Introduction

Back-barrier lagoons are home to recreational marinas and fishing ports. With a few exceptions, most vessels using these facilities are relatively small, with lengths in the 5–30 m range and a maximum draft of 5 m. To access the lagoon, vessels need to navigate the ebb delta channel and the inlet. This requires that both channel and inlet are relatively stable, have sufficient depth and an alignment relative to the wave direction that allows safe access and passage. Not many natural inlets satisfy these requirements and measures are needed to remedy the shortcomings. A distinction is made between soft and hard measures. Soft measures include the opening of a new inlet, inlet relocation, dredging and artificial sand bypassing. Hard measures are jetty construction and weir-jetty systems. In addition to providing boating access, inlets play a role in maintaining the water quality of the back-barrier lagoon; they serve as conduits for the exchange of lagoon and ocean water.

Artificial Opening of a New Inlet

The objectives of the artificial opening of a new inlet are to provide passage for vessels to the back-barrier lagoon and/or to improve water quality. With regards to the passage of vessels, design requirements include sufficient channel depth, width, alignment and stability. Improving water quality requires sufficient exchange, implying a large enough tidal prism. Examples of inlets that were artificially opened, but with different objectives, are Bakers Haulover Inlet (FL), Faro-Olhão Inlet (Portugal) and Packery Channel (TX). Bakers Haulover Inlet (Fig. 14.1a) was opened in 1925 for the prime purpose of improving water quality in the northern part of Biscayne Bay (Dombrowsky and Mehta, 1993). Faro-Olhão Inlet (Fig. 14.1b) was opened in 1929 to improve navigational access to the city of Faro (Pacheco et al., 2011). Packery Channel (Fig. 14.1c) was opened in 2006 with the objectives to facilitate recreational fishing and boating and to improve the exchange between the Gulf of Mexico and Corpus Christi Bay (Williams et al., 2007).

Introduction

In the preceding chapters, the emphasis is on tidal inlets where tidal currents are dominant and river flow is of secondary importance. Sand is carried towards the inlets by longshore sand transport and cross-shore sand transport is small. Inlets are open at all times. The few that closed did so gradually through spit formation, thereby increasing the inlet length and decreasing the inlet velocity. Examples are Captain Sam's Inlet and Mason Inlet, both located in South Carolina and described, respectively, in Sections 4.4 and 4.5.

A different category of inlets is where river flow is dominant and the tide is of secondary importance in keeping the inlet open. Inlets in this category are found in Vietnam (Lam, 2009; Tung, 2011), South Africa (Cooper, 2001; Whitfield, 1992) and Australia (Baldock et al., 2008; Hinwood and McLean, 2015b; Hinwood et al., 2012; Morris and Turner, 2010; Ranasinghe and Pattiaratchi, 2003). Many of these inlets connect to small lagoons and have a small tidal range, resulting in a small tidal prism. In addition to longshore sand transport, cross-shore sand transport plays an important role in carrying the sand towards the entrance. The river flow shows strong inter-annual variations with periods of high alternating with periods of low river flow. The height and the period between peak flows have an important bearing on whether the inlets stay open or close. In this respect, a distinction is made between inlets that remain open at all times and inlets that are open only seasonally or intermittently.

Even though only open part of the year, many seasonally and intermittently closed inlets are used extensively as harbors for small fishing boats and as recreational areas for swimming and boating. Closure presents a three-fold problem. Firstly, ocean access for boats that use the back-barrier lagoon as a harbor is limited to when the inlet is open. Secondly, the water quality in the lagoon could deteriorate during the months of inlet closure. Thirdly, flooding of low-lying land may disrupt land use and access and lead to land siltation. Consequently, there is an interest in keeping the inlet permanently open.

Introduction

Morphodynamic models come in two categories. Based on their architecture a distinction is made between process-based models and empirical models. In the present chapter the focus is on process-based modeling. Process-based models start with small-scale physics and integrate the results over the larger timescales. Because at this time the state of the art of process-based modeling limits the time period over which can be integrated, most model applications focus on problems with timescales of months to decades. Examples are the adaptation of the inlet cross-section after a storm, the formation of an ebb delta after the opening of a new inlet, migration and breaching of channels and spit formation (Nahon et al., 2012; Tung et al., 2012; van der Wegen et al., 2010). To address problems with larger timescales, parallel to the process-based models, empirical models have been developed. They are the subject of Chapter 12. A common characteristic of process-based and empirical morphodynamic models is the feedback between morphology (bathymetry) and hydrodynamics; the hydrodynamics causes a change in bathymetry and in turn this affects the hydrodynamics.

Model Concept and Formulation

Process-based morphodynamic models consist of a series of computational modules as shown in Fig. 11.1. Starting with a known bathymetry and water level boundary conditions, the hydrodynamic equations (Lesser et al., 2004) are solved in the Flow module. Given the wave boundary conditions, wave transformation including wave height and direction is calculated in the Waves module. To account for tidal stage and wave-current interaction, information on water levels and current velocities is transferred from the Flow to the Waves module. Radiation stresses are calculated and the results are transferred to the Flow module. Exchange between the two modules takes place at specified time intervals.

In general this interval is much larger than the computational time step used in either of the modules. Using the information on currents and waves from the Flow and Waves modules, sediment transport is calculated in the Sediment Transport module using selected sediment transport formulae. With the results of the sand transport calculations the bathymetry is updated in the Bathymetry module.

Introduction

Depending on their origin, tidal inlets are identified as primary or secondary inlets. Regardless of the origin, the morphology is characterized by three major elements: the inlet, the ebb delta and the flood delta. The morphology of each element is determined by tide and waves. In particular, the tidal prism (the volume of water entering on the flood and leaving on the ebb) and the wave-induced longshore sand transport play an important role in determining the cross-sectional area of the inlet and the size and shape of the ebb delta.

Origin of Tidal Inlets

Following Ehlers (1988), in tracing the origin of tidal inlets a distinction is made between primary and secondary inlets. Primary inlets are those where pre-existing relief, characterized by troughs and adjacent highs, plays a decisive role in the formation of the inlet. During the Holocene, starting some 10,000 BP, onshore sand transport associated with the rapid rise in sea level caused these existing troughs to fill while barrier islands formed on the adjacent highs (Jelgersma, 1983). Examples of primary inlets are the Ameland Inlet (Fig. 4.7) and the Frisian Inlet (Fig. 12.4) along the Dutch Wadden Sea, both relics of drowned river valleys (Beets and van der Spek, 2000).

Apart from these primary tidal inlets, secondary inlets can be identified. Secondary inlets originate from flooding of narrow and shallow parts of barrier islands during a storm. Once the fore-dune ridge is dismantled as a result of storm erosion, a shallow washover channel develops. As the storm passes and winds change direction, return flow forces water against the landward side of the barrier. Often the return flow is funneled across the low portion of the barrier island through the washover channel. Depending on the tidal prism and the longshore sand transport, the washover channel closes or remains open. When remaining open, this channel is then gradually enlarged by the ensuing tidal currents. Sand from the channel is deposited both offshore and in the basin, forming the onset to, respectively, the ebb delta and the flood delta. All these secondary or washover inlets are located in a sand-rich environment. As discussed in more detail in the following chapters, the ultimate shape and size of newly opened inlets depends on tide and waves.

Introduction

Process-based models are a valuable tool when the relevant timescales are measured in months to years (Section 11.5). For timescales of decades to centuries, recourse is often taken to empirical models, also referred to as long-term behavior models or aggregate models. Empirical models start with the premise that, after a perturbation, the morphology tends towards an equilibrium state. The equilibrium is defined by equations of state. Examples are the relationship between inlet cross-sectional area and tidal prism (Eqs. (5.1) and (5.2)) and the relationship between ebb delta volume and tidal prism (Eq. (5.14)). Examples of perturbations are changes in the inlet morphology resulting from a storm and changes resulting from such engineering activities as dredging and basin reduction. The objective of empirical modeling is to predict the transition from the old to the new equilibrium.

Modeling Concepts

In applying empirical modeling to tidal inlets, the morphology is divided into a number of large-scale geomorphic elements, e.g., inlet, ebb delta and flood delta. Each of these elements is viewed on an aggregated scale and characterized by either a sand or a water volume. When themorphology as a whole tends to an equilibrium, so do the individual elements.

Examples of empirical models are presented in Kraus (2000), van de Kreeke (2006) and Stive et al. (1998). Kraus (2000) applied an empirical model to simulate the ebb delta development after the opening of Ocean City Inlet (MD). van de Kreeke (2006) used a similar empirical model to explain the transition from the old to the new equilibrium of the Frisian Inlet (The Netherlands) after basin reduction. In both studies, the sand transport entering and leaving an element is prescribed in terms of the ratio between the actual and equilibrium sand or water volume of the element. The model by Stive et al. (1998) is fundamentally different from the models used by Kraus (2000) and van de Kreeke (2006) in that the sand transport entering and leaving an element is formulated as a diffusive transport.

Historically, interest in tidal inlets originates from their importance for commercial shipping and recreational boating. Unfortunately, when in a natural state, most inlets are less than ideal from a navigational point of view and need improvement. They are unstable, i.e., as a result of tide and waves they have a tendency to migrate and shoal. Initially, to stabilize inlets, common sense and practical experience was used as the sole guide. It was not until the nineteen-twenties that research, using field observations, mathematical analysis and laboratory experiments, led to an improved understanding of the complex physical processes that govern the water motion and morphology of tidal inlets. This knowledge could then be used to arrive at science-based improvements.

This book summarizes and synthesizes the scientific advances in inlet research with emphasis on the period 1978 to present. It is a sequel to the earlier books, Stability of Coastal Inlets by Per Bruun and Gerritsen (1960) and Stability of Tidal Inlets: Theory and Engineering by Per Bruun et al. (1978). The focus is on natural (no man-made modifications) tidal inlets in a sandy environment. The book is intended for anyone who is interested or has dealings with tidal inlets, including coastal engineers, coastal scientists, students and managers. The two authors made an equal contribution to the contents of this book.

Per Bruun and Frans Gerritsen, through their afore mentioned book, were central in introducing Co van de Kreeke to the field of tidal inlets. Discussions with Per Bruun, Robert Dean, Murrough O'Brien and Ashish Mehta have further stimulated this interest. Ronald Brouwer was introduced to the field of tidal inlets by Co van de Kreeke. They worked closely together during his graduate work on tidal inlets at Delft University of Technology, The Netherlands. The support of Henk Schuttelaars and Pieter Roos during that period is acknowledged.

In preparing the manuscript, a number of chapters have benefited greatly from discussions with colleagues. They include Henk Schuttelaars and Pieter Roos on Chapters 9 and 10, Zheng Wang on Chapter 12 and Erroll Mclean and Jon Hinwood on Chapter 13. Albert Oost was helpful in explaining the geology and sedimentology of the Wadden Sea.

In the context of this book, tidal inlets are defined as the relatively short and narrow passages between barrier islands. They are sometimes referred to as passes or cuts. Tidal inlets are a common occurrence as barrier island coasts cover some 10 percent of the world's coasts (Glaeser, 1978). According to Hayes (1979), their presence is limited to coasts where the tidal range is less than 4 m.

The earliest interest in tidal inlets originates from their importance to commercial shipping. The relatively protected back-barrier lagoons were a favorite location for harbors. Later, with the increase in recreational boating, small boat basins and marinas were located in back-barrier lagoons. In addition to these commercial and recreational aspects, tidal inlets are ecologically important. Through the exchange of lagoon and ocean water, they contribute to the increase of water quality in the lagoon. Unfortunately, there is also a downside: tidal inlets interrupt the flow of sand along the coast. They not only interrupt but also capture part of the sand, causing erosion of the downdrift coast. For example, in Florida, with some eighty inlets, much of the beach erosion has been attributed to tidal inlets.

Most natural tidal inlets are less than ideal from a navigational point of view. The many shoals, the strong tidal current and the exposure to ocean waves make entering difficult. In addition, on timescales of years to decades, the morphology shows considerable variation, and maintaining sufficient depth and alignment of the channels requires substantial dredging. To minimize dredging and to improve navigation conditions, many inlets have been modified by adding jetties and breakwaters. As a result, tidal currents, waves and sand transport pathways differ from those at inlets without these structures. Nevertheless, in this book, emphasis is on tidal inlets that have not been modified. The reasoning is that understanding the physical processes governing the behavior of tidal inlets in a natural state is a prerequisite for the proper design of engineering measures. This includes the determination of undesirable side effects such as erosion of the adjacent beaches.

Introduction

The dynamics of the flow in the inlet are described by the equation for uniform unsteady open channel flow. Variations in depth with tidal stage are neglected. The dynamic equation is complemented with a continuity condition that assumes a pumping mode for the back-barrier lagoon, i.e., the water level in the back-barrier lagoon fluctuates uniformly. Although these are simplifications, the advantage is that they allow relatively simple analytical solutions that are helpful in identifying mechanisms responsible for phenomena such as resonance, tidal choking and generation of (odd) overtides. As examples, analytical solutions by Keulegan (1951, 1967) and Mehta and Özsoy (1978) are presented. Results of the analytical solutions are applied to a representative inlet and compared with numerical results.

Inlet Schematization

The tidal inlet system is schematized to an inlet and a back-barrier lagoon (Fig. 6.1). The inlet connects the back-barrier lagoon and the ocean. Its geometry is simplified to a prismatic channel with diverging sections at both ends. The backbarrier lagoon is schematized to a basin with uniform depth. Referring to Chapter 2, in the real world inlets have varying widths and depths and back-barrier lagoons are characterized by tidal flats and marsh areas. Therefore, the schematization presented in Fig. 6.1 is only a rough representation of an actual inlet.

Governing Equations and Boundary Condition

Dimensional Equations

In deriving the governing equations, the major assumptions are 1) one-dimensional unsteady uniform flow in the inlet, 2) a uniformly fluctuating water level in the basin (pumping or Helmholz mode) and 3) negligible variations in cross-sectional area of the inlet and basin surface area with tidal stage. With these assumptions, the equation for the flow in the inlet is (Appendix 6.A):

In this equation u is the cross-sectionally averaged velocity, positive in the flood direction, L is length of the prismatic part of the inlet, g is gravity acceleration, t is time, F = f /8 where f is the Darcy–Weisbach friction factor, R is hydraulic radius, m is entrance/exit loss coefficient, η0 is the ocean tide and ηb is the basin tide.

Introduction

Instead of one inlet, many back-barrier lagoons, bays and inland seas are connected to the ocean by multiple inlets. Examples are the Ría Formosa in south Portugal (Salles et al., 2005), the Dutch, German and Danish Wadden Sea (Ehlers, 1988) and the Venice Lagoon in Italy (Tambroni and Seminara, 2006); see Fig. 1.1. This chapter concerns the interaction of these inlets, with emphasis on cross-sectional stability.

Depending on the hydraulic efficiency, inlets connecting the same back-barrier lagoon capture a smaller or larger part of the tidal prism. The tidal prism is the volume of water entering and leaving the back-barrier lagoon during a tidal cycle. The fraction of the tidal prism entering and leaving an individual inlet is the prime parameter determining the cross-sectional stability of that inlet. If this fraction is too small, the inlet closes. In this respect the opening of a new inlet is of interest. Potentially, the new inlet could lead to a decrease of the tidal prisms of the already existing inlet(s) and chances are that some of these inlets close. In that case, it has to be decided to either close the new inlet or leave it open

An example of a recently opened inlet is the Breach at Old Inlet on Fire Island, NY (Fig. 2.1). The inlet was opened in October 2012 during hurricane Sandy. Together with the already existing Fire Island Inlet, the Breach at Old Inlet connects Great South Bay to the ocean. To determine the behavior of the new inlet and its effect on Fire Island Inlet, both inlets are being monitored (National Park Service, 2012). As of March 2015, the Breach at Old Inlet was still open. Based on the monitoring results it might be possible to arrive at a rational decision to either close the inlet or leave it open.

In this chapter, as a first step to determine the cross-sectional stability of tidal inlets connecting the same back-barrier lagoon to the ocean, the method used to determine the cross-sectional stability of a single inlet system (Chapter 8) is expanded and applied to a double inlet system.

Introduction

This chapter describes sand transport patterns and sand bypassing at seven inlets; five of these are located on the east coast of the USA (Price Inlet, Breach Inlet, Captain Sam's Inlet, Mason Inlet and Wachapreague Inlet), one inlet is located in the Bay of Plenty on the North Island of New Zealand (Katikati Inlet) and another is part of the Dutch Wadden Sea coast (Ameland Inlet). The inlets are selected because they are still in their natural state and have been extensively studied. Emphasis is on the mode of bypassing, location stability and their relationship with the P/M ratio. In judging the results, it should be pointed out that estimates of longshore sand transport have limited accuracy.

Price Inlet

Price Inlet (Fig. 4.1) is located on the coast of South Carolina. Tides are semidiurnal with a mean tidal range of 1.5 m and a spring tidal range of 2.1 m. The annual average deep water significant wave height is 0.6 m. The mean tidal prism is 14×106 m3 and the spring tidal prism is 20×106 m3. The throat cross-sectional area is 894 m2. From this, maximum cross-sectionally averaged velocities are 1.1 m s-1 for mean tide conditions and 1.56 m s-1 for spring tide conditions.

The ebb delta has a volume of 6 × 106 m3 and extents approximately 800 m offshore. The gross longshore sand transport is 0.25 × 106 m3 year-1 and is predominantly from the north. Tide- and wave-generated currents carry the sand through marginal flood channels and across the channel margin linear bars to the main ebb channel. The lateral inflow of sand causes the channel to meander on timescales of decades. With ebb currents stronger than flood currents, most sand deposited in the ebb channel is ultimately transported to the seaward portion of the ebb delta. At low tide, waves break on the seaward edge of the delta and transport sand along the periphery of the delta towards the downdrift beaches and onto the ebb delta platform.

Introduction

The major elements, inlet, ebb delta and flood delta, together with the adjacent coast constitute a sand sharing system (Dean, 1988); sand is transported among these elements by tide- and wave-generated currents. Because at tidal inlets direct measurements are difficult, much of what is known of sediment transport and sediment transport pathways has been inferred from migration and shape of bed forms and swash bars, dredging records, comparison of sequences of bathymetric maps and aerial photographs (Bruun and Gerritsen, 1959; Hanisch, 1981; Hine, 1975).

Sand is transported towards a tidal inlet by longshore currents. Longshore currents and the resulting longshore sand transport result from waves approaching the coast at an oblique angle (Kamphuis, 2006). Some of the longshore sand transport is carried into the inlet by the flood currents and is deposited in the back-barrier lagoon. Another part is jetted to the deeper parts of the ocean and some of it is transported over the ebb delta to the downdrift coast. The sand stored in the lagoon and the deeper parts of the ocean is lost to the littoral zone. As a result, the supply of sand to the downdrift coast is less than the longshore sand transport causing erosion of this part of the coast. The details of the transport of sand from the updrift to the downdrift coasts are discussed in Section 3.3.

An example of sand entering and leaving an inlet is presented in Fig. 3.1. Sand enters through the porous breakwater and is temporarily stored on the updrift side of the inlet in the form of a protruding sand bank. During ebb, sand is carried from the bank in an offshore direction. A similar process was observed in a small inlet in the Bay Islands, Honduras. In that case the clarity of the water and the size of the inlet (width 3 m, depth 0.3 m) made it possible to visually observe the deposition and formation of the sand bank on the updrift side of the inlet and the subsequent removal of some of the sand during ebb.

As already explained in Chapters 1 to 3, there are two basic types of quasibrittle failure and size effect, types 1 and 2. They have different large-size asymptotes of the size effect and different statistical contributions of material randomness. Type 1 (Bažant & Li 1995b; Bažant 1997; Bažant & Novák 2000a, 2000b; Bažant 2005) occurs when the maximum load is attained already at macrocrack initiation, and type 2 (Bažant 1984a; Bažant & Pfeiffer 1987; Bažant & Kazemi 1990a, 1990b; Bažant 2005) occurs when, at maximum load, there is a large notch or a large stress-free (or fatigued) crack (note that in Bažant 2005 Type 1 is called Case 2, and Type 2 Case 1).

If the structure is much larger than the size of the representative volume element (RVE) or, equivalently, the size of the fracture process zone (FPZ), type 1 exhibits a large statistical effect of material randomness on the mean of structural strength, particularly on its coefficient of variation (CoV), while at small sizes the type 1 size effect is essentially deterministic. By contrast, the type 2 size effect on the mean structural strength is essentially deterministic at all sizes, owing to energy release and the associated stress redistribution, while the material randomness affects only the CoV of structural strength.

Progress in the modeling of concrete fracture and introduction of fracture concepts into the design codes and practice has been impeded by the unavailability of a comprehensive database for fracture. The literature features a vast amount of fracture data (e.g., Sabnis & Mirza 1979; Petersson 1981; Nallathambi 1986; Bažant & Pfeiffer 1987; Malvar & Warren 1988; Carpinteri, Chiaia, & Ferro 1995a; Rocco 1995; Tang, Bažant, Yang, & Zollinger 1996; Bažant & Planas 1998; Becq-Giraudon 2000; Bažant & Becq- Giraudon 2002; Karihaloo, Abdalla, & Xiao 2003, Hoover et al. 2013). But all these data except the last cover only rather limited ranges of specimen size, initial notch depth, and post-peak response, and have been performed on different concretes, on different batches of supposedly the same concrete, at different ages, at different environmental conditions, at different rates, with different test procedures, and on specimens of different types and dimensions.