Calculator Inputs
Example Data Table
| Case | H (m) | T (s) | d (m) | y (m) | L (m) | Umax (m/s) | Wmax (m/s) | Vmax (m/s) |
|---|---|---|---|---|---|---|---|---|
| Pipeline near seabed | 2.4 | 8.0 | 12.0 | 1.5 | 75.850 | 0.815 | 0.101 | 0.821 |
| Harbor sediment check | 1.2 | 6.0 | 8.0 | 0.5 | 45.224 | 0.465 | 0.032 | 0.466 |
| Jacket member review | 3.5 | 10.0 | 18.0 | 3.0 | 116.787 | 0.988 | 0.158 | 1.001 |
Formula Used
Wave amplitude: a = H / 2
Angular frequency: ω = 2π / T
Dispersion relation: ω² = gk tanh(kd)
Wave length: L = 2π / k
Horizontal excursion amplitude: X = a cosh(ky) / sinh(kd)
Vertical excursion amplitude: Z = a sinh(ky) / sinh(kd)
Maximum horizontal velocity: Umax = ωX
Maximum vertical velocity: Wmax = ωZ
Instant horizontal velocity: u = Umax cos(θ)
Instant vertical velocity: w = Wmax sin(θ)
Dynamic pressure amplitude: p′ = ρga cosh(ky) / cosh(kd)
Here, H is wave height, T is wave period, d is water depth, y is elevation above seabed, k is wave number, ρ is water density, and θ is phase angle.
The calculator applies Airy wave theory for regular waves. It is especially useful for preliminary checks on seabed pipelines, marine structures, sediment transport, and near-bed stability assessments.
How to Use This Calculator
- Enter wave height, wave period, and local water depth.
- Set the elevation above seabed where you want particle motion.
- Provide phase angle if you need instantaneous velocity components.
- Keep gravity and density at standard seawater values unless needed.
- Adjust tolerance and iteration count for stricter numerical convergence.
- Press the calculate button to generate velocities and related outputs.
- Review maximum, instantaneous, bed, and surface motion metrics.
- Use the CSV button for tabular export and the PDF button for print-ready output.
Engineering Notes
Regular wave assumption Linear wave theory Dispersion solved iteratively Useful for scour checks Supports pipeline assessments Includes pressure amplitudeFor strongly nonlinear waves, breaking waves, very steep waves, or highly irregular sea states, this simplified approach should be supplemented with more advanced hydrodynamic analysis.
Frequently Asked Questions
1) What does wave orbital velocity represent?
It represents the speed of water particles moving in orbital paths under a wave. Engineers use it to estimate local motion around seabeds, pipelines, and offshore members.
2) Why is water depth important?
Water depth controls how strongly the seabed influences particle motion. Shallower water usually increases bed interaction and changes the velocity distribution through the depth.
3) Why does the calculator solve for wave number?
Wave number links period, depth, and wave length through the dispersion equation. Many orbital velocity formulas require wave number before any reliable velocity estimate can be produced.
4) What is the elevation above seabed input used for?
It selects the vertical location where particle motion is evaluated. Use zero at the seabed and water depth at still water level for a quick profile check.
5) What is the difference between maximum and instantaneous velocity?
Maximum velocity is the peak orbital speed amplitude. Instantaneous velocity includes the chosen phase angle, so it represents the velocity at one point in the wave cycle.
6) When is bed orbital velocity especially useful?
It is useful for pipeline stability, scour potential, and sediment movement reviews. Near-bed motion often drives practical seabed design decisions in coastal and offshore work.
7) Can I use this for irregular sea states?
This file is best for regular-wave screening calculations. For irregular seas, combine spectral methods, design sea states, or time-domain analysis for more realistic loading and motion estimates.
8) Why is there a density input?
Density is used for dynamic pressure amplitude. It lets you compare freshwater and seawater conditions when reviewing pressure-sensitive elements or supporting hydrodynamic checks.