Coastal engineering basics

In short

Coastal engineering deals with waves, tides, currents and sediment at the land–sea boundary, and with the structures built there: breakwaters, seawalls, groynes, jetties, ports and beach nourishment schemes. India has about 7,500 km of coastline (mainland plus islands; the figure was re-measured upward to roughly 11,000 km in recent government mapping using finer-resolution data, so quoted lengths differ), 12 major and more than 200 non-major ports, and roughly a third of the mainland shoreline under erosion. It appears in GATE Civil under water resources and in the "Harbour and Coastal Engineering" elective, and is applied daily by port authorities, CWPRS Pune, NIOT, dredging contractors and consultants on Sagarmala projects. The core skills examined are wave transformation calculations, armour-stone sizing, littoral drift estimation and CRZ compliance.

Explained

Waves: description and linear (Airy) theory

• A wave is described by height H (crest to trough), period T, wavelength L, celerity C = L/T, amplitude a = H/2, wave number k = 2π/L, angular frequency ω = 2π/T and steepness H/L.
• Airy (small-amplitude, linear) theory assumes H ≪ L and H ≪ d, sinusoidal surface, irrotational flow. It gives the dispersion relation ω² = gk tanh(kd), i.e. L = (gT²/2π) tanh(2πd/L), solved by iteration.
• Water-depth classes (d = still-water depth): deep water d/L > 1/2 (tanh → 1), transitional 1/20 < d/L < 1/2, shallow water d/L < 1/20 (tanh kd → kd, so C = √(gd), independent of period).
• Particle orbits: circular in deep water, decaying with depth (negligible below d = L/2 — why wave loads on deep foundations are small); flattening to ellipses and finally horizontal to-and-fro motion in shallow water.
• Group celerity Cg = nC with n = ½[1 + 2kd/sinh 2kd]: Cg = C/2 in deep water, Cg = C in shallow water. Energy travels at Cg, not C.
• Higher-order and nonlinear theories (examined by name): Stokes 2nd–5th order for steep deep-water waves, cnoidal for long shallow waves, solitary wave theory near breaking, stream-function theory for design. Selection uses H/gT² and d/gT² charts (Le Méhauté) or the Ursell number HL²/d³.
• Wave generation depends on wind speed, fetch and duration; fully developed sea when all three are large. Sea = short, irregular, locally generated; swell = long-crested, regular, travelled from distant storms (the long south-west swell on the Kerala–Karnataka coast, locally called *kallakkadal* when it floods the shore).

Random waves and wave statistics

• A real sea record is irregular; it is reduced to significant wave height Hs = H1/3 (mean of the highest one-third of waves) and a representative period (Tz zero-crossing, Tp peak, Tm mean).
• Individual heights follow a Rayleigh distribution: Hrms = Hs/1.416, H1/10 ≈ 1.27 Hs, Hmax ≈ 1.86 Hs in a 1,000-wave storm.
• Spectral description: energy density S(f) versus frequency; standard forms are Pierson–Moskowitz (fully developed) and JONSWAP (fetch-limited). Hs = 4√m0, where m0 is the spectrum's zeroth moment.
• Design wave is obtained by extreme-value analysis (Gumbel/Weibull) of long records to a return period — commonly 50 years or 100 years for breakwaters, 25–50 years for shore protection; the choice follows the structure's life and the consequence of failure.
• Measurement and modelling: wave-rider buoys of the NIOT/INCOIS network, pressure and acoustic (ADCP) gauges, satellite altimetry; numerical models SWAN, MIKE 21, Delft3D for nearshore transformation and CWPRS Pune physical models for harbour layouts.

Wave transformation in shallow water

• Shoaling: as depth falls, Cg falls, so for constant energy flux H rises — shoaling coefficient Ks = √(Cg0/Cg). Period stays constant throughout.
• Refraction: wave crests bend to become parallel to the bottom contours; Snell's law sin α/C = constant. Energy concentrates on headlands and shoals (Kr > 1) and spreads in bays and over canyons (Kr < 1) — which is why headlands erode and bays accrete.
• Diffraction: energy spreads laterally into the sheltered region behind a breakwater or island; the diffraction coefficient Kd falls with distance and angle behind the tip, read from Wiegel/SPM charts. This decides wave tranquillity inside a harbour.
• Reflection: Kr(reflection) ≈ 0.9–1.0 for a vertical wall, 0.3–0.6 for a rubble mound, 0.05–0.2 for a flat beach. High reflection creates standing waves, toe scour and choppy berths — hence perforated (Jarlan) caissons.
• Breaking: waves break when H/d ≈ 0.78 (solitary-wave limit) or H/L ≈ 1/7 in deep water. Breaker types by surf similarity ξ0 = tan θ/√(H0/L0): spilling (ξ0 < 0.5, flat beaches), plunging (0.5–3.3), collapsing, surging (> 3.3, steep beaches).
• Wave set-up (raised mean water level inside the surf zone, roughly 10–20% of Hb), run-up on the slope, and overtopping discharge together fix crest levels.

Tides, water levels and surges

• Tide is the astronomical rise and fall from the gravitational pull of the moon (dominant) and sun. Chief harmonic constituents: M2 (12.42 h), S2 (12.00 h), N2, K1 (23.93 h), O1.
• Types by form factor F = (K1 + O1)/(M2 + S2): semi-diurnal F < 0.25, mixed 0.25–3, diurnal F > 3. The Indian coast is largely semi-diurnal to mixed semi-diurnal.
• Spring tides at new/full moon (sun and moon aligned, maximum range), neap tides at quadrature. Tidal range is macrotidal (> 4 m) in the Gulf of Khambhat and Gulf of Kachchh — Bhavnagar/Khambhat spring ranges reach about 9–11 m, among the world's largest — and microtidal (about 1–1.5 m) along the Tamil Nadu and Andhra coast.
• Datums: Chart Datum (CD) in India is approximately the lowest astronomical tide, so charted depths are conservative; MSL (Survey of India's land levelling datum, fixed from tide-gauge observations at Indian ports), MHWS/MLWS, HAT/LAT. The National Hydrographic Office (Indian Navy, Dehradun) publishes the annual Indian Tide Tables with predictions for Indian ports.
• Storm surge = pressure set-up (about 1 cm rise per 1 hPa drop) + wind set-up over a shallow shelf + wave set-up, worst on a wide shallow shelf at high tide. Odisha's 1999 super cyclone produced a surge of roughly 5–6 m. IMD issues cyclone and surge warnings; INCOIS (Hyderabad) runs surge and tsunami forecasting and the Indian Tsunami Early Warning Centre, set up after the 2004 Indian Ocean tsunami.
• Design water level = astronomical tide + surge + set-up + a sea-level-rise allowance (north Indian Ocean trend of roughly 1.5–2 mm/yr historically, higher in recent satellite records — project-specific values should be taken from current IPCC/INCOIS guidance).

Littoral processes and sediment transport

• Beach profile zones: dune – backshore with berm – foreshore/swash zone – surf zone – breaker zone – offshore, down to the depth of closure beyond which the profile hardly changes seasonally.
• Cross-shore transport: steep storm waves pull sand offshore into bars (winter/storm profile, eroded berm); long swell pushes it back onshore (summer/accretion profile). Dean's equilibrium profile h = A x^2/3.
• Longshore (littoral) drift is driven by oblique breaking waves; the CERC/SPM formula relates it to the longshore energy flux. On the Indian east coast net drift is generally northward in the south-west monsoon and reverses in the north-east monsoon, with net drift of the order of 0.5–1.5 million m³/yr at many sites; the west coast has strong seasonal reversal.
• Sediment budget: for a littoral cell, accretion/erosion = inflow − outflow + sources (rivers, cliff erosion, nourishment) − sinks (inlets, canyons, dredging, sand mining, dune transport). A deficit anywhere shows up as shoreline recession.
• Causes of Indian coastal erosion: interception of drift by port breakwaters and groynes (classic downdrift erosion north of Chennai Port, and near Ennore), reduced river sand supply because of dams and in-stream mining, beach and dune sand mining, mangrove and reef loss, and relative sea-level rise. NCCR's shoreline-change atlas (1990–2018 analysis) reports roughly one-third of the mainland coast eroding, about a quarter accreting and the rest stable.

Coastal protection and harbour structures

• Hard, shore-parallel: seawall (vertical/curved, protects the land but reflects waves and starves the beach), revetment (sloping rock/concrete armour), bulkhead (retains fill), detached offshore breakwater (reduces wave energy, forms a salient or tombolo), submerged reef.
• Hard, shore-normal: groyne (traps drift, builds the updrift beach, erodes downdrift — always designed as a field with a tapered terminal groyne and often with filling nourishment), jetties at tidal inlets and river mouths to keep channels open, training walls.
• Soft solutions: beach nourishment (sacrificial sand, needs periodic renourishment; the preferred modern approach because it keeps the beach), dune reconstruction with vegetation, geotextile sand-tube embankments (used successfully at Pentha, Odisha), mangrove and shelterbelt bioshields, and managed retreat/setback lines.
• Breakwaters: (a) rubble mound — core, filter/underlayer, armour (rock or concrete units: tetrapod, accropode, dolos, core-loc), toe berm, crown wall; flexible and forgiving, dominant in India; (b) vertical/caisson — concrete caissons on a rubble bed, needs good foundation, design pressures by Goda's formula; (c) composite; (d) berm (reshaping) breakwater.
• Armour design: Hudson's formula (SPM) for a single design wave; Van der Meer's formulae additionally account for storm duration, permeability, allowable damage level S and surf similarity, and are preferred for modern design.
• Harbour layout considerations: entrance oriented away from the dominant wave and drift direction, approach channel aligned with prevailing winds/currents, turning circle about 1.5–2 times vessel length, basin wave height limited to about 0.3 m for small craft and 0.5–1.0 m for cargo berths, avoidance of harbour resonance (seiche), and minimum littoral-drift siltation to cut maintenance dredging.
• Pile and jetty loads: wave forces on slender members from the Morison equation (inertia + drag); for large-diameter bodies, diffraction theory (MacCamy–Fuchs).

Indian codes, law and institutions

• IS 4651 (Parts 1–5) — Code of practice for planning and design of ports and harbours: site investigation, earth pressures, loading, general design, and layout/functional requirements.
• IS 9527 series — design and construction of port and harbour structures (concrete monoliths, sheet-pile and cellular structures, breakwaters); part numbering is best checked against the current BIS listing.
• International references used in Indian port practice: USACE Shore Protection Manual / Coastal Engineering Manual, BS 6349, PIANC guidelines.
• CRZ Notification 2019 (under the Environment (Protection) Act, 1986) regulates the 500 m landward belt from HTL and 100 m along tidal water bodies: CRZ-I (ecologically sensitive, I-A, and the intertidal zone, I-B), CRZ-II (developed, built-up municipal areas), CRZ-III (rural — III-A, densely populated, with a 50 m no-development zone; III-B with 200 m NDZ), CRZ-IV (water area to 12 nautical miles). Islands are covered by the ICRZ/Island Protection Zone notification. Clearances: State Coastal Zone Management Authority for CRZ-II/III, MoEFCC for CRZ-I and CRZ-IV. Coastal Zone Management Plans and the Survey of India hazard line are the governing maps.
• Other statutes and programmes: Indian Ports Act, 1908 and the Major Port Authorities Act, 2021; Sagarmala and Maritime India Vision; World Bank-aided ICZM/ENCORE projects in Gujarat, Odisha and West Bengal; institutions — CWPRS Pune (model studies), NIOT, NCCR and INCOIS (MoES), and IMD for cyclone and surge warnings.

Key points

• Dispersion relation – L = (gT²/2π)tanh(2πd/L); period is invariant, wavelength and celerity shrink as depth falls.
• Deep water – d/L > 0.5; L0 = 1.56T² m, C0 = 1.56T m/s, Cg = C/2.
• Shallow water – d/L < 0.05; C = √(gd), non-dispersive, Cg = C.
• Shoaling coefficient – Ks = √(Cg0/Cg) > 1; raises wave height as the wave approaches shore.
• Refraction – crests align with contours by Snell's law; concentrates energy on headlands, spreads it in bays.
• Diffraction – lateral energy spread behind a barrier; governs harbour tranquillity, quantified by Kd charts.
• Breaking criterion – H/d ≈ 0.78 in shallow water; breaker type from ξ0 = tan θ/√(H0/L0).
• Significant wave height – Hs = H1/3 = 4√m0; Hmax ≈ 1.86 Hs over about 1,000 waves (Rayleigh).
• Group celerity carries energy – wave power P = (1/8)ρgH²·Cg, about 39 kW/m for a 2 m, 10 s deep-water wave.
• Hudson's formula – armour weight ∝ H³; halving the design wave cuts stone weight to one-eighth.
• Van der Meer – includes storm duration, permeability and damage level; preferred over Hudson for design.
• Littoral drift – driven by sin 2αb; blocking it by a structure causes updrift accretion and downdrift erosion.
• Depth of closure – seaward limit of significant profile change; sets the nourishment and modelling boundary.
• Chart datum – approximately LAT in India; dredged and charted depths are referred to it, deck levels to MHWS plus freeboard.
• Storm surge – pressure set-up (about 1 cm per hPa of pressure drop) plus wind and wave set-up; worst on a wide shallow shelf at spring high tide.
• Seawall versus nourishment – a seawall saves the land but loses the beach; nourishment keeps the beach but must be repeated.
• CRZ 2019 – four zones; NDZ of 50 m (CRZ-III-A) or 200 m (CRZ-III-B); CRZ-IV extends to 12 nautical miles.
• Erosion status – roughly a third of India's mainland coastline is eroding (NCCR 1990–2018 assessment).

Formulas and examples

Example 1 — Wave transformation from deep to shallow water. A swell of H0 = 2.0 m, T = 10 s approaches from 30° to the shore normal; find the height at d = 6 m.

• L0 = 1.56 × 10² = 156 m; C0 = 15.6 m/s; Cg0 = C0/2 = 7.8 m/s.
• d/L0 = 6/156 = 0.0385 → transitional. Iterating L = 156·tanh(2π×6/L): L ≈ 73.6 m, so C = 73.6/10 = 7.36 m/s (the shallow-water shortcut √(9.81×6) = 7.67 m/s is 4% high).
• kd = 2π×6/73.6 = 0.512; 2kd = 1.024; sinh 1.024 = 1.213; n = ½[1 + 1.024/1.213] = 0.922; Cg = 0.922 × 7.36 = 6.79 m/s.
• Ks = √(7.8/6.79) = 1.072. Refraction: sin α = 0.5 × (7.36/15.6) = 0.236 → α = 13.6°; Kr = √(cos 30°/cos 13.6°) = √(0.866/0.972) = 0.944.
• H = 2.0 × 1.072 × 0.944 = 2.02 m. Check H/d = 0.34 < 0.78, so the wave has not yet broken.
• Deep-water power P = 0.125 × 1,025 × 9.81 × 2.0² × 7.8 = 39.2 kW per metre of crest.

Example 2 — Armour stone by Hudson's formula. Design wave H = 4.0 m; rock ρr = 2,650 kg/m³ (γr = 26.0 kN/m³); seawater 1,025 kg/m³ → Sr = 2.59, take 2.6; slope 1:2 (cot θ = 2); KD = 4.0 (non-breaking waves at the trunk).

• Denominator = 4.0 × (2.6 − 1)³ × 2 = 4.0 × 4.096 × 2 = 32.77.
• W = 26.0 × 4.0³/32.77 = 26.0 × 64/32.77 = 50.8 kN ≈ 5.2 tonnes per armour unit.
• Nominal diameter Dn = (W/γr)^1/3 = (50.8/26.0)^1/3 = 1.25 m; underlayer stone ≈ W/10 ≈ 0.52 t, core ≈ W/200 ≈ 25 kg.
• If the design wave were cut to 3.0 m by a submerged berm, W = 26 × 27/32.77 = 21.4 kN ≈ 2.2 t — the cube law makes wave-height accuracy the single most valuable input.

Example 3 — Littoral drift from one wave condition. Hb = 1.5 m (rms breaker height, matching K = 0.77), T = 8 s, breaker angle αb = 10°.

• db = Hb/0.78 = 1.92 m; √(g·db) = √(9.81 × 1.92) = 4.34 m/s.
• Pl = (1,025 × 9.81/16) × 1.5² × 4.34 × sin 20° = 628.4 × 2.25 × 4.34 × 0.342 = 2,101 W/m.
• (ρs − ρ)g(1 − n) = 1,625 × 9.81 × 0.6 = 9,565 N/m³; Q = 0.77 × 2,101/9,565 = 0.169 m³/s.
• Sustained for a full year this is 5.3 million m³ — far above the 0.5–1.5 million m³/yr actually measured on Indian coasts. The lesson: drift must be integrated over the directional wave climate (wave height, angle and frequency of occurrence, including monsoon reversal), never extrapolated from one condition.

Example 4 — Berth dredge level and deck level. Design vessel draught 12.0 m, under-keel clearance 1.0 m; at the site MSL = +1.8 m CD and MHWS = +3.4 m CD.

• Dredge level = −(12.0 + 1.0) = −13.0 m CD; available depth at MSL = 13.0 + 1.8 = 14.8 m.
• Quay deck level = MHWS + 1.5 m freeboard = +4.9 m CD (raise further for surge-prone sites).
• Seawall crest check: MHWS 3.4 + surge 1.2 + set-up 0.3 + run-up 2.6 (ξ-based, with roughness factor) + sea-level-rise allowance 0.3 = 7.8 → adopt crest +8.0 m CD.

Example 5 — Wave statistics. A storm record gives Hs = 3.0 m over 3 hours with Tz = 7 s (N ≈ 10,800/7 ≈ 1,540 waves).

• Hrms = 3.0/1.416 = 2.12 m; H1/10 = 1.27 × 3.0 = 3.81 m.
• Hmax = 3.0 × √(ln 1,540/2) = 3.0 × √(7.34/2) = 3.0 × 1.92 = 5.75 m — the height a crown wall must survive, not Hs.

Where it is used

• Major and non-major ports: breakwater and berth design, channel dredging and siltation studies at JNPA, Mundra, Paradip, Vizhinjam, Ennore and Sagarmala projects; roles of port engineer, marine structures designer, hydrographic surveyor.
• Shore protection by state agencies: Kerala Irrigation Department's seawalls, Odisha's Pentha geotube revetment, Tamil Nadu and Puducherry groyne and nourishment schemes, West Bengal's Digha protection works.
• Research and modelling institutions: CWPRS Pune (physical and mathematical models for every major Indian harbour), NIOT Chennai, NCCR, INCOIS; roles in numerical modelling with MIKE 21, SWAN and Delft3D.
• Energy and offshore infrastructure: ONGC offshore platforms and single-point moorings, LNG terminals, submarine outfalls and intakes for coastal thermal and desalination plants (Chennai, Minjur), offshore wind survey work off Gujarat and Tamil Nadu.
• Environmental consultancy and regulation: CRZ clearance applications, HTL/LTL demarcation, EIA for ports and reclamation, coastal zone management plans, shoreline-change and hazard-line mapping.
• Disaster management: cyclone and surge inundation mapping, multipurpose cyclone shelters, bioshield plantation and tsunami evacuation planning on the east coast and in the Andaman and Nicobar Islands.

Interview questions

• Q: Why does wave period stay constant while wavelength and celerity reduce as a wave shoals? A: The number of crests arriving per second cannot change in a steady train, so T is conserved; the dispersion relation then forces L and C to fall as tanh(kd) reduces with depth.
• Q: What is the difference between wave celerity and group celerity, and which one matters? A: Celerity is the speed of an individual crest; group celerity is the speed at which wave energy travels, equal to C/2 in deep water and C in shallow water. Energy flux calculations — shoaling, wave power, drift — use Cg.
• Q: Why do headlands erode while bays accrete? A: Refraction bends crests to follow the contours, so orthogonals converge on headlands (higher waves, more energy per metre) and diverge in bays, where lower energy allows deposition.
• Q: A new breakwater is built on a coast with strong northward drift. What happens to the adjoining beaches? A: Sand accumulates on the updrift (southern) side while the downdrift side, starved of supply, erodes — the classic pattern north of Chennai Port, remedied by sand bypassing or nourishment.
• Q: Why is armour weight proportional to H³ in Hudson's formula? A: Stability requires the submerged weight of a unit (∝ Dn³) to resist the drag and lift of the breaking wave, which scale with velocity squared (∝ H) times projected area (∝ Dn²); this gives Dn ∝ H, so W ∝ H³.
• Q: What are the limitations of Hudson's formula? A: It uses a single design wave with no account of storm duration, wave period, core permeability or allowable damage, is calibrated for no-damage regular-wave tests, and gives only the mean unit weight — Van der Meer's formulae address these.
• Q: Why is chart datum taken near the lowest astronomical tide? A: So that charted depths are the minimum a mariner will ever find; actual depth is almost always greater, which is the safe direction for navigation.
• Q: How is wave tranquillity achieved inside a harbour? A: By orienting and overlapping the entrance so that diffracted energy decays before reaching berths, limiting entrance width, avoiding reflective vertical faces inside, and checking for seiche resonance — verified by model or numerical study.
• Q: Seawall or beach nourishment — which would you recommend and why? A: Nourishment where the beach has amenity or ecological value and a sand source exists, since it preserves the beach and dissipates energy naturally; a seawall only where high-value assets sit immediately behind and space for a soft solution does not exist, accepting beach loss and toe scour.
• Q: What is the depth of closure and why does a designer need it? A: The depth beyond which the profile shows no significant seasonal change; it sets the seaward boundary for nourishment volumes, sediment-budget control volumes and shoreline models.
• Q: Under CRZ 2019, how wide is the regulated zone and who grants clearance? A: 500 m landward of HTL along the sea (100 m or the creek width along tidal water bodies); the State CZMA clears CRZ-II and CRZ-III projects while MoEFCC clears CRZ-I and CRZ-IV projects, as per the current notification and its amendments.
• Q: Why are rubble mound breakwaters preferred in India over caissons? A: Most Indian sites are shallow with soft or uneven beds, local quarry stone is available, construction needs no specialised floating plant, and failure is gradual and repairable rather than catastrophic.

Common mistakes

• Applying the shallow-water shortcut C = √(gd) in transitional depths, or using L0 instead of the local L, instead of iterating the dispersion relation.
• Using C instead of Cg in shoaling, energy flux or wave power calculations, or forgetting that Cg = C/2 only in deep water.
• Taking the design wave as Hs when a crown wall or armour check needs Hmax, or quoting Hmax ≈ 1.86 Hs without stating the number of waves.
• Sizing armour with a 1.0 safety factor on Hudson's W, taking a breaking-wave KD as 4 instead of about 2, and ignoring that W is a mean unit weight requiring a graded quarry run — and mixing kN with tonnes.
• Treating a single wave condition as the annual littoral drift, or using K = 0.77 with a significant wave height instead of the rms height, instead of integrating a directional wave climate with its monsoon reversal.
• Confusing datums: dredging to a depth below MSL instead of chart datum, or setting deck levels from MSL without adding tide, surge and freeboard.
• Designing a groyne field or seawall without assessing the downdrift consequence, and ignoring CRZ zoning, HTL demarcation and clearance before fixing the layout.

Related topics

Open channel flow · Flood control and river engineering · Hydrology · Environmental impact assessment · Fluid properties and statics · Dams and spillways