mass flux, 200

second law, 144Field

differentiation, 41Filter, 187Fingering, 267First Coriolis parameter, 36, 151First law of thermodynamics, 69, 78, 83, 136Fish rope, 241Fishline, 222Flow

simple shear, 339wind-driven, 327

Fluctuation, 185, 187Fluid

barotropic, 223elastic, 223Euler, 224homogeneous, 235ideal, 224incompressible, 234linearly stratified, 339

Fluid body, 123Flux, 72

of entropy, 80of spin, 76

Force, 67potential, 129

Fourierexpansions, 229integral, 229series, 229

Fourier’s lawof heat conduction, 200

Free (ideal, frictionless)slip, 337Free convection approximation, 147Free surface, 208Friction, 290

coefficient, 291force, 290

Froude number, 22Fundamental equation, 83Fundamental equations, 297

GGauss

law, 136Geostrophic motion, 264, 267Gradient, 44

of tensor field, 50of vector field, 50

Gradient-type closure, 210Gravity, 263

current, 18, 268, 269thermally-induced, 271

force, 110, 132variation, 263

Green’s functions, 369, 371, 375Groundwater accretion, 208Group velocity, 232, 238

long-wave, 240Gyre, 7, 338

HHarmonic oscillator, 287Heat

flux, 279latent, 265sensible, 265

transfer coefficient, 279Heat conduction, 224Heat conductivity, 389, 412–415Heat flow, 77, 139Heat supply

radiation, 77Hodograph plane, 344, 360Holo, 15Holomictic, 15–17Holomictic lake, 16, 17Homogeneous water, 2Homogenisation, 276

of water masses, 274

Subject Index 429

Homothermy, 266Horizontal exchange coefficient, 213Horizontal velocities, 259, 260Hydrodynamics of lakes, 1Hydrogen, 389Hydrogen bonds, 389Hydrologic front, 271Hydrostatic

equation, 129pressure assumption, 154

Hydrostatic force balance, 297Hydrostatics, 110, 128Hypolimnion, 8, 15, 275, 283, 296, 297, 308,

310, 311, 330, 333, 337

IIdeal fluid, 83, 127Impurities, 414

elliptical particles, 415spherical particles, 415

Incompressibility, 107Incompressible, 107Inertial reference system, 68Infinitesimal cube, 103Infrared radiation, 264Inland sea, 10Instability, 285

transition to, 339Internal

energy, 77oscillations, 2pressure, 131wave, 18

Internal oscillations, 294Invariant, 93, 94Inverse stable

temperature stratification, 15Inversely stably

stratified, 15Irreversibility, 80Irreversible, 69Irrotational, 58Isomorphic, 31Isopycnal

depth-time series, 296surfaces, 296time series, 297

Isothermdepth-time series, 296, 311

Isotropic, 190tensor, 210tensor function

of tensors of second rank, 214turbulence, 190, 192

KKelvin

temperature, 69Kinematic

viscosity, 124, 185turbulent, 204

Kinematics, 84Kinetic energy, 77Kinetic theory of gases, 405Kronecker Delta, 32

LLagrangean

description, 86representation, 86

Lakemorphology, 5narrow homogeneous, 322stratified in two layers, 330

Lake-level data, 376Lake-level-time series, 382Lake-surface fluctuations, 376Laminar, 6

flow, 185Langmuir circulation, 268Laplace operator, 128, 300Laplacean operator, 223Large Eddy Simulation, 210, 212Law

of conservation of energy, 67Left Cauchy–Green deformation tensor, 91Left stretch tensor, 90Length of a vector, 27LES, 189, 210, 212Limnetic, 18, 20Limnigraph, 245, 377, 382, 385Limnology, 396Linearly independent, 29Littoral, 3, 18, 20Littoral water, 271Local balance law, 103

of internal energy, 139of mass, 105of momentum, 118

Local derivative, 87Logarithmic

singularity, 352, 358spiral, 343

Longitudinal eigenmode, 254Longitudinal waves, 110

430 Subject Index

MMass, 68

concentration of tracer, 143density, 100fraction, 143

Materialbehavior, 123body, 25particle, 84time derivative, 86

Matrix of the Cauchy stress tensor, 118Mean strain rate tensor, 214Mean value, 187Mechanics, 68Mero, 16Meromictic, 16, 266Meromictic lake, 17Metalimnion, 8, 15, 264, 282, 296, 297, 306,

308, 310–312, 332, 333thickness, 311

Method of separation of variables, 231Mictic, 15Mineralization, 390, 409Mixing, 274Mixing length, 201Mode, 305

baroclinic, 305, 307, 311higher order, 311, 313

internal, 310number, 308of the horizontal velocity component, 311of the vertical velocity component, 311

Model-(k − �), 202Model-(k − ω), 202Model-(k − ε), 202Model-(k − ε), 203

for Boussinesq fluids, 203for density preserving, 203

Molecularheat capacity, 399heat conductivity, 412

Momentof a force, 37of a vector, 37of flux

of linear momentum, 76of supply

of linear momentum, 76Moment of momentum, 76Momentum, 68

equationfor a Newtonian Boussinesq fluid, 128

flux, 74of the body, 110

Mono-lake, 17Monomictic, 17Mooring, 296Motion, 84

function, 84Munk’s turbulence parameterization, 218

NNavier-Stokes

equation, 200fluid, 198

Navier-Stokes-Fourier-Fick equation, 212Net transport, 307Newton’s law, 279

second, 286Newton’s second law, 68, 74, 118

of motion, 67Newtonian Boussinesq fluid, 127nth longitudinal mode, 254No-slip condition, 208Nodal lines, 249Nonequilibrium stress, 125Norm of a vector, 27Normal stress, 114

OODF integrators, 241Oil spill trajectories, 355Oligomictic, 17One equation model, 201, 202Orthogonal, 29Orthonormal basis, 30Oscillations in rectangular basins, 252Oseen-type correction, 412Out of phase, 249Overturn, 266Oxygen, 389

PPartial derivative, 45Particle trajectories, 250, 251Particulate tracers, 410Pascal paradoxon, 131Pelagial, 3, 18Perturbation pressure, 234, 237, 246Phase

speed, 228, 231, 245velocity, 230, 238

long-wave, 240Phenomenological coefficients, 389Photosynthesis, 8Physical balance law, 73

Subject Index 431

Physical law, 68Physical limnology, 1Physically realizable process, 212Physics of lakes, 1Phytoplankton population, 205Pointing vector, 205Poiseuille flow, 404Polar decomposition theorem, 90, 91Polymictic, 17Potential energy, 79, 277Power due to the wind action, 278Power of working, 277, 404Power of working of the pressure, 140Prandtl

layer, 357, 380mixing length, 328

Prandtl number, 204, 210Present configuration, 84Pressure, 111, 235, 255, 394

absolute, 392barometric, 391gauge, 247work parameter, 153

Principia, 124Principle of determinism, 67Process

adiabatic, 224homentropic, 224isentropic, 224

Process variables, 77Processes

baroclinic, 263, 267barotropic, 263, 267external, 264, 267internal, 264, 267

Production, 72, 142of entropy, 80

Production rate densityof species c, 206

Profundal zone, 18Projection, 211

filter, 211Proper value, 252

problem, 252Protium, 389Pseudoplastic, 123, 124Pure longitudinal mode, 258Pure transversal mode, 258

RRadiating source, 139Radiation, 263, 299RANS, 189, 210, 211

Real number, 26Rectangular basin, 254Reference configuration, 84Reflection, 244, 247Relative

acceleration, 97system, 95velocity, 97

Reynoldsaveraged equation, 211averaging procedure, 195hypothesis, 198number, 21, 185stress, 214stress tensor, 196, 199, 213, 217theorem, 136transport theorem, 119, 137versus Favre average, 192

Richardson number, 21, 339Right Cauchy–Green deformation tensor, 91Right stretch tensor, 90Rigid lid, 302Rigid spherical inclusions, 410River

inflow, 362outflow, 362

Rossbynumber, 21, 153, 154radius of deformation, 21

Rotation, 57of tensor field, 50of vector field, 50

Roughness length, 355

SSalinity, 390, 394, 396Scalar, 25

product, 27Schmidt number, 204Seasonal variation

of the temperature, 3of the thermocline, 8

Second Coriolis parameter, 36, 151Second law of thermodynamics, 69Second rank tensor, 53Second statistical moment, 190Seiche, 5Separation of variables technique, 302Set-up, 325, 378, 379, 382, 383

current, 327Shallow shore region, 246Shallow water

approximation, 20, 150, 154

432 Subject Index

equation, 150scaling, 218

Shearinstability, 339stress, 111, 114vertical structure, 328, 336viscosity, 127

Shear traction, 277Sigmoidal curve, 339Sigmoidal density profile, 282, 295Simple shear experiment, 125Skewness, 339Skewsymmetric, 52Slidig friction law, 329Solar irradiation, 2Solar radiation, 264, 266Solid body, 123Space scale, 185Specific density, 131Specific heat, 389, 399

at constant pressure, 400, 401, 403at constant volume, 403

Speed of sound, 223adiabatic, 224

Spin, 76Spin tensor, 57, 89Spring circulation, 15, 18Stability, 285Stable direct summer stratification, 15Standard litre, 391State variables, 77Stationary random process, 187Steady, 106Stokes

assumption, 217Strain rate, 126

deviator, 126tensor, 89

Strain rate tensor, 351Stratification, 17, 264, 312

linear, 304, 308neutrally stable, 268stable, 266, 267, 274, 287, 289summer, 308unstable, 267, 268, 287, 289

locally, 294Stratified, 2Streaklines, 6Stream

line, 243, 250lines, 327, 328, 337, 338

Stream function, 364, 367boundary conditions, 364volume transport, 366

Stream line, 243, 250Stream track, 379Stress, 110

factor, 380turbulent shear, 351vertical shear, 330, 338viscous, 323, 330wind shear, 322, 343, 362

Stress tensor, 113, 114Stress vector, 111, 113Stretch tensor

left, 91right, 91

Stretching deviator, 126Stretching tensor, 89, 126Structural front, 19Sturm-Liouville eigenvalue problem, 302Subgrid behavior, 201Subgrid eddy momentum exchange, 212Summary of (k − ε)-equation, 206Summer stratification, 14Supply, 72

of angular momentum, 76of entropy, 80of spin, 76

Surfacebasal, 235displacement, 246elevation, 245, 255, 259, 260free, 235

Surface force, 76, 111Surface gravity waves, 234

linearizeddispersion relation, 238

Surface tension, 389Surface wall layer, 356Surface water

penetration to depth, 268Surges, 376Suspended matter, 398, 410Suspended substance, 141Symbolic notation, 31Symmetric, 52

TTemperature, 394

boiling, 389freezing, 390melting, 389of maximum density, 397

Subject Index 433

Temperature correlation, 197Tensor, 25, 38

product, 39Tetrahedron, 116Thermal

bar, 271, 273conductivity, 413, 414

of a mixture, 414convection, 268diffusion, 296, 299diffusivity, 389, 413, 415equation of state, 297, 393expansion, 275, 283

Thermal bar, 19Thermal equation of state, 107, 126Thermals, 269Thermistor chain, 245, 294, 296Thermobaric effect, 274Thermocline, 15, 264, 295, 330, 339

depth, 279Thermodynamic pressure, 126, 140Thermodynamics, 68Thermometry of lakes, 5Tides

on Lake Erie, 376Time scale, 185Torsion pendulum, 404Total transport, 344Trace operator, 53Tracer, 2, 141Traction vector, 111Trajectories, 240, 243, 244

particle, 242, 250Trajectory, 87Transfer matrix, 314Transport, 2Transport stream function, 361Transport theorem, 103Transpose of tensor, 52Transversal modes, 254Transverse eigenmode, 254Transverse waves, 110Tritium, 389Turbidity, 2Turbidity currents, 269Turbocline, 8, 265, 268Turbulence, 6, 18Turbulence activity, 266Turbulent

diffusivity, 201dissipation rate, 198, 201, 202eddies, 268exchange coefficient, 199

flow, 185heat flux, 199heat flux vector, 196kinematic viscosity, 199kinetic energy, 190, 198, 201, 202mass flux vector, 196mixing, 268motion, 185Prandtl number, 200Schmidt number, 200shear stress, 199species diffusivity, 204species mass flux, 196, 199thermal diffusivity, 204viscosity, 125, 201vorticity, 202

Two equation model, 201, 202

VVapour, 389Vector, 25

field, 54product, 33space, 26valued field, 50

Velocity, 85of the surface current, 348

Velocity components, 255Velocity measurements, 311Vertical exchange coefficient, 213Viscometer, 404Viscosity

bulk, 404, 405dynamic, 389, 406–412kinematic, 389, 407shear, 404, 405, 409

Viscous contributionto the stress, 140

Viscous flow, 410Viscous fluid, 83Volume

force, 76preserving, 107

Volume fraction, 398, 410, 412Volume transport, 348, 361, 371

gyre, 366vector, 382

Vortex stretching, 95Vortex tilting, 95Vorticity, 89

tensor, 89vector, 89

434 Subject Index

WWarm monomictic, 17Water

standard seawater, 393anomalies, 389cascade, 19density maximum, 14mineralized, 413natural, 390pure, 390, 395, 400, 405–409, 413rainwater, 389saline, 390, 403, 406, 409, 413, 414

Water waves, 222, 244Wave, 221

backward moving, 250crest, 250forward moving, 250frequency, 227, 230, 238length, 238number, 227, 230, 232, 238

vector, 230, 231phase, 227, 230, 233plane, 230propagation

dispersive, 232non-dispersive, 232

quasi-standing, 248standing, 248, 249

gravity, 251solution, 253

surface, 234trough, 250

Wave guide, 295Waves

deep-water, 246dispersive, 234linear acoustic, 224non-dispersive, 234, 247plane, 224shallow water, 246, 247standing, 247, 258surface water, 253

Weather station, 377Wind, 263

data, 376–378factor, 345, 355induced current, 212mixing, 268set-up, 18stress, 380vector, 380

Wind-tide, 378computation, 382

Winterholomixis, 18homothermy, 14, 15, 18stagnation, 15

Winter cascading, 270Wonder of the rising water, 4