Managing Coastal Inlets

Coastal inlets represent a hydrodynamic connection between two water bodies – the open coastal water on the one hand, and the inland sheltered water body, waterway or lagoon on the other. The name itself suggests that inlets are openings or discontinuities in the shoreline to let oceanic influences such as tide, wave, storm surge and tsunami to propagate inside. They are usually narrow channels that have been historically utilized to install bridges. Another historical significance is that pioneering explorers used the inlets to sail inside into harbors and upriver to discover new lands. 
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1. Inlet Types
Four different types are usually distinguished – the geological, the hydrological, the human-made and the alluvial-tidal. The first represents a fixed-shore setting that has been formed during the geological processes – straits and many narrows in fjords are of this type. The second represents delta distributaries – the long outlets draining out the river flow into the ocean. In addition to describing them as Estuaries, hydrodynamics and morphological stabilities of this type are better treated as channels – mostly belonging to the deltaic processes discussed in the Coastal River Delta piece on the NATURE page. The third is a dredged-out channel connecting a closed water body to open water. In most cases, the purpose of opening of such an inlet is to develop marinas by facilitating navigation of pleasure boats to and from the marina.
The fourth type, also known as the tidal inlet – is the natural response of sandy alluvium to establish a connection between the open coastal water and the inland lagoon. Mostly formed or cut during storm surges, they represent a discontinuity in the barrier island along many littoral shores. These inlets are usually a narrow waterway – its length scaling with width – typically varying from 1 to 5 times the width. Literature is full of materials discussing these types of inlets – their stability, sedimentation, navigation, and technical and economic management issues.   
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2. Estuary - the Hydrological Inlet
Before moving into discussing further, perhaps spending a little time to clarify the term ESTUARY – the hydrological inlet, would be useful.
Let me try to do this based on my 1990 paper: In Search of the Definition of an Estuary published in the BD Journal of the Institution of Engineers. The estuary definition evolved through time starting from investigators like BH Ketchum (1951) and JC Dionne (1963) to the comprehensive syntheses of several papers compiled by the American Association for the Advancement of Science (1967) and the National Academy of Sciences (1977). Dionne’s definition focusing on the St. Lawrence Estuary divides an estuary length into: (1) a marine or lower estuary in free connection with the open sea, (2) a middle estuary subject to strong salt and fresh water mixing, and (3) an upper or fluvial estuary subject to daily tidal action. But the 1967 definition by DW Pritchard focusing primarily on Chesapeake Bay is mostly cited in literature: an estuary is a semi-enclosed coastal body of water which has a free connection with the open sea and within which sea water is measurably diluted with fresh water derived from land drainage. Three terms stand out in this definition: semi-enclosed body of coastal water, open-connection to sea, and measurable dilution.
Compared to the Dionne suggestion, tide is excluded from this definition with the understanding that its role is primarily in mixing of waters. In addition the tidal arm of the fresh-water river reach is not considered as an estuary. An additional problem appears with this definition – that in most large river systems like the Amazon, the Ganges-Brahmaputra and the Mississippi, the measurable dilution occurs in open sea water during high river stages – outside their physical land boundary. Therefore according to the Pritchard definition such systems do not have an estuary during this time! In reality estuarial reaches translate back and forth in response to the strength of unidirectional fresh-water flow. To address this problem and by focusing to include large river systems, my suggested definition in the 1990 paper reads as: an estuary is either a semi-enclosed coastal body of water which has a free connection with the open sea or part of the open sea or both, within which sea water is measurably diluted with fresh water derived from land drainage. Basically then, an estuary is any open and/or semi-enclosed coastal water body, where sea water salinity is measurably diluted by fresh-water derived from land drainage.
Moving on – some materials of this piece are based on my Ports2013 paper, presented at the conference in Seattle and published by ASCE: Integrated Modeling and Sedimentation Management: the Case of Salt Ponds Inlet and Harbor in Virginia. This particular inlet was human-made, dredged to develop a marina in parts of the Salt Ponds water body, and connect it to Chesapeake Bay. In this work, sedimentation problems of Salt Ponds Inlet were addressed by coupled numerical modeling {tide + wave + sediment transport + morphology} together with some analytical approaches – among others by comparing wave and tidal powers.
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3. Coastal Inlet Hydraulics
Inlet opening, closure or its stability depend on four basic oceanic forcings: (1) regular tidal pumping, (2) wave actions and littoral sand mobilization, (3) episodic but seasonal storm actions, and (4) rarer but powerful tsunami events. The effects of the last two can hardly be overemphasized – in addition to cutting new inlets or closing the existing ones, they impose new boundary conditions that are reworked by the regular forces of tide and wave – to achieve new dynamic equilibrium.
Sands are continuously mobilized at the mouth of a tidal inlet by cross-shore and longshore wave actions. If tidal actions do not have the ability to flush out the wave-mobilized sediments, an inlet is doomed to closure. Each year billions of dollars are spent across the world to dredge out sandy shoals of an inlet.
The inland parameters influencing an inlet stability is the size of the lagoon, its inter-connection with other systems and the freshwater that drains into the lagoon. The last but not the least is the textural composition of the littoral material, and the amount of sediment loads. Perhaps discussing more of this topic in 3 groups would help streamlining the rest of this piece.
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3.1 Cross-sectional Stability of Tidal Inlets.
Three easily identifiable features characterize an alluvial tidal inlet system – the ebb-tidal delta on the ocean end, the flood-tidal delta on the bay end, and a relatively narrow deep inlet channel in-between. There had been considerable interests in the cross-sectional stability of tidal inlets – starting from the beginning of 20th century {to name some investigators: LJ LeConte 1906; MP O’Brien (Morrough Parker O’Brien Jr., 1902 – 1988, considered father of coastal engineering) 1931; FF Escoffier 1940; P Bruun and F Gerritsen 1960; JW Johnson 1973; JT Jerrett 1976; MO Hayes 1980}. In its utmost simplicity, the stability was conceived as a simple behavioral model relating the measured inlet cross-sectional area to the tidal prism – as a central fitting, A = CP^n; with a coefficient C and an exponent n on the tidal prism P.
​Tidal prism is the volume of water an ocean tide forces through an inlet to fill the inland basin {the prism can either be estimated by integrating, for example the hourly-tidal-flows through an inlet for the window of rising tide – from trough to crest; or as a product of the inland basin area and the tidal height within the basin}. The coefficient and the exponent are adjustable and verifiable parameters and vary from inlets to inlets – but Jarrett’s analyses show that they are in the order of: C = 3.8*10^-5 to 7.5*10^-4; n = 0.86 to 1.03 in SI unit. They were determined {in general, the coefficient is high when the exponent is low; and vice versa} for all the measured jettied and unjettied inlets along the US coast.
The simple, yet very insightful model have drawn many follow-up works. It turns out that such a relationship can be established for any tide dominated estuarial channels – e.g. the paper I have presented along with my good friend and mentor Fred Koch in 1986 {Characteristic morphological relationship for tide dominated channels of the lower Meghna estuary, UNESCO, BUET} shows such a possibility.
The discussed tidal inlet cross-sectional stability model immediately indicates the following:

1. the first thing to note is its limitations – four obvious ones are: absence of any parameter describing the sediment characteristics, wave actions, freshwater inflow, and flood- and ebb-tidal delta morphodynamics;
   
2. that any work of the inland bay – either increasing or decreasing its size will affect the inlet cross-sectional area by such morphological responses as shore-erosion, seabed scour or sedimentation. The effects are not immediate however, but occur within a time-scale characteristic of the system – short for high energy systems than the low energy ones;
   
3. that inlet cross-sectional area and morphologies are likely to be different in different tidal regimes (e.g. commonly referred tidal range terminology: micro < 2 m; meso 2 – 4 m; and macro > 4 m); and
   
4. fixation effects of the inlet banks by measures such as bridge abutments and rock riprap are not included.
   

Some aspects of the first characteristic or limitation has been addressed by NC Kraus (1998), who proposed a relation accounting for channel roughness, tidal asymmetry and longshore sand transport.  
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3.2 Inlet-Bay Hydraulics
Despite providing a first-order understanding of the inlet stability and more, the reality of the problem is much more complex than the simple inlet cross-sectional stability formula. One way to appreciate this is to examine the one-dimensional Saint-Venant hydrodynamic equation applicable in long inlets (French mathematician Adhémar Jean Claude Barré de Saint-Venant, 1797 – 1886). This equation is only solvable by numerical modeling, but an analytical solution to the problem was offered by GH Keulegan (1951) and DB King (1974). This can be very useful to have an improved impression of the inlet current and the bay tidal response.
To illustrate its application, an image is included showing the ocean tide, bay tide and cross-sectional current. It is applicable for: inlet length 5 km; inlet width 3 km; inlet depth 15 m; bay depth 10 m; bay area 300 million square meter; tidal period 12.42 hours; and tidal range 2 m. In this particular example, the bay tide is slightly amplified and lags behind the ocean tide.
The illustrated example is only good for preliminary assessment. To better understand the complicated inlet-system processes – a coupled shallow-water numerical model may prove to be the best recourse – like the one described in my Ports2013 paper. Since opening of the Salt Ponds Inlet in 1979, the City of Hampton is required to dredge the inlet every 2 to 3 years to maintain its navigability. This frequency of recurring dredging is quite a burden and has not decreased despite the construction of jetties at the inlet mouth. Presented as a comparison of tide and wave powers – it turns out the tidal prism of the inlet is quite inadequate to flush out the sands mobilized by wave actions – active in the Chesapeake Bay. 
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4. Managing Tidal Inlets on Littoral Shores
The problem of such inlets primarily hinges upon keeping them functional, open and navigable – this is necessary because most large inlets cater to the needs of ports, harbors and marinas – for in-and-out sailing of different types of vessels. What issues must one look for sound management of such an inlet? Let me try to highlight some briefly.
Requirement of the year-round navigable depth for the highest-draft vessel allowed to call on the port and marina (for deep-draft harbors > 4.6 m; for small-craft harbors ≤ 4.6 m; for marinas according to design specifications). If outer anchorage idling is allowed and available, then a vessel can take advantage of the high tide by riding on it. 
Maneuverability of the exiting and entering vessels – overall lengths and widths of the allowable vessel – and maximum currents and vortices within the inlet-bay system. Smaller vessels have low tolerance thresholds of such factors than the large ones.
Hydrodynamic actions on the inlet – the tidal pumping (period, range, inlet-bay hydraulics of tidal amplification or attenuation, volume of fresh water inflow), the wave actions on the inlet mouth (wave height and period – their spectral and directional distributions and seasonality); and the frequency and magnitude of extreme events such as storm surge and tsunami. One can classify an inlet as high, medium or low energy inlet based on wave and tidal actions and powers.
Textural composition of sediments, in particular in the ebb- and flood-tidal deltas, the inlet and the beach. And the amount of sand mobilized and transported by both longshore and cross-shore processes – their reworking by flood- and ebb-tidal flow.       
Ebb- and flood-tidal delta morphodynamics – their identifiable morphological patterns and causal relationships with the forcing hydrodynamic parameters. Morphodynamics of the scour holes that typically develop at the constriction and at the head of jetties and breakwaters.
If jetties (these are shore-perpendicular structures made of rocks or sheet piles placed at the updrift and downdrift sides of the inlet) are planned to address the problem – then some new issues appear: (1) most often such structures interrupt the continuity of longshore sand transport – the interruption causes updrift sedimentation and downdrift erosion; (2) what should be their lengths (for example, longer updrift jetty than the downdrift one? and how far should they extend beyond the surf zone?) and height; (3) if sand bypassing (such as by mechanical measures – e.g. pump dredging) is considered to re-establish the continuity of longshore transport – a totally new evaluation and design is required; (4) should weir be installed on the updrift jetty to allow some sand to pass through – only to be collected from pits and sumps for downdrift replenishment; and (5) should the jetties be permeable to some extent, to let some sands to pass through, and implications.
Examining the potentials and feasibility of series of groynes (shore-perpendicular) both at updrift and downdrift locations to train the beach morphodynamics such that the inlet will not be overwhelmed by longshore and onshore transports.
Examining the potentials and feasibility of reducing the wave actions by installing submerged offshore reefs. Or by installing series of offshore breakwaters both at updrift and downdrift areas beyond the surf zone.
If dredging is unavoidable either as a stand-alone measure or as a supporting activity to other measures – then it is important to streamline and customize it, so that recurring costs can be minimized.             
As usual this topic turned out to be another long piece in the WIDECANVAS. Without further adieu, let me finish it with a line of wisdom from Leo Tolstoy (1828 – 1910): there is no greatness where there is no simplicity, goodness and truth. 

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- by Dr. Dilip K. Barua, 16 March 2018

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