Engineering & Technology · Water, Hydraulic & Coastal Infrastructure
Waves, tides, coastal processes and protective infrastructure
A coast experiences changing water level and moving waves at the same time. A stillwater elevation, a wave crest and the highest runup on a shore are different quantities. Confusing them can make a plausible-looking calculation physically misleading.
Review fluid continuity, pressure and hydraulic head, energy per unit weight, groundwater/ground interaction, and area under a rate–time graph. Use SI units, with 1 L/s=.001 m³/s and 1 h=3600 s. Water density 1000 kg/m³ and g = 9.81 m/s² are declared where used. New channel, coastal and hydrological terms are introduced in the lessons.
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Separate waves, tides, surge and reference levels, then compare coastal interventions through their process and sediment effects.
Define the timescale and vertical reference
Astronomical tides arise from the gravitational forcing of the moon and sun and the response of ocean basins. Their period and range differ by location. Storm surge is the storm-related departure from the predicted astronomical level; wind, atmospheric pressure, coast shape and depth influence the response.
Wave height is crest-to-trough distance, amplitude is departure from the mean for a symmetric wave, period is time between cycles and wavelength is distance between corresponding phases. Wind waves usually vary in height, period and direction. A single sinusoid is a component model, not a complete sea state.
All elevations need compatible datums and clearly defined components. An observed storm-water level may already include tide and some wave setup. Adding these again double-counts them. Wave setup is a mean level change associated with breaking; runup is the varying reach of waves on the shore. Neither is established by simply adding half a deep-water wave height to a tide table.
Use a wave model within its depth regime
For small-amplitude long waves in uniform shallow water, phase speed is approximately c=√(gh). Here h is stillwater depth, not wave height. Wavelength is c times period. “Shallow” is relative to wavelength: water can be geographically deep yet shallow for a very long wave. Shorter waves need a depth-dependent dispersion relation.
As waves encounter changing depth, refraction, shoaling, breaking, reflection and currents can alter their direction, height and loading. The original plotted sinusoid has no shoreline, current, breaking or structure. It checks definitions and model scales rather than predicting impact or overtopping.
A protective intervention changes the coastal system
Seawalls, revetments, breakwaters, dunes, nourished beaches, habitat-based and hybrid features influence different processes. A wall may hold a land edge while reflection, local scour, habitat loss or restricted sediment movement remain concerns. A measure that traps moving sediment can affect another location’s supply.
Suitability depends on wave exposure, water-level range, ground, sediment, space, ecology, access and consequences over time. A habitat-based approach suited to a sheltered shore is not automatically suitable for an exposed ocean coast. Maintenance, sediment replacement, degradation and future water levels belong in the comparison. Protection reduces particular risks under conditions; it does not remove all coastal change.
Let space and sediment change the next investigation
Consider an original hypothetical sheltered estuarine shore. The service is to retain a usable public path while limiting loss of the adjoining intertidal habitat over a stated planning period. Supply that the path can be moved into an available 20 m landward corridor, and that local native marsh vegetation could tolerate the salinity and tidal setting. Those are case assumptions requiring evidence at a real site; the corridor is not a general design width.
Compare A, a wall at the existing land edge, with B, moving the path landward and restoring a vegetated shore in the available corridor. A is intended to hold the present land edge, but fixes that edge while the intertidal area may need room to migrate. Wave reflection, local scour and effects on sediment movement need investigation; holding the path’s present line would not by itself meet the habitat part of the service. Maintenance includes the structure and changing conditions at its toe and neighbouring shore.
B uses space to keep the path away from the moving edge and allow a vegetated intertidal zone. Vegetation can interact with waves and trap sediment, but persistence also depends on exposure, ground levels and sediment availability relative to water-level change. Sediment arriving along or across the shore is part of the system; a planting proposal cannot manufacture that supply. Establishment, erosion after storms, vegetation condition and continuing access remain maintenance and service questions.
Under the supplied sheltered setting, compatible vegetation and available relocation space, B is a reasoned candidate for the next investigation because it can address both parts of the service without first fixing the present edge. This is not a performance approval or a universal preference. Observed wave conditions, sediment pathways and elevation change could contradict its assumptions. Compare the same service period and neighbouring-shore consequences for both options, then retain the unresolved evidence rather than declaring either option protective from its name.
| Question | A: fixed edge wall | B: setback path and vegetated shore |
|---|---|---|
| Exposure | Investigate reflection, loading and local scour under actual conditions. | Sheltered exposure is supplied; stronger waves could invalidate the assumed setting. |
| Space and habitat | Fixes current edge; investigate restricted habitat migration. | Uses the supplied relocation corridor and room for intertidal change. |
| Sediment pathway | Check effects on the toe, adjacent shore and sediment movement. | Check whether sufficient sediment reaches and remains in the vegetated zone. |
| Continuing service | Structure/toe condition and path access need evidence. | Establishment, elevation, vegetation and relocated access need evidence. |
| Present decision | Keep comparable consequences and remaining evidence explicit. | Investigate this candidate first under the supplied conditions; approval remains open. |
Check one long wave and a separate water-level scenario
Assume uniform depth h=1.00 m, g=9.81 m/s², period 10 s and sinusoidal height .10 m. The long-wave approximation gives c≈3.132 m/s and wavelength≈31.32 m. Depth/wavelength≈.0319 and amplitude/depth=.05; these support using a small long-wave teaching model. The figure plots surface departure at one instant, with vertical scale exaggerated relative to distance.
Separately define a constructed baseline shift +.20 m, a tide component +.80 m relative to that shifted mean, and storm residual +.70 m. If they are compatible, distinct and coincident, stillwater elevation is +1.70 m relative to the original datum. The numbers are assumed components, not return levels or a climate projection.
A supplied offshore wave height cannot convert that elevation into shore runup or a wall crest requirement by itself. Need wave transformation, shore/structure geometry, joint event conditions and a consistent definition of any setup already included. Combining separate rare component maxima does not automatically preserve their individual annual probabilities.
Try the reasoning
Is water depth h the same as wave height in c=√(gh)?
Show the answer and reasoning
No. It is the stillwater depth in the long-wave approximation.
Why inspect a storm-level dataset before adding tide?
Show the answer and reasoning
The recorded level may already contain the tide; adding it again would double-count that component.
Can one stabilization approach be ranked best for every coast?
Show the answer and reasoning
No. Exposure, sediment pathways, ground, space, ecology, maintenance and the defined service differ.
The path now serves an immovable facility, and the landward corridor is unavailable. Does the earlier preference for investigating B still follow? Does that make A an approved solution?
Show the answer and reasoning
B loses the supplied space and relocation assumption that made its two-part service plausible; the earlier inference must be reopened. That does not establish A’s performance or habitat consequences. The next comparison needs a feasible service boundary, evidence on exposure/sediment/ground and access, and consideration of whether another or hybrid approach can satisfy it. A wall’s ability to hold one line cannot substitute for those checks, and no real design is approved by this changed classroom case.
What to carry forward
Keep the datum, component definitions and wave regime explicit before interpreting a coastal level or protective measure.
References
Teaching resources and research supporting this lesson’s explanations and examples.