Green's Law states that tidal long-wave elevation • and tidal transport Q vary with width b and depth h according to • _= b-lt2h -1/4 and {2 -= b +l/2h +•t4. This solution is of limited utility because it is restricted to inviscid, infinitesimal waves in channels with no mean flow and weak topography (those with topographic scale L > wavelength •.). An analytical perturbation model including finite-amplitude effects, river flow, and tidal flats has been used to show that (1) wave behavior to lowest order is a function of only two nondimensional parameters representing, respectively, the strength of friction at the bed and the rate of topographic convergence/divergence; (2) two different wave equations with nearly constant coefficients can be derived that together cover most physically relevant values of these parameters, even very strong topography; (3) a single, incident wave in a strongly convergent or divergent geometry may mimic a standing wave by having a _= 90 ø phase difference between Q and • and a very large phase speed, without the presence of a reflected wave; (4) channels with strong friction and/or strong topography (L n: •.) show very large deviations from Green's Law; and (5) these deviations arise because both frictional damping and the direct dependence of IQI and I•l on topography (topographic funnelling) must be considered. INTRODUCI•ON Long-wave propagation in narrow channels of variable width and depth has been the subject of analysis for more than 150 years. One of the first major results was that of Green [1837], after whom Green's functions were named. Green's Law states that the wave amplitude • in a frictionless channel with slowly changing section varies as b-mh 4/4, where b is the width (more exactly the width of the momentum-conveying flow or stream width) and h is the depth below a mean tidal datum. Tidal transport Q varies as b+mh +m. All tidal channel flows are strongly frictional, most are short relative to the tidal wavelength •, and their topographic scale L is often much less than the length of the channel. Green's Law is therefore not directly applicable to tidal flows. Most subsequent treatments of wave propagation have at least implicitly followed Green and assumed weak topographic variation (L > 3•). Only Lighthill [1978] and Prandle and Rahman [1980] have explicitly considered the influence of the topographic convergence rate on wave propagation. The former, however, treated inviscid waves exclusively, and inviscid waves do not exist in the strong topography limit. Dronkers [1964], Parker [1984], and Godin [1991] have all focused on the role of frictional nonlinearities in tidal propagation and override generation. LeBlond [1978] and C. Friedrichs and O. Madsen (manuscript in preparation, 1991) have examined the "diffusive" behavior of strongly frictional waves in a channel of uniform depth and width. The latter included tidal flats in the analysis. None of these studies explored the very different character of frictional wave propagation over strong topography or the inte...

Tidal rivers are a vital and little studied nexus between physical oceanography and hydrology.It is only in the last few decades that substantial research efforts have been focused on the interactions of river discharge with tidal waves and storm surges into regions beyond the limit of salinity intrusion, a realm that can extend inland hundreds of kilometers. One key phenomenon resulting from this interaction is the emergence of large fortnightly tides, which are forced long waves with amplitudes that may increase beyond the point where astronomical tides have become extinct. These can be larger than the linear tide itself at more landward locations, and they greatly influence tidal river water levels and wetland inundation. Exploration of the spectral redistribution and attenuation of tidal energy in rivers has led to new appreciation of a wide range of consequences for fluvial and coastal sedimentology, delta evolution, wetland conservation, and salinity intrusion under the influence of sea level rise and delta subsidence. Modern research aims at unifying traditional harmonic tidal analysis, nonparametric regression techniques, and the existing understanding of tidal hydrodynamics to better predict and model tidal river dynamics both in single-thread channels and in branching channel networks. In this context, this review summarizes results from field observations and modeling studies set in tidal river environments as diverse as the Amazon in Brazil, the Columbia, Fraser and Saint Lawrence in North America, the Yangtze and Pearl in China, and the Berau and Mahakam in Indonesia. A description of state-of-the-art methods for a comprehensive analysis of water levels, wave propagation, discharges, and inundation extent in tidal rivers is provided. Implications for lowland river deltas are also discussed in terms of sedimentary deposits, channel bifurcation, avulsion, and salinity intrusion, addressing contemporary research challenges.

River-tide dynamics remain poorly understood, in part because conventional harmonic analysis (HA) does not cope effectively with nonstationary signals. To explore nonstationary behavior of river tides and the modulation effects of river discharge, this work analyzes tidal signals in the Yangtze River estuary using both HA in a nonstationary mode and continuous wavelet transforms (CWT). The Yangtze is an excellent natural laboratory to analyze river tides because of its high and variable flow, its length, and the fact that there are do dams or reflecting barriers within the tidal part of the system. Analysis of tidal frequencies by CWT and analysis of subtidal water level and tidal ranges reveal a broad range of subtidal variations over fortnightly, monthly, semiannual, and annual frequencies driven by subtidal variations in friction and by variable river discharges. We employ HA in a nonstationary mode (NSHA) by segregating data within defined flow ranges into separate analyses. NSHA quantifies the decay of the principal tides and the modulation of M 4 tide with increasing river discharges. M 4 amplitudes decrease far upriver (landward portion of the estuary) and conversely increase close to the ocean as river discharge increases. The fortnightly frequencies reach an amplitude maximum upriver of that for over tide frequencies, due to the longer wavelength of the fortnightly constituents. These methods and findings should be applicable to large tidal rivers globally and have broad implications regarding management of navigation channels and ecosystems in tidal rivers.

Particle trapping in estuarine turbidity maxima (ETM) is caused primarily by convergent mean and/or tidal fluxes of sediment. The result is an approximately bell-shaped along-channel distribution of vertically integrated, tidal cycle mean suspended sediment concentration. Observations from the Columbia River estuary suggest that (1) strong two-layer or internal along-channel residual and override flows are generated by rime-varying stratification and (2) correlations between the near-bed velocity and the suspended sediment fields at these frequencies are important in landward transport of sediment. A new sparially and temporally integrated form of the sediment conservation equation has been derived to analyze this trapping process. Time changes in tidally averaged sediment concentration between two estuarine cross sections can be shown to be related to the divergence of the seaward, river flow transport; the divergence of velocity shear-sediment stratification correlations for the mean flow and each tidal constituent; and net erosion or deposition at the bed. Vertically integrated variables other than seaward fiver transport are absent from this integrated balance. Analysis of sediment fluxes using this balance supports the idea that internal residual and override circulations are primarily responsible for the landward sediment transport on the seaward side of ETM found near the upstream limits of salinity intrusion. The balance also shows that attempts to represent fluxes causing trapping of sediment in an ETM as a product of a time-mean, vertically integrated, along-channel gradient and a diffusivity inevitably lead to the appearance of countergradient transport and thus a negative diffusivity on the seaward side of the ETM. This result occurs because the trapping process is inherently nonlinear and at least two-dimensional and because a one-dimensional representation is physically unrealistic.

Tides are changing worldwide at rates not explained by astronomical forcing. Rather, the observed evolution of tides and other long waves, such as storm surges, is influenced by shelf processes and changes to the roughness, depth, width, and length of embayments, estuaries, and tidal rivers. In this review, we focus on processes in estuaries and tidal rivers, because that is where the largest changes to tidal properties are occurring. Recent literature shows that changes in tidal amplitude have been ubiquitous worldwide over the past century, often in response to wetland reclamation, channel dredging, and other environmental changes. While tidal amplitude changes are sometimes slight (<1%) or even negative, we identify two types of systems that are particularly prone to tidal amplification: ( a) shallow, strongly damped systems, in which a small increase in depth produces a large decrease in effective friction, and ( b) systems in which wave reflection and resonance are strongly influenced by changes to depth, friction, and convergence. The largest changes in amplitude occur inland, some distance from the coast, and can sometimes be measured in meters. Tide changes are a leading indicator that the dynamics of storm surges and river flood waves have also changed and are often associated with shifts in sediment transport, salinity intrusion, and ecosystem properties. Therefore, the dynamics of tidal evolution have major implications for coastal management, particularly for systems that are sensitive to changes in geometry induced by sea-level rise and anthropogenic development.

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Abstract. A comprehensive study of the strongly wind driven midlatitude buoyant plume from the Columbia River, located on the U.S. west coast, demonstrates that the plume has two basic structures during the fall/winter season, namely, a thin (---5-15 m), strongly stratified plume tending west to northwestward during periods of southward or light northward wind stress and a thicker (---10-40 m), weakly stratified plume tending northward and hugging the coast during periods of stronger northward stress. The plume and its velocity field respond nearly instantaneously to changes in wind speed or direction, and the wind fluctuations have timescales of 2-10 days. Frictional wind-driven currents cause the primarily unidirectional flow down the plume axis to veer to the right or left of the axis for northward or southward winds, respectively. Farther downstream, currents turn to parallel rather than cross salinity contours, consistent with a geostrophic balance. In particular, during periods when the plume is separated from the coast, currents tend to flow around the mound of fresher water. At distances exceeding about 20 km from the river mouth, the along-shelf depth-averaged flow over the inner to midshelf is linear, and depth-averaged acceleration is governed to lowest order by the difference between surface and bottom stress alone. In this region, along-shelf geostrophic buoyancy-driven currents at ---5 m (calculated from surface density) and along-shelf geostrophic wind-driven currents (computed from a depth-averaged linear model) are comparable in magnitude (---10-25 cm s-•).

Scientists and engineers have observed for some time that tidal amplitudes at many locations are shifting considerably due to nonastronomical factors. Here we review comprehensively these important changes in tidal properties, many of which remain poorly understood. Over long geological time scales, tectonic processes drive variations in basin size, depth, and shape and hence the resonant properties of ocean basins. On shorter geological time scales, changes in oceanic tidal properties are dominated by variations in water depth. A growing number of studies have identified widespread, sometimes regionally coherent, positive, and negative trends in tidal constituents and levels during the 19th, 20th, and early 21st centuries. Determining the causes is challenging because a tide measured at a coastal gauge integrates the effects of local, regional, and oceanic changes. Here, we highlight six main factors that can cause changes in measured tidal statistics on local scales and a further eight possible regional/global driving mechanisms. Since only a few studies have combined observations and models, or modeled at a temporal/spatial resolution capable of resolving both ultralocal and large‐scale global changes, the individual contributions from local and regional mechanisms remain uncertain. Nonetheless, modeling studies project that sea level rise and climate change will continue to alter tides over the next several centuries, with regionally coherent modes of change caused by alterations to coastal morphology and ice sheet extent. Hence, a better understanding of the causes and consequences of tidal variations is needed to help assess the implications for coastal defense, risk assessment, and ecological change.