Shallow Wave Analysis

[Eddie W. Shore]

The program H2OWAVES calculates wave speed, impedance, and wave flux for shallow ocean waves. The following are assumed:

1. The criteria of λ < D/20 is assumed where λ is the length of the wave.
2. The water assumed to be 0°C, where the density (ρ) is 1,000 kg/m.
3. SI units are used. For gravity, g = 9.80665 m/s^2 is used.

Formulas Used

Wave Speed (m/s): v = √(g * D)
Wave Impedance (Mks): Z = ρ * v
Wave Energy Flux (W/m): I = (ρ * g * H)^2/(2 * Z)
Maximum Possible Length (m): λ = 20 * D

HP Prime Program H2OWAVES

Code:

EXPORT H2OWAVES()
BEGIN
// EWS 2017-04-21
// Shallow Wave Analysis
// for D/L<1/20
// SI Units

LOCAL D,H;
LOCAL v,Z,I;

INPUT({D,H},
"Wave Analysis",
{"D: ","H: "},
{"Depth (m)","Wave Height (m)"});

v:=√(9.80665*D);
Z:=1000*v;
I:=(9806.65*H)^2/(2*Z);

PRINT();
PRINT("Wave speed (m/s): "+v);
PRINT("Impedance (Mks): "+Z);
PRINT("Wave Flux (W/m): "+I);

RETURN {v,Z,I};

END;

Example

Input:
Depth: 3.2 m
Height: 0.49 m

Output:
Wave Speed: 5.601899678 m/s
Impedance: 5601.899678 Wks
Wave Flux: 2060.953478 W/m

Source:

Ingard, K.U. Fundamental of Waves and Oscillations Cambridge University Press: New York 1988. IBSN 0 521 32734