Wave Orbital Velocity At Bottom
Calculate finite-depth Airy bottom orbital velocity amplitude using solved dispersion and an overflow-safe inverse-sinh form; linear-wave assumptions exclude breaking and strong nonlinearity.
Description
Linear wave motion decays with depth.
Linear wave motion decays with depth. Bottom orbital velocity depends on wave height and finite-depth dispersion.
Calculate finite-depth Airy bottom orbital velocity amplitude using solved dispersion and an overflow-safe inverse-sinh form; linear-wave assumptions exclude breaking and strong nonlinearity.
When to use Wave Orbital Velocity At Bottom
Use this tool to calculate finite-depth Airy bottom orbital velocity amplitude using solved dispersion and an overflow-safe inverse-sinh form; linear-wave assumptions exclude breaking and strong nonlinearity.
Gather the water, wave, current or profile observations and any supplied calibration constants. Confirm units and the stated coordinate and pressure conventions.
How to use Wave Orbital Velocity At Bottom and understand its results
- Gather the water, wave, current or profile observations and any supplied calibration constants. Confirm units and the stated coordinate and pressure conventions.
- Enter waveHeightM, periodSeconds, waterDepthM, gravityMPerSecondSquared using the field table and calculation rules, then run the tool.
- Read bottomOrbitalSpeedAmplitudeMPerSecond. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| waveHeightM | Wave height m | number | Required |
| periodSeconds | Period seconds | number | Required |
| waterDepthM | Water depth m | number | Required |
| gravityMPerSecondSquared | Gravity m per second squared | number | Required |
Use nonnegative wave height and positive period, depth and gravity. Solve dispersion, then use an exponential inverse-sinh expression to avoid overflow in deep water.1
bottom amplitude = wave height × angular frequency/[2sinh(kdepth)] Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| bottomOrbitalSpeedAmplitudeMPerSecond | Bottom orbital speed amplitude m per second | number |
{
"input": {
"waveHeightM": 0.2,
"periodSeconds": 6.283185307179586,
"waterDepthM": 1,
"gravityMPerSecondSquared": 1.3130352854993315
},
"output": {
"bottomOrbitalSpeedAmplitudeMPerSecond": 0.08509181282393216
}
}Limitations and assumptions
Airy-wave assumptions exclude breaking and strong nonlinearity; this is an oscillatory amplitude, not a mean current.
Numbers and computed results must be finite; overflow produces an error. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Wave Dispersion Relation Root Solver: Solve finite-depth linear dispersion omega²=g k tanh(kh) by bounded dimensionless bisection, returning phase/group speeds without deep/shallow aliases. For a complementary task, use Stokes Drift Surface Velocity: Evaluate monochromatic deep-water Stokes drift at caller depth below surface, not Eulerian mean current; supplied amplitude is half wave height.
References
-
Wave Orbital Velocity At Bottom — tool.io
Similar or alternative tools
- Wave Dispersion Relation Root Solver
Solve finite-depth linear dispersion omega²=g k tanh(kh) by bounded dimensionless bisection, returning phase/group speeds without deep/shallow aliases.
- Stokes Drift Surface Velocity
Evaluate monochromatic deep-water Stokes drift at caller depth below surface, not Eulerian mean current; supplied amplitude is half wave height.