Shallow Water Wave Celerity Transition Calculator
Linear finite-depth dispersion c=sqrt(g tanh(kh)/k) bridging shallow/deep limits; no nonlinear shoaling model.
Description
Calculate linear finite-depth gravity-wave phase speed from wavelength and depth.
Linear gravity-wave speed depends on wavelength and water depth. The finite-depth dispersion expression connects the shallow- and deep-water limits without switching between two separate formulas.
When to use this tool
Calculate linear finite-depth gravity-wave phase speed from wavelength and depth. Use it when the input measurements and conventions below match the operation you need.
- Prepare wavelengthM, depthM, gravityMPerS2, respecting the measurement basis and boundaries below.
- Compare the worked example with your intended operation before reusing its result.
How to use the tool and how it works
- Enter every field in the input table using the stated units and exact supported selector spelling where applicable.
- Run the tool. Correct input errors before interpreting an output.
- Read the result fields below; use accompanying flags and the stated sign, boundary or model convention when interpreting a number.
Wavelength, depth and gravitational acceleration must be positive. With k = 2 pi divided by wavelength, the tool returns sqrt(g times tanh(k times depth) divided by k).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| wavelengthM | Wavelength m. Meters. | Finite number; greater than zero |
| depthM | Depth m. Meters. | Finite number; greater than zero |
| gravityMPerS2 | Gravity m per s2. Meters per second squared. | Finite number; greater than zero |
| Output field | Interpretation |
|---|---|
| result | Object containing the following named result fields. |
| result.phaseSpeedMPerS | Phase speed mper s; use the stated units and sign convention. |
{
"input": {
"wavelengthM": 6.283185307179586,
"depthM": 1,
"gravityMPerS2": 1
},
"output": {
"result": {
"phaseSpeedMPerS": 0.8726936208978296
}
}
}Limitations and assumptions
- This is phase celerity under a linear, uniform-depth model. No current, breaking, bathymetric transformation or nonlinear wave correction is included.
- Every declared field is required and unexpected fields are rejected. Numeric inputs must be finite; input errors are distinct from a valid false result or an explicitly qualified output.
- Extremely large inputs and nonfinite or excessively large outputs are rejected. List positions reported by the tool use zero-based indices unless stated otherwise.
Alternative or Complementary methods
Compare the result with independently checked observations or a model that covers the omitted dynamics. Use compatible frames, units and sampling conventions when carrying the value into another calculation. Compare the scope of the nearby tools below before substituting one.
References
Similar or alternative tools
- Long Wave Shallow Water Speed Calculator
Linear shallow-water non-dispersive gravity wave speed sqrt(gh); caller must establish long-wave regime.
- baroclinic rossby wave speed
Baroclinic Rossby waves have a westward beta-plane phase speed modified by wave numbers and deformation radius.