1. Wave-Structure Interaction

The nature of wave-structure interaction depends primarily on the ratio of structure diameter D to wave length L. Two regimes are distinguished:

  • Morison regime (D/L < 0.2): Slender members such as jacket legs and braces fall in this category. Wave forces are dominated by drag (viscous) and inertia (pressure gradient) effects, computed using the Morison equation.
  • Diffraction regime (D/L > 0.2): Large-volume structures such as gravity base structures, tension leg platform columns, and FPSO hulls scatter and diffract incoming waves. Forces are computed using potential flow theory (panel methods such as WAMIT or HydroD).

For jacket platforms, the Morison equation is universally applicable, as all members are slender relative to typical design wave lengths.

2. The Morison Equation

The Morison equation gives the in-line force per unit length on a circular cylinder:

f(t) = ½ ρ Cd D |u(t)| u(t)  +  ρ Cm (π/4) D² ˙u(t)

Where:

  • ρ = seawater density (typically 1025 kg/m³)
  • Cd = drag coefficient (typically 0.65–1.05 for smooth/rough cylinders)
  • Cm = inertia coefficient (typically 1.5–2.0)
  • D = member outer diameter (m)
  • u(t) = horizontal wave particle velocity (m/s)
  • ˙u(t) = horizontal wave particle acceleration (m/s²)

Drag and inertia forces are 90° out of phase, with the drag term peaking when velocity is maximum (at wave crest and trough) and the inertia term peaking at zero water surface elevation. The total force must be integrated over the length of the submerged member.

"The Morison equation is simple and robust, but the selection of Cd and Cm remains a source of engineering judgement. Marine growth, surface roughness, and Reynolds number all influence the appropriate coefficient values."

3. Regular vs Irregular Waves

Two main wave modelling approaches are used in offshore structural analysis:

  • Regular (deterministic) design wave: A single, representative sinusoidal or stream function wave characterised by design wave height Hd and associated period Td. This approach is used for extreme strength checks (100-year return period storm). Stokes 5th order or stream function wave theories are used to compute accurate kinematics for steep waves in intermediate water depths.
  • Irregular (stochastic) spectral approach: The sea state is represented by a wave energy spectrum, most commonly the JONSWAP spectrum for storm seas in fetch-limited environments, or the Pierson-Moskowitz spectrum for fully developed open ocean seas. The structural response is computed in the frequency domain using transfer functions, enabling fatigue damage accumulation across the full range of sea states.

The JONSWAP spectral density function is:

S(ω) = α g² ω-5 exp[−1.25(ωp/ω)4] × γexp[−(ω−ωp)²/(2σ²ωp²)]

Where Hs (significant wave height) and Tp (peak period) define the sea state, and γ is the peak enhancement factor (typically 3.3 for the North Sea). The JONSWAP spectrum produces more peaked spectral shapes than the Pierson-Moskowitz spectrum, reflecting the narrower frequency content of storm-generated seas in semi-enclosed basins.

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4. Design Wave vs Spectral Approach

The choice between deterministic and spectral analysis depends on the design limit state:

  • Extreme Strength (ULS): The deterministic design wave approach is most common. A 100-year return period Hs is used to define an associated design wave height (Hmax = 1.86 Hs for a 3-hour storm), and the structure is analysed under this single deterministic event. Non-linear wave kinematics and dynamic amplification must be accounted for.
  • Fatigue (FLS): The spectral approach is mandatory. The long-term distribution of sea states (wave scatter diagram) is combined with the structural transfer functions to compute cumulative fatigue damage at critical joints using Miner's rule. Rainflow cycle counting is applied for time-domain analysis.
  • Accidental Limit State (ALS): Robustness checks against progressive collapse often use the design wave approach with reduced partial safety factors.

5. Current Loads and Directionality

Ocean currents add to the wave-induced particle velocities, increasing the drag component of the Morison force. Current profiles are typically depth-varying: steady near-surface tidal and wind-driven currents decay with depth, while loop and eddy currents (significant in the Gulf of Mexico) may persist to considerable depths.

Load directionality is critical for jacket analysis. The maximum base shear and overturning moment typically occur when wave, wind, and current loads are co-aligned with the principal axis of the jacket. Eight or more wave approach directions are typically analysed to identify the critical direction for each structural component.

6. Dynamic Amplification

Jacket structures have natural periods in the range 1.5–4 seconds for typical water depths. Since significant wave energy exists at these periods, dynamic amplification of the quasi-static response can be important. The Dynamic Amplification Factor (DAF) is defined as the ratio of dynamic to quasi-static response:

For most jacket structures in depths up to 150 m, the DAF is modest (1.05–1.15). In deeper water or for slender structures, full dynamic time-domain analysis is required, using aero-elastic or hydrodynamic simulation software such as SACS, USFOS, or OrcaFlex.

7. Conclusion

Wave load analysis is at the heart of offshore structural engineering. Understanding the Morison equation, appropriate hydrodynamic coefficients, wave theories, and the choice between deterministic and spectral approaches equips engineers to design safe and economical offshore structures. Use our free Morison Wave Force Calculator for quick preliminary wave load estimates.