**HP Prime and TI-84 Plus CE: Shallow Wave Analysis**

**Introduction**

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**

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;

**TI-84 Plus CE Program H2OWAVES**

"EWS
2017-04-23"

"SHALLOW
WAVES"

"D<F/20"

Disp
"SHALLOW WAVES"

Input
"DEPTH (M): ",D

Input
"HEIGHT (M): ",H

√(9.80665*D)→V

1000*V→Z

(9806.65*H)^2/(2*Z)→I

Disp
"WAVE SPEED (M/S):",V

Disp
"IMPEDANCE (WKS):",Z

Disp
"WAVE FLUX (W/M):",I

**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
Surf’s
up! Eddie

This
blog is property of Edward Shore, 2017.