API

SteadyWaves is an implementation of Rienecker and Fenton (1981) Fourier Approximation Method to steady, periodic, nonlinear waves propagating in water of constant depth.

u[2N+C_INDEX]: wave celerity c√(k/g)

u[2N+D_INDEX]: mean water depth kη̄

u[2N+H_INDEX]: wave height kH

u[2N+Q_INDEX]: volume flux due to waves q√(k³/g)

u[2N+R_INDEX]: Bernoulli constant rk/g

u[2N+U_INDEX]: mean flow velocity Ū√(k/g)

u[eta_indexes(N)]: free surface elevations kη

u[psi_indexes(N)] : stream function coefficients B

wave_period(u, d, N; g=G)

Calculate dimensional wave period T from solution u.

wavelength(u, d, N)

Calculate dimensional wavelength L from solution u.

wave_height(w, df)

Calculate dimensional wave height H from solution w and dimensional factor df.

wave_number(w, df)

Calculate dimensional wave number K from solution w and dimensional factor df.

wave_period(w, df)

Calculate dimensional wave period T from solution w and dimensional factor df.

wavelength(w, df)

Calculate dimensional wavelength L from solution w and dimensional factor df.

topo_approx(d, H, L; cc=2, N=10, g=G)

Calculate shoaling coefficients K in range of depth values d for wave of length L and height H.

Arguments

• d: vector of decreasing water depths (m)
• L: initial wavelength (m) - corresponding to d[1]
• H: initial wave height (m) - corresponding to d[1]
• cc: current criterion; cc=1, cc=CC_STOKES - Stokes (default), cc=2, cc=CC_EULER - Euler
• N: number of solution eigenvalues, defaults to N=10
• g: gravity acceleration (m/s^2), defaults to g=9.81

Output

• K: vector of shoaling coefficient values

update_depth_fourier_approx(u, d, d_p, F, T; cc=1, N=10, g=G)

Update approximate solution u of a steady wave of power F and period T propagating in water of changing depth from d to d_p using Fourier Approximation Method.

Arguments

• u: solution matrix being mutated
• d: initial water depth (m)
• d_p: target water depth (m)
• F: wave power (kg m/s)
• T: wave period (s)
• cc: current criterion; cc=1, cc=CC_STOKES - Stokes (default), cc=2, cc=CC_EULER - Euler
• N: number of solution eigenvalues, defaults to N=10

fourier_approx(d, H, P; pc=1, cc=1, N=10, M=1, g=G)

Approximate solution u of a steady wave of height H and length L propagating in water of depth d using Fourier Approximation Method.

Arguments

• d: water depth (m)
• H: wave height (m)
• P: wave parameter - length L (m) or period T (s)
• pc: parameter criterion; pc=1, pc=PC_LENGTH - length (default), pc=2, pc=PC_PERIOD - period
• cc: current criterion; cc=1, cc=CC_STOKES - Stokes (default), cc=2, cc=CC_EULER - Euler
• N: number of solution eigenvalues, defaults to N=10
• M: number of height steps, defaults to M=1
• g: gravity acceleration (m/s^2), defaults to g=9.81

Output

• u[1:N+1]: free surface elevation kη
• u[N+2:2N+1]: stream function coefficients B
• u[2N+2]: wave celerity c√(k/g)
• u[2N+3]: mean water depth kη̄
• u[2N+4]: volume flux due to waves q√(k³/g)
• u[2N+5]: Bernoulli constant rk/g
• u[2N+6]: mean flow velocity Ū√(k/g)
• u[2N+7]: wave height kH