An Introduction to Ocean Turbulence

Index

abyssal ocean, 25, 83, 208, 220

abyssal plain, 25, 216

acoustic Doppler current profiler (ADCP), 71–73

acoustic methods of estimating , 73

acoustic scattering, 26, 135

Advanced Microstructure Profiler (AMP), 45, 47, 52, 64

advection–diffusion balance, 140, 154, 220

Agulhas Retroflection Zone, 177

air-foil probe, 60–65

along-shore currents, 11

Antarctic Bottom Water (AABW), 207, 212–215

Antarctic Circumpolar Current, 208

Archimedes, 22

ARGOS satellite tracking, 177

Atlantic Ocean, 24, 141, 177, 179, 212

atmospheric boundary layer

Autonomous Lagrangian Circulation Explorer (ALACE) floats, 179

autonomous underwater vehicle (AUV), 66

Autosub, 66

Baltic Sea, 160

Bahamas, 90

Banda Sea, 137

baroclinic instability, 32

Bay of Fundy, 215

Bénard, 81

benthic boundary layer (see also bottom boundary layer), 25, 45, 77, 100–102, 210, 216, 222

benthic nephloid layer, 102

billow, 37, 118, 121, 139, 153

black-smoker hydrothermal vent, 84, 161

boils, 13

Bosphorus, 215

bottom boundary layer (see also benthic boundary layer), 25, 77, 100–102, 105

boundary layer (see atmospheric boundary layer; benthic boundary layer; bottom boundary layer; mixed layer; viscous sublayer)

Brazil Basin, 99, 185, 202, 213, 223

breaking internal waves (see also wave breaking), 28, 117, 136, 149, 153, 183

breaking surface waves (see also whitecaps; foam; rate of energy dissipation in a breaking wave; wave breaking), 1, 8, 32, 95, 108, 205, 206–207, 219

bubbles, 8, 67, 108, 162, 173, 175

buoyancy, 22

buoyancy flux, 42, 59, 79, 207

buoyancy force, 22

buoyancy frequency, N, 23, 25

cabelling, 145, 157

caesium, 47–48, 188

CAMELION, 74, 94, 102

canonical value (see Munk’s canonical value of KT)

canyons (see submarine canyons)

Camarinal Sill (in the Strait of Gibraltar), 45, 139, 140, 151, 215

cascade of energy, 38, 49–50

Chain Fracture Zone, 213

channels, 210, 223

coastlines, 221

coherent structures (see also Langmuir circulation; plumes; vortex pairs), 38, 101

collapsing mixed layer, 29, 31, 125

conductivity–temperature–depth probe (CTD), 21, 130

continental slope, 203

convection, 81, 89, 107, 207

convective overturn, 116

convergence, 18

cool skin, 112

Coriolis force, 31

Coriolis frequency, f, 30, 183

Cox number, C, 131

critical frequency (of internal waves on a slope) 209

critical Richardson number, Ri_c, 120–123

critical Reynolds number, 5

cross-correlation coefficients, 51

CTD (see conductivity–temperature–depth probe)

cumulus clouds, 78, 82

density

   of air, 88

   of seawater, 20–22

density gradient ratio, R_ρ, 146–147

density overturns, 57, 130, 138

density profile (see also reordering (of density profile)), 23

detrainment, 15–18

detritus, 114

diapycnal mixing, 28, 139–144, 200

diatoms, 111

diffusion, 15

dimensional arguments

   characteristics of a jet (Problem, 3.3) 110

   characteristics of a plume (Problem, 3.2) 110

   Kolmogorov length scale, l_K (Section, 2.3.4) 48

   maximum rise of a plume in stratified environment (Problem, 3.4) 111

   Monin–Obukov length scale, L_MO (Section, 3.4.1) 88

   one-dimensional wavenumber spectrum of turbulence, Φ(k) (Problem, 2.5) 52

   Ozmidov length scale, L_O (Section, 4.4.1) 129

   rate of energy loss from breaking wave (Problem, 6.5) 221

   Reynolds number, Re (Section, 1.2) 4

   Richardson’s 4/3 power law (Problem, 5.1) 192

   tidal mixing parameter in shallow seas (Section, 3.4.5) 103

   vertical velocity frequency spectrum, Φ_w(σ) (Problem, 2.6) 76

Discovery Gap, 155

Discovery Passage, 60

dispersant, 13, 158, 162, 163

dispersion, 15, 158–189

dispersion relation, 28, 34

diurnal change, 23

diurnal cycle, 83, 90

diurnal migration

Doppler shift, 27

double diffusive convection, 144–149, 150

   diffusive regime of, 146

   doubly stable regime of, 146

   finger regime of, 146, 147, 149

drag coefficient on the seabed, C_D, 68, 87, 210

drag coefficient of the wind on the sea surface, C_Da, 88

drogue, 175

dust, 164, 194

Earth’s rotation (effect of), 111, 175, 183

East Australia Current, 177

East Greenland Sea, 83, 207

East Pacific Rise, 158, 161

eddy diffusion coefficient of density, K_ρ, 132, 133, 199

eddy diffusion coefficient of heat, KT, 42, 131, 203

eddy diffusion coefficient of mass (see eddy diffusion coefficient of density)

eddy diffusion coefficient of momentum (see eddy viscosity)

eddy dispersion coefficient, 169–170, 177, 180–182, 183, 185

eddy lifetime, 167

eddy viscosity, K_ν, 41, 133, 183

efficiency, 125

efficiency factor, Γ, 132, 148

ejection, 67

electromagnetic current meter, 67

energy balance equation, 54–56

energy cascade (see cascade of energy)

energy-containing eddies, 49

energy density, 33, 35

energy flux, 200, 204, 208, 209

engulfment, 11

ensemble, 54

entrainment, 11, 15, 83, 110, 111

entrainment assumption, 83

entrainment velocity, 84, 135

equation of state, 20

Equator, 47, 94

Equatorial currents, 177

Equatorial Undercurrent, 47

European continental shelf, 102, 105

external processes, 79, 106

fall speed (of particles), 22, 192

Fickian diffusion, 174, 179, 180

filaments, 165

fine-structure, 117, 122, 123

flocs, 156, 160

Floating Instrument Platform, FLIP, 138

floats (see also subsurface floats), 174–180

Florida Current, 45

flow separation, 81

fluorescent dye, 142

flux of buoyancy (see buoyancy flux)

flux of energy (see energy flux)

flux Richardson number, R_f, 132, 148

foam (see also whitecaps), 8, 13, 95, 206

fossil turbulence, 125

four-thirds power law (see Richardson’s four-thirds power law)

free-fall instrument (see also Advanced Microstructure Profiler (AMP); High Resolution Profiler (HRP); Multi-Scale Profiler (MSP)), 45, 64, 65

   measurements using, 139–144

freezing point, 20, 111

freshwater, 20, 111

friction velocity, u▤, 85, 88

front (see also tidal mixing front), 161

gas transfer, 8, 107, 109

Gaussian pdf, 68

geostrophic balance, 31

geostrophic turbulence, 177, 192

geothermal heat flux, 83, 110, 113, 216–217

gradient Richardson number, R_i, 119, 125–128, 138

group velocity, c_g, 26

Gulf of Lions, 83, 107

Gulf Stream, 177, 188

hairpin vortex, 17, 94, 101, 102

halocline, 24

harmful algal bloom (HAB), 158

Hatteras Abyssal Plain, 103, 106, 222

Hawaiian Ocean Mixing Experiment (HOME), 203, 219

Hawaiian Ridge, 202

heat flux, 3, 5, 39, 42, 43, 112, 207

helium, 3 (³He) 158, 161

High Resolution Profiler (HRP), 64, 130

Holmboe instability, 135, 150

hot-film anemometer, 60

hot spots, 144

‘h over u cubed’ criterion, 105

Hunter Channel, 213

hurricane force winds, 88, 163

hydraulic jump, 11, 208, 210, 213

hydrothermal heat flux, 217

hydrothermal plume, 83, 85, 110, 161

hydrothermal vent, 83, 85, 224

ice, 111

inertia, 194

inertial forces, 49

inertial period, 31

inertial subrange, 52

instability (see double diffusive instability; Holmboe instability; Kelvin–Helmholtz instability)

instantaneous release, 88, 163

integral scales, 169

intermediate nephloid layer, 102, 109

internal inertial waves, 205, 209

internal processes, 79, 106, 116

internal Rossby radius, L_Ro, 31–32, 177

internal-wave radiation, 25, 26

internal waves (see also internal inertial waves) 23, 25–28, 54, 57, 125, 135–139, 205, 208, 209

intrusion, 31

inverse problems, 218

Irish Sea, 33, 67, 104, 105, 188, 191, 201

isopycnal mixing, 28

isopycnal surface, 28

isotropic (see isotropy)

isotropy, 44–45, 49–50, 75, 123, 131

isotropy parameter, I, 50

jet, 110

Joule, J. P., 6

Joule’s experiment, 6–8

Juan de Fuca Ridge, 217

Kattegat, 133

Kelvin–Helmholtz instability, 119, 122, 126–127, 135

kinematic viscosity, 3, 43

kinetic energy (see also rate of production of turbulent kinetic energy), 39, 125

Knight Inlet, British Columbia, 55

Kolomogorov, A. N., 48, 52

Kolmogorov length scale, l_K, 48–49, 52, 65, 111

Kolmogorov’s minus five-thirds power law, 52

Kuroshio, 141, 177

kurtosis, 54

Labrador Sea, 83, 207

Lagrangian frequency spectrum, 55

Lagrangian integral length scale, L_L, 169, 177, 180

Lagrangian integral time scale, T_L, 169, 177, 180

laminar flow, 3, 56, 125

Langmuir cells (see also Langmuir circulation), 97–99, 107, 171

Langmuir circulation (see also Langmuir cells; Y junction), 95, 107, 172, 194

Langmuir turbulence (see also turbulent Langmuir number, La_turb), 97

large eddy simulation (LES), 99

law of the wall, 86

length scale (see internal Rossby radius, L_Ro; Kolmogorov length scale, l_K; Lagrangian integral length scale, L_L; mixing length; Monin–Obukov length scale, L_MO; Ozmidov length scale, L_O; Rhines scale roughness length; scale height; significant wave height, H_s; thermal compensation depth; Thorpe length scale, L_T)

main thermocline, 25

Malta, 117

marine fluff, 156

marine snow, 156

mean circulation, 205

meanders, 163

Mediterranean Sea, 83

Mediterranean Water, 47, 139, 148, 159, 187

Meddies, 159, 187

meridional diffusivity, 184–187

mesoscale eddy, 32, 175–179, 187, 205, 208

micro-fronts, 99

microstructure, 64, 65, 135

Mid-Atlantic Ridge, 142, 185, 202

Miles–Howard theorem, 119

minus five-thirds power law (see Kolmogorov’s minus five-thirds power law)

mixing, 15

   diapycnal, 28

   isopycnal, 28

mixed layer, 23, 91, 135, 205

mixing length, 170

molecular conductivity, 15

molecular diffusion, 14

momentum, 11, 39

momentum flux, 40, 79

Monin–Obukov length scale, L_MO, 88–89, 113, 216

Monterey Bay, California, 136

Multi-Scale Profiler (MSP), 45

Munk’s canonical value of KT, 140, 150

natural tracers, 187

Nasmyth universal spectrum, 52, 65

near-inertial internal waves, 136, 209

nepheloid layer (see benthic, intermediate and surface nepheloid layer)

New England Continental Shelf, 152, 183

non-dimensional numbers (see Cox number, C; critical Richardson number, Ri_c; critical Reynolds number; flux Richardson number, R_f; gradient Richardson number, Ri; Rayleigh number; Reynolds number, Re; turbulence Langmuir number; von Kármán’s constant)

normal pdf (see Gaussian pdf)

North Atlantic Tracer Release Experiment (NATRE), 142, 150, 182–185

North Sea, 102, 104, 164, 191

nuclear bomb testing, 187

ocean gyres, 208

oil film, 160

oil plume, 164

Okubo’s relationship, 180, 191, 194

Oregon continental shelf, 26, 86, 114

overshoot, 85

overstability, 146

overturns (see density overturns)

Ozmidov length scale, L_O, 129–131

Pacific Ocean, 47, 58, 141, 177, 202

pair of vortices (see vortex pairs)

pairing, 123, 167

parametric representation of , 128, 152

parsnips, 174

particle image velocimetry (PIV), 44

particle paths, 172, 193

particles, 35, 50, 173, 168–174

patches, 163, 165

perpetual salt fountain, 145

phase velocity, c, 27, 31, 34

piezoelectric air-foil shear probe (see air-foil probe)

planktonic organisms, 50

plumes (see also hydrothermal plume; oil plume), 15, 82, 83–85, 89, 159, 163, 164, 172

plunging breaker, 11

polynya, 207

potential density, 22, 45

potential energy, 56–59, 83, 125, 208

potential temperature, 22

probability distribution function (pdf) (see also Gaussian pdf), 54, 67

processes, 8, 77–79, 95, 197

potential temperature, 22

pycnocline, 24

rain, 111, 113

rate of energy dissipation in a breaking wave, 206, 221

rate of loss of salinity variance, χS, 48

rate of loss of temperature variance, χT, 47–48, 117

rate of loss of turbulent kinetic energy per unit mass, , 43–47, 56, 59, 73, 117, 127, 129–130, 133

rate of transfer of heat (see heat flux)

rate of transfer of momentum (see stress, Reynolds stress)

Rayleigh number, 81

reduced acceleration, 22

regions of freshwater influence (ROFI), 105

reordering (of density profile), 57

Reynolds, Osborne, 3, 6, 39

Reynolds’ experiment, 3, 5, 32

Reynolds number, Re, 3, 5, 19, 52, 60

Reynolds stress, 39–41, 56, 67–73, 85, 88

Rhines scale, 179

Richardson, L. F., 49, 170

Richardson number (see gradient Richardson number; flux Richardson number)

Richardson’s four-thirds power law, 171, 174, 179, 181, 192

rip-currents, 11

River Severn, 215

Romanche Fracture Zone (RFZ), 212, 213

Rossby radius (see internal Rossby radius)

Ross Sea, 207

roughness elements, 101

roughness length, 86

salinity, 20–21, 158

salt fingers, 146

scale height, 22

Schlieren, 27

seasonal cycle, 92

seasonal thermocline, 24

shadowgraph, 37, 122

shear, 18

shelf break, 136

shelf seas

Sierra Nevada, 211

sigma-T, 21, 157

significant wave height, H_s, 86

sill (see also Camarinal Sill), 210

skewness, 54, 99

slippery sea, 89

smoke plume, 15

SOFAR, sound fixing and ranging, 179

Southern Ocean

spaghetti diagram, 175

specific heat at constant pressure, c_p, 6

spectrum of turbulent energy, 52–54

sphere, fall speed (see fall speed (of particles))

spread of mixed patch (see collapsing mixed region)

spring bloom, 114

spring–neap tidal cycle, 202

stable stratification, 22

stability diagram, 120

static instability, 22, 146

stirring, 13

Stokes drift, 9, 204

Stommel, Henry, 174

strain, 18, 139

Strait of Gibraltar, 45, 139, 158, 159, 215

Straits of Florida, 45, 134

stratification, 20, 25

streaks, 100, 114, 183–185

stress, 39, 87

subduction, 81, 107, 161

submarine canyons, 144, 204, 210, 220

subsurface floats, 179–180

sulphur hexafluoride, SF₆, 142, 182, 185

surface mixed layer (see also mixed layer), 150

surface nephloid layer, 102

surf zone, 8–13, 34, 43, 162

Swallow floats

swath zone, 34

Taylor, G. I., 33, 51, 70, 73, 169

Taylor hypothesis, 51–52

temperature, 6, 20–22

temperature ramps, 99–100

thermal compensation depth, 112

thermal expansion coefficient

thermals, 82

thermocline, 24

thin layer, 18

Thorpe length scale, L_T, 129

tidal force, 197

tidal energy, 200, 219

tidal mixing front, 105, 109

tidal straining, 105–106

tides

   internal (baroclinic), 201–204, 220

   M₂ 200

   surface (barotropic), 200–201

TOPEX-POSEIDON satellite altimeter, 202

tracers, 142, 158

transition, 5, 123

tritium (³H), 187

T–S diagram, 157

T–S staircase, 147

turbulent decay, 123, 125

turbulent Langmuir number, La_turb (see also Langmuir turbulence), 98

turbulent dissipation (see rate of loss of turbulent kinetic energy per unit mass, )

Turner, J. S., 15, 149, 150

unstable stratification, 22

upper ocean boundary layer, 95

Vancouver Island, 117

velocity autocorrelation function, 168

Vema Channel, 155, 213, 223

viscosity (see kinematic viscosity)

viscous sublayer, 86, 100, 114, 115

von Kármán’s constant, 85, 88, 107

V⊘ring Plateau, Norwegian coast, 114

vortex pairs, 16, 174

vortical mode, 109, 183, 192

wave breaking (see also breaking internal waves, breaking surface waves), 28

wave energy flux, 33

wavenumber spectrum, 52, 141

Weddell Sea, 207

whitecaps (see also breaking surface waves), 206

windrow, 95

wind stress, 204

Y junction, 97

zonal diffusivity, 184–187

zooplankton, 52, 14