The Wave Calculator works in metric, taking deepwater wave height, period (seconds) or frequency (Hz), and wave direction (in degrees), and determining the wave length (L, in m), the wave number (k, in 1/m), wave celerity (C = L/T, in m/s), direction (degrees), shoaling and refraction coefficients (Ks, Kr), wave height, (H) and the group velocity Cg=n C at the shallow water depth you specify. The wave height is not allowed to exceed 0.8 of the water depth and is denoted `breaking' if this condition is met.

Additional results are the wave energy, E, per square meter of the water surface, the wave energy flux per meter of crest length, E_f, and the pressure response factor at the bottom, K_p. The bottom pressure, p_b=K_p * surface displacement* rho* g, where rho is the density of the water and g is the acceleration of gravity. The magnitude of the bottom velocity u_b (m/s) is also calculated.

The calculations are based on the dispersion relationship for progressive linear water waves: (sigma is 2 pi/T, k=2 pi/L) and Snell's Law for straight and parallel offshore contours. (Ref: Dean and Dalrymple, **Water Wave Mechanics for Engineers and Scientists,** World Scientific Press.)

Note: There is a very good approximation for the wave length given the water depth and wave period that does not require numerical iteration due to Fenton and McKee (1989) as quoted by Fenton, The Sea, vol. 9, A, 1990.
This equation is:

where L_o is the deep water wave length, L_o=g T^2/(2 pi).

** Problem: ** Determine the wave period of the wave that would just be 'feeling' the bottom in 10 m of water. The bottom begins to affect waves when the depth of the water is half the length of the wave, therefore for which wave period is the wave length equal to 20 m? Note that the wave height (for linear theory) does not affect the calculation. Click here for answer.

Comments: Robert Dalrymple

Center for Applied Coastal Research

University of Delaware, Newark DE 19716

USA