An Ocean Wave Parameter Calculator

The simple JavaScript calculator below will allow you to compute any wave parameter (other than amplitude) from any other. Just type in a value in any field and hit return. The gravity and capillary buttons at the bottom of the calculator indicate whether you have computed a gravity or a capillary wave. These buttons are normally controlled by the script because your selection of a value determines the type of wave. But it turns out that for a certain range of phase or group speeds, there can be two possible choices of frequency, wavelength, and the other parameters. One choice corresponds to a gravity wave and one corresponds to a capillary wave. If you select a speed within this ambiguous range, these buttons are no longer under program control and you can use them to select between the two different wave modes. For example, try selecting a phase speed of 0.4 m/s, and then clicking on the Gravity and Capillary buttons.

WaveCalc - A Palm OS Wave Calculator:

An improved version of this calculator, called WaveCalc, is now available for the Palm OS. Click on the image of the Palm to read more about this free program or to download WaveCalc.

Discussion:

Ocean waves are fascinating to watch and study. The theory of ocean waves was first worked out in the 18th century, although not all details of ocean wave dynamics is even understood today.

Ocean waves are created by winds acting on the surface. The exact growth mechanism is poorly understood, but when the wind first starts blowing, short waves (a few centimeters in length) are the first to be generated. Then as the wind becomes stronger, the dominant wave grows larger in amplitude and longer in wavelength. For a steady wind, the waves get longer and larger until the speed of the waves nearly matches the speed of the wind. The final distribution of energy among the waves is determined by the complex nonlinear interactions of the different wave components.

Waves can travel great distances. Long waves travel faster than shorter waves and so long waves created by a distant storm will out race the shorter waves to a distant shore. Long waves created by a distant storm are called swell. The waves created by the local wind field are called wind waves.

Waves are described by several parameters:

• amplitude (A) - wave height
• wavelength (lambda) - horizontal distance from peak to peak, measured in m or cm
• wavenumber (k) - defined to be 2*pi/wavelength in units of radians per meter (rad/m)
• frequency (f) - the number of wave cycles passing a point in one second (Hz)
• radian frequency (omega) - the number of radians passing a point in one second = 2*pi*frequency (rad/s)
• period (T) - time between successive peaks in seconds = 1/frequency
• phase speed (cp) - the speed of the individual wave crests (m/s)
• group speed (cg) - the speed of a group of waves or how fast energy is propagating along with the waves (m/s)

Wavenumber and radian frequency may seem redundant, but these are often used within scientific calculations. The concepts of phase speed and group speed may be new to you, but it turns out that groups of gravity waves travel at 1/2 the speed of the wave crests themselves. Thus the wave at the back of the group propagates to the front as the group moves along, only to be replaced by a following wave. This may seem odd, but this is how surface gravity waves work.

The term gravity wave is used here to indicate that the restoring force in the wave is gravity. These are the waves of 10 cm to 100 m wavelengths that you normally think of when you go to the beach. There are also surface waves where the restoring force is surface tension. These are called capillary waves. Surface tension takes over from gravity for only the smallest waves, at scales of 1.7 cm or smaller.

You may notice that the depth of the water does not affect things very much when the wavelengths are short with respect to the depth. When the wavelength grows long with respect to the depth, the speed of the wave becomes dominated by the depth, approaching a value of sqrt(g*H), where g is the gravitational acceleration of 9.8 m/s/s and H is the depth in m. This is the case for tides in the open ocean where the wavelengths may be tens of kilometers long but the water depth is 5 km deep on average. In this case the limiting speed of a tide is sqrt(9.8*5000) = 221 m/s!