Wave orbital velocity worksheet calculator

Calculate horizontal orbital velocity amplitude and vertical orbital velocity amplitude with your own figures.

Your numbers

Use the units shown. Results update as you change valid inputs.

Use horizontal orbital velocity amplitude and vertical orbital velocity amplitude to compare changes to your inputs. The method and limits below explain the scope.

Examples

Examples

Try the starting example

Regular wave height (m)
2
Period (seconds)
10
Water depth (m)
20
Observation elevation relative to still water (m)
-5
Horizontal orbital velocity amplitude (m/s)
0.671711
Vertical orbital velocity amplitude (m/s)
0.437487

Try another scenario

Regular wave height (m)
2.2
Period (seconds)
10
Water depth (m)
20
Observation elevation relative to still water (m)
-5
Horizontal orbital velocity amplitude (m/s)
0.738882
Vertical orbital velocity amplitude (m/s)
0.481236
Calculation method

Calculation method

Horizontal orbital velocity amplitude (m/s)

pi H/T × cosh(k(z+h))/sinh(kh).

Vertical orbital velocity amplitude (m/s)

pi H/T × sinh(k(z+h))/sinh(kh); finite-depth linear-wave model.

Symbols and units
a
Regular wave height (m)
b
Period (seconds)
c
Water depth (m)
d
Observation elevation relative to still water (m)

Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.

Assumptions & limits

Assumptions & limits

  • Height, period, depth, observation elevation. Returns Linear-wave orbital velocity estimate. All coefficients and observations are user supplied; results describe only the stated mathematical model. Quantities are deterministic calculations from supplied observations and assumptions; no external data is fetched. Supported limits: Finite inputs only; numeric fields bounded as labelled. Lists and JSON records are limited to 256 entries unless a stricter tool bound is stated. No automatic design approval, legal conclusion, treatment recommendation or safety certification. Regular wave height (m): minimum 0, maximum 1000000000000.0. Period (seconds): minimum 1e-12, maximum 1000000000000.0. Water depth (m): minimum 1e-12, maximum 1000000000000.0. Observation elevation relative to still water (m): minimum None, maximum 1000000000000.0.
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Further reading

Method reference ↗

Background reading; this does not imply endorsement or independent review of SumFizz.

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