Cover -- Half-title -- Title -- Copyright -- Contents -- Symbols -- 1 Introduction -- 1.1 Objectives and scope -- 1.1.1 Processes -- 1.1.2 Historical developments -- 1.2 Challenges -- 1.2.1 Evolving science and technology agendas -- 1.2.2 Key questions -- 1.3 Contents -- 1.3.1 Sequence -- 1.3.2 Tidal dynamics -- 1.3.3 Currents -- 1.3.4 Saline intrusion -- 1.3.5 Sediment regimes -- 1.3.6 Synchronous estuary: dynamics, saline intrusion and bathymetry -- 1.3.7 Synchronous estuary: sediment trapping and sorting - stable morphology -- 1.3.8 Strategies for sustainability -- 1.4 Modelling and observations -- 1.4.1 Modelling -- Resolution -- 1.4.2 Observations -- Teleconnections -- 1.5 Summary of formulae and theoretical frameworks -- Appendix 1A -- 1A.1 Tide generation -- 1A.2 Non-rotating Earth -- 1A.3 Rotating Earth -- 1A.4 Declination -- 1A.5 Elliptic orbit -- 1A.6 Relative magnitude of the Sun's attraction -- 1A.7 Equilibrium constituents -- 1A.8 Tidal amphidromes -- 1A.9 Monthly, fortnightly and quarter-diurnal constituents -- References -- 2 Tidal dynamics -- 2.1 Introduction -- 2.2 Equations of motion -- 2.3 Tidal response - localised -- 2.3.1 Linearised solution -- 2.3.2 Synchronous estuary solution -- Results -- Current amplitudes U -- Role of bed friction -- Rate of funnelling in a synchronous estuary -- 2.4 Tidal response - whole estuary -- 2.4.1 Breadth and depth varying with powers of distance X (Prandle and Rahman, 1980) -- Quarter-wavelength resonance -- 2.4.2 Depth and breadth varying exponentially (Hunt, 1964 Prandle, 1985) -- 2.5 Linearisation of the quadratic friction term -- 2.5.1 Single constituent -- 2.5.2 Two constituents -- 2.5.3 Triangular cross section -- 2.5.4 Q factor (Garrett and Munk, 1971) -- 2.6 Higher harmonics and residuals -- 2.6.1 Trigonometry -- 2.6.2 Non-linear terms in the tidal equations -- Inertial term.

Convective term -- Surface gradient -- Quadratic friction -- Coriolis -- 2.6.3 Ebb-flood asymmetry -- 2.7 Surge-tide interactions -- 2.8 Summary of results and guidelines for application -- References -- 3 Currents -- 3.1 Introduction -- 3.1.1 Convective term -- 3.1.2 Density gradients -- 3.1.3 Wind forcing -- 3.1.4 Approach -- 3.2 Tidal current structure - 2D (X-Z) -- 3.2.1 2D analytical solution -- Boundary conditions -- Continuity -- Velocity profiles -- 3.2.2 Comparisons with observations -- 3.2.3 Eddy viscosity formulation, Strouhal number -- 3.3 Tidal current structure - 3D (X-Y-Z) -- 3.3.1 Tidal ellipse resolved into clockwise and anti-clockwise components -- 3.3.2 3D analytical solution -- 3.3.3 Sensitivity to friction factor and eddy viscosity -- 3.3.4 Sensitivity to latitude -- 3.3.5 Surface to bed changes in tidal ellipses -- 3.3.6 Currents across the inter-tidal zone -- 3.4 Residual currents -- 3.4.1 Wind-driven currents -- 3.4.2 Tidal current residuals -- 3.5 Summary of results and guidelines for application -- Appendix 3A -- 3A.1 Tidal current ellipse -- Appendix 3B -- 3B.1 Turbulence model -- References -- 4 Saline intrusion -- 4.1 Introduction -- 4.1.1 Classification systems -- 4.1.2 Mixing in estuaries -- 4.1.3 Present approach -- 4.2 Current structure for river flow, mixed and stratified saline intrusion -- 4.2.1 Current structure for river flow Q -- 4.2.2 Current structure for a well-mixed horizontal density gradient -- 4.2.3 Current structure for a stratified two-layer density regime -- 4.2.4 Current structure for a constant surface wind stress tw -- 4.2.5 Time-averaged vertical salinity structure (mixed) -- 4.2.6 Summary -- 4.3 The length of saline intrusion -- 4.3.1 Experimental derivation -- 4.3.2 Derivations from velocity components -- 4.3.3 Derivation for a stratified salt wedge.

4.3.4 Mean value for saline intrusion length, LI -- Observed versus computed values -- 4.3.5 Axial location of saline intrusion -- 4.4 Tidal straining and convective overturning -- 4.4.1 Rates of mixing -- 4.4.2 Modelling approach (Prandle, 2004a) -- 4.4.3 Model formulation -- 4.4.4 Model results -- Currents -- Salinity -- Tidal cycle and depth profiles -- 4.4.5 Model applications for a range of estuarine conditions -- Tidal velocities -- Bed-to-surface residual current differences du and sea level gradient… -- Bed-to-surface density differences,… -- 4.4.6 Mixing processes -- 4.5 Stratification -- 4.5.1 Flow ratio, FR -- 4.5.2 Energy and time requirements -- 4.5.3 Richardson number -- 4.5.4 Stratification number -- 4.5.5 Vertical salinity difference -- 4.6 Summary of results and guidelines for application -- Appendix 4A -- 4A.1 The annual temperature cycle -- 4A.2 Components of heat exchange at the sea surface -- 4A.3 Analytical solutions in vertically mixed water -- 4A.5 The atmospheric model - solar energy input, reflection, absorption and radiation -- 4A.6 Global expressions -- References -- 5 Sediment regimes -- 5.1 Introduction -- 5.1.1 Sediment dynamics -- 5.1.2 Modelling -- 5.1.3 Approach -- 5.2 Erosion -- 5.2.2 Spring-neap cycle -- Influence of U0 -- 5.2.3 Erosion in shallow cross sections -- 5.2.4 Advective component -- 5.3 Deposition -- 5.3.1 Advective settlement versus turbulent suspension (Peclet number) -- 5.3.2 Bottom boundary conditions -- 5.4 Suspended concentrations -- 5.4.1 Time series of sediment concentration profiles -- 5.4.2 Exponential deposition, half-lives in suspension, t50 -- 5.4.3 Vertical profile of suspended sediments -- 5.5 SPM time series for continuous tidal cycles -- 5.6 Observed and modelled SPM time series -- 5.6.1 Observational technologies -- 5.6.2 Observed time series -- 5.6.3 Modelled time series.

5.7 Summary of results and guidelines for application -- 5.7.1 Sediment suspension -- 5.7.2 Deposition -- 5.7.3 Tidal spectra of SPM -- Appendix 5A -- 5A.2 Dispersion equation -- 5A.4 Boundary condition at the surface z =1 -- 5A.5 Boundary condition at the bed z = 2, 4, 6, etc. -- References -- 6 Synchronous estuaries: dynamics, saline intrusion and bathymetry -- 6.1 Introduction -- 6.2 Tidal dynamics -- 6.2.1 Synchronous estuary approach -- 6.2.2 Analytical solution for 1D momentum and continuity equations (Prandle, 2003) -- 6.2.3 Explicit formulae for tidal currents, estuarine length and depth profile -- Current amplitudes U -- Depth profile and estuarine length L -- 6.2.4 Sensitivity to bed friction coefficient (f) -- 6.2.5 Rate of funnelling in a synchronous estuary -- 6.3 Saline intrusion -- 6.3.1 Stratification levels and flushing times -- 6.3.2 Location of mixing zone, residual current associated with river flow -- 6.4 Estuarine bathymetry: theory -- 6.4.1 Morphological zone determined by tidal dynamics and stratification -- 6.4.2 Estuarine depths as a function of river flow -- Observed versus computed estuarine bathymetries -- 6.5 Estuarine bathymetry: assessment of theory against observations -- 6.5.1 Statistical analyses -- 6.5.2 Theory versus observed morphologies -- Length (L ~ ADP) and depth (D) -- Depth (D ~ AQP) and river flow (Q) -- Bathymetric zone -- 6.5.3 Minimum depths and flows for estuarine functioning -- 6.5.4 Spacing between estuaries -- 6.6 Summary of results and guidelines for application -- What determines estuarine shape, length and depth? -- Tidal currents and frictional influence -- Lengths and shape -- Range of estuarine morphologies -- Assessment of bathymetric framework -- Theoretical Frameworks -- Corollary -- References -- 7 Synchronous estuaries: sediment trapping and sorting - stable morphology -- 7.1 Introduction.

7.1.1 Earlier studies -- 7.1.2 Approach -- 7.2 Tidal dynamics, saline intrusion and river flow -- 7.2.1 Analytical solution for 1D tidal propagation (Chapter 6 Prandle, 2003) -- 7.2.2 Saline intrusion (Chapter 4) -- 7.2.3 River flow -- 7.3 Sediment dynamics -- 7.3.1 Suspension, erosion, deposition and vertical profiles -- Erosion -- Deposition -- Vertical profile of suspended sediments -- 7.4 Analytical emulator for sediment concentrations and fluxes -- 7.4.1 Erosional velocity components -- Mean concentration -- 7.4.2 Mass of sediments in suspension -- 7.4.3 Net sediment fluxes -- 7.5 Component contributions to net sediment flux -- 7.5.1 Components of sediment flux: river flow, salinity and tidal current constituents -- 7.5.2 Conditions for zero net flux of sediments -- 7.5.3 Sensitivity to fall velocity, Ws -- 7.5.4 Sensitivity to bed friction, f, and fall velocity, Ws -- 7.6 Import or export of sediments? -- 7.6.1 Sensitivity to half-life, t50, and phase difference, theta, between tidal elevation and current -- 7.6.2 Sediment trapping and turbidity maxima -- 7.6.3 Link to tidal energetics -- 7.7 Estuarine typologies -- 7.7.1 Bathymetry -- 7.7.2 Sediment regimes -- 7.8 Summary of results and guidelines for application -- 7.8.1 Component contributions and sensitivity analyses -- 7.8.2 Conditions for zero net flux of sediments (i.e. bathymetric stability) -- 7.8.3 Neap to spring, coarse to fine, mouth to head variations in net import versus export -- 7.8.4 Typological frameworks -- References -- 8 Strategies for sustainability -- 8.1 Introduction -- 8.2 Model study of the Mersey Estuary -- 8.2.1 Tidal dynamics, sediment regime and bathymetric evolution of the Mersey -- Suspended sediments and net deposition -- Bathymetry -- 8.2.2 Modelling approach -- 8.2.3 Lagrangian, random-walk particle module for non-cohesive sediment.

8.2.4 Simulations for fall velocities, WS = 0.005 and 0.0005 ms-1.