An Introduction to Ocean Turbulence

	Preface	Page ix
	Notes on the text	xi
	Acknowledgements	xiii
	Abbreviations	xv
	Standard parameters and symbols	xvi
	Units and their symbols	xviii
	SI prefixes	xix
	Approximate values of commonly used measures	xx
1	Turbulence, heat and waves	1
	1.1 Introduction	1
	1.2 Reynolds’ experiment	3
	1.3 Joule’s experiment	5
	1.4 The surf zone: waves and turbulence	8
	1.5 The nature of turbulent flow	13
	1.5.1 Stirring + diffusion = mixing	13
	1.5.2 Entrainment and detrainment	15
	1.6 Shear, convergence and strain	18
	1.7 Ocean stratification and buoyancy	19
	1.7.1 Density	19
	1.7.2 Buoyancy, and the buoyancy frequency, N	22
	1.7.3 The oceanic density profile	23
	1.8 Consequences of stratification	25
	1.8.1 Internal waves and turbulent motion	25
	1.8.2 Isopycnal and diapycnal mixing	28
	Suggested further reading	32
	Further study	32
	Problems for Chapter 1	33
2	Measurement of ocean turbulence	37
	2.1 Characteristics of turbulence	37
	2.1.1 Structure	37
	2.1.2 Stress and flux	39
	2.1.3 Dissipation	39
	2.2 Transport by eddies	39
	2.2.1 Reynolds stress	39
	2.2.2 Heat and buoyancy flux	42
	2.3 Energetics	43
	2.3.1 Turbulent dissipation, ∊, and isotropy	43
	2.3.2 The range and observed variation of ∊	45
	2.3.3 The rate of loss of temperature variance, v__T	47
	2.3.4 The Kolmogorov length scale, l__K	48
	2.3.5 The turbulence cascade and the structure of turbulence	49
	2.3.6 The Taylor hypothesis and the spectrum of turbulent energy	51
	2.4 The terms in the energy balance equation	54
	2.4.1 The rate of production of turbulent kinetic energy by the mean flow	56
	2.4.2 The turbulent potential energy	56
	2.4.3 The rate of dissipation	59
	2.5 Measurement techniques and instruments	59
	2.5.1 The first measurements of turbulence: spectra	60
	2.5.2 The air-foil probe: the measurement of ∊	60
	2.5.3 First measurements of Reynolds stress, and the related dissipation per unit area	67
	2.5.4 Estimates of Reynolds stress and ∊ using an ADCP	71
	Suggested further reading	73
	Further study	74
	Problems for Chapter 2	75
3	Turbulence in oceanic boundary layers	77
	3.1 Introduction: processes, and types of boundary layers	77
	3.2 Convection in the absence of shear	81
	3.2.1 Convection below a cooled surface or over a heated seabed	81
	3.2.2 Buoyant plumes and entrainment	83
	3.3 Stress and no convection; the law of the wall	85
	3.4 Stress and buoyancy flux	87
	3.4.1 The Monin–Obukov length scale	87
	3.4.2 Diurnal and seasonal heat cycling of the mixed layer	89
	3.4.3 Other mixing processes in the upper ocean	95
	3.4.4 The benthic (or bottom) boundary layer	100
	3.4.5 Tidal mixing and straining in shallow seas	102
	Suggested further reading	106
	Further study	107
	Problems for Chapter 3	110
4	Turbulence in the ocean pycnocline	116
	4.1 Introduction	116
	4.1.1 Processes of turbulence generation	116
	4.1.2 The first observations of turbulence in the thermocline	117
	4.2 Shear-flow instability and the transition to turbulence	119
	4.3 The Richardson number in the ocean	125
	4.4 Further turbulence parameters derived from microstructure measurements	129
	4.4.1 Estimation of v	129
	4.4.2 Estimation of eddy diffusion coefficients	131
	4.4.3 R_f and the ratio of the eddy coefficients of mass and momentum	133
	4.5 Entrainment into the surface mixed layer	135
	4.6 Observations of mid-water mixing processes	135
	4.7 The rate of diapycnal mixing	139
	4.8 Double diffusive convection	144
	Suggested further reading	149
	Further study	150
	Problems for Chapter 4	152
5	Turbulent dispersion	158
	5.1 Introduction	158
	5.1.1 The properties of dispersants	158
	5.1.2 Appropriate measures	163
	5.1.3 Effects of relative eddy and patch sizes	164
	5.2 The dispersion of particles	168
	5.2.1 Autocorrelation and integral scales	168
	5.2.2 Richardson’s four-thirds power law	170
	5.2.3 Dispersion of pairs of particles	171
	5.2.4 Effects of closed vertical circulations on buoyant particles	171
	5.3 Observations of the dispersion of floats	174
	5.3.1 Surface floats	174
	5.3.2 Subsurface floats	179
	5.4 The dispersion of solutes: methods and observations	180
	5.4.1 Dispersion (or horizontal diffusion) of a solute	180
	5.4.2 Dye releases in the surface boundary layer	180
	5.4.3 Tracer releases in the pycnocline	182
	5.4.4 Natural and anthropogenic tracers	187
	Suggested further reading	189
	Further study	190
	Problems for Chapter 5	192
6	The energetics of ocean mixing	197
	6.1 Introduction	197
	6.2 How much energy is required to mix the abyssal ocean?	199
	6.3 The tides	200
	6.3.1 The surface or barotropic tides	200
	6.3.2 The internal or baroclinic tides	201
	6.4 The atmospheric input of energy through the sea surface	204
	6.4.1 The wind stress	204
	6.4.2 Surface waves	205
	6.4.3 Buoyancy flux	207
	6.5 The mean circulation and mesoscale eddies	208
	6.6 Internal waves	209
	6.7 Dissipation produced by bottom stress	210
	6.8 Flow through and around abyssal topography	210
	6.9 Geothermal heat flux	216
	6.10 Discussion	217
	Suggested further reading	218
	Further study	219
	Problems for Chapter 6	220
	References	225
	Index	235

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S. A. Thorpe

University of Wales, Bangor

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