Long Wave Shallow Water Speed Calculator
Linear shallow-water non-dispersive gravity wave speed sqrt(gh); caller must establish long-wave regime.
Description
Calculate the linear shallow-water speed sqrt(g h).
Long gravity waves in sufficiently shallow water have a speed controlled mainly by depth. This calculator evaluates that model for a supplied depth and gravitational acceleration.
When to use this tool
Calculate the linear shallow-water speed sqrt(g h). Use it when the input measurements and conventions below match the operation you need.
- Prepare 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.
Both depth and acceleration must be positive. The returned speed is sqrt(g times depth), with compatible input units giving meters per second.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| 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.speedMPerS | Speed mper s; use the stated units and sign convention. |
{
"input": {
"depthM": 4,
"gravityMPerS2": 9
},
"output": {
"result": {
"speedMPerS": 6
}
}
}Limitations and assumptions
- No wavelength is supplied, so the shallow-water assumption is not checked. Currents, changing bathymetry, breaking and nonlinear amplitudes are outside the model.
- 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
- Shallow Water Wave Celerity Transition Calculator
Linear finite-depth dispersion c=sqrt(g tanh(kh)/k) bridging shallow/deep limits; no nonlinear shoaling model.
- baroclinic rossby wave speed
Baroclinic Rossby waves have a westward beta-plane phase speed modified by wave numbers and deformation radius.