Salinity and Tides in Alluvial Estuaries

211 Pages·2006·1.86 MB·English

by  H.H.G. Savenije

SALINITY AND
TIDES IN ALLUVIAL
ESTUARIES
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SALINITY AND
TIDES IN ALLUVIAL
ESTUARIES
by
HUBERT H.G. SAVENIJE
DelftUniversityof Technology
2600GA Delft, The Netherlands
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CONTENTS
Preface ix
Notation xi
1.0 Introduction: Description and Classification of Alluvial Estuaries 1
1.1 Importance of estuaries to mankind 2
1.2 Classification of estuaries 4
1.3 Estuary numbers 8
1.4 Alluvial estuaries and their characteristics 10
1.4.1 The shape of alluvial estuaries 11
1.4.2 Dominant mixing processes 13
1.4.3 How the tide propagates 14
1.4.4 How the salt intrudes 17
1.5 What will follow 22
2.0 Tide and Estuary Shape 23
2.1 Hydraulic equations 24
2.1.1 Basic equations 24
2.1.2 The seventh equation 28
2.1.3 The one-dimensional equations for depth and velocity 32
2.1.4 The effect of density differences and tide 35
2.2 The shape of alluvial estuaries 43
2.2.1 Classification on estuary shape 43
2.2.2 Assumptions on the shape of alluvial estuary
in coastal plains 48
2.2.3 Assumptions on estuary shape in short estuaries 53
2.3 Relating tide to shape 56
2.3.1 Why look for relations between tide and shape? 56
2.3.2 Theoretical derivations 56
3.0 Tidal Dynamics 69
3.1 Tidal movement and amplification 69
3.1.1 Why is the tidal wave amplified or damped? 69
3.1.2 Derivation of the tidal damping equation 70
v
vi Contents
3.1.3 Application of the derived formula to observations 77
3.1.4 Conclusions 78
3.2 Tidal wave propagation 79
3.2.1 The relation between tidal damping and wave celerity 79
3.2.2 Theory of wave propagation 82
3.2.3 Empirical verification in the Schelde and Incomati estuaries 92
3.2.4 The wave celerity according to Mazure 95
3.2.5 Conclusion 96
3.3 Effect of river discharge and other higher order effects
on tidal damping 98
3.3.1 Which higher order effects are important 98
3.3.2 Incorporating river discharge into the derivation of
the Celerity equation 99
3.3.3 Incorporating river discharge into the derivation of
the Damping equation 100
3.3.4 Application to the Schelde-estuary 104
3.3.5 Conclusion 105
3.4 The influence of climate change and human interference
on estuaries 105
4.0 Mixing in Alluvial Estuaries 109
4.1 Types of mixing, their relative importance, and interaction 109
4.2 Gravitational circulation 113
4.3 Mixing by the tide 115
4.4 Residual circulation through flood and ebb channels 116
4.5 The decomposition method and why it is not very useful 122
4.6 Longitudinal effective dispersion 126
4.7 Van den Burgh’s equation 132
4.7.1 The physical meaning of Van den Burgh’s K 133
4.7.2 Correspondence with other methods 134
4.8 General equation for longitudinal dispersion 135
5.0 Salt Intrusion in Alluvial Estuaries 137
5.1 Types of salt intrusion and shapes of salt intrusion curves 137
5.2 Salt balance equations 139
5.3 Influence of rainfall and evaporation 144
5.4 Time scales and conditions for steady state 149
5.5 Predictive model for steady state 153
5.5.1 Expressions for HWS, LWS, and TA 153
5.5.2 Empirical relations for the predictive model 159
5.5.3 The predictive model compared to other methods 169
5.6 Unsteady state model 171
5.6.1 System response time 171
Contents vii
5.6.2 Unsteady state dispersion 176
5.6.3 Application of the unsteady state model 177
5.7 Hypersaline estuaries 181
5.8 Concluding remarks 183
References 185
Index 191
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PREFACE
Since the publication of ‘‘Mixing in Inland and Coastal Waters’’ by Fischer et al.
(1979) and ‘‘Estuaries, a Physical Introduction’’ by Dyer (1973, revised in 1997),
no comprehensive textbook has been published on salinity and tides in estuaries.
Although considerable knowledge has been gained since, and several articles have
been written on the subject, this has not yet resulted in a book that combines this
knowledge within one consistent theoretical framework.
An estuary is the transition between a river and a sea. There are two main
drivers: the river that discharges fresh water into the estuary and the sea that fills
the estuary with salty water, on the rhythm of the tide. The salinity of the estuary
water is the result of the balance between two opposing fluxes: a tide-driven
saltwater flux that penetrates the estuary through mixing, and a freshwater flux
that flushes the saltwater back. Both fluxes strongly depend on the topography.
The salt water flux, because the amount of water entering the estuary depends on
thesurfaceareaoftheestuary,andthefreshwaterflux,becausethecross-sectional
area of the estuary determines the efficiency of the fresh water flow to push back
the salt.
So,thetopographyiscrucial.Itprovidesthemostimportantboundarycondition
fortidalhydraulics,mixing,andsaltintrusion.Oneoftheinnovationsofthisbook
isthatitmakesuseofthenaturaltopographyofalluvialestuaries,throughout.The
naturaltopographyofalluvialestuariesisonewithconvergingbanksfollowingan
exponential function. Both the width and the cross-sectional area obey an expo-
nential function. Moreover, in coastal plain estuaries, the depth is constant and
thereisnobottomslope.Estuariesincoastalareaswithastrongreliefaregenerally
too short for this type of estuary to develop. They form a special category of
alluvial estuaries where standing waves occur and where the depth decreases in
upstream direction. These estuaries are described e.g. by Wright et al. (1973) and
Prandle (2003). The length scale of the convergence rate is a key parameter for
understandingtidalandmixingprocesses.Thisbooksystematicallyintegratesthese
natural topographies with tidal movement, mixing, and salt intrusion.
Mixing in estuaries is driven by both the tide and the density gradient. The
densitygradientinducesverticalmixing;thetidemainlyhorizontalmixingthrough
tidaltrappingandresidualcirculation(andtoaminor extentturbulentmixing).It
is recognized that residual circulation is a dominant mechanism, particularly near
the mouth of the estuary, but it is poorly understood. Several mixing mechanisms
have been well documented in the literature, such as the vertical density-driven
ix