Continuous Spectrums

Bretschneider(Hs, Tp)

Creates a Bretschneider spectrum instance (also known as a Modified Pierson-Moskowitz). - Hs: Significant wave height (m) - Tp: Peak period (s)

The Bretschneider spectrum is self-normalizing and follows an f⁻⁵ slope.

Donelan(Hs, Tp, U10)

Creates a Donelan spectrum instance. - Hs: Significant wave height (m) - Tp: Peak period (s) - U10: Wind speed at 10m height (m/s)

The Donelan spectrum follows an f⁻⁴ slope in the high-frequency equilibrium range.

JONSWAP(Hs, Tp, γ=nothing)

Creates a JONSWAP (JOint North Sea WAve Project) spectrum instance with given: - significant wave height Hs (m) -> Average height of the highest third of waves - peak period Tp (s) -> Period of waves with the most energy - optional peak enhancement factor γ -> Controls the sharpness/height of the spectrum's peak, If γ is not provided, estimated based on Hs and Tp.

OchiHubble(Hs1, Tp1, λ1, Hs2, Tp2, λ2)

Bimodal spectrum defined by two independent Ochi-Hubble components. Typically Component 1 is Swell and Component 2 is Wind Sea.

RegularWave(H, T)

Defines a regular (monochromatic) wave spectrum with: - wave height H (m) - wave period T (s) Implements AbstractSpectrum interface.

TMA(Hs, Tp, h, γ=nothing)

The TMA spectrum (Texel-Marsen-Arsloe) is a shallow-water extension of the JONSWAP spectrum (mathematically defined as a JONSWAP spectrum multiplied by the Kitaigorodskii factor Φ(f, h) ). The Φ function is essentially a depth-scaling law that describes how the equilibrium range of the spectrum (the high-frequency tail) is limited by water depth. In this model we will be implementing a Kitaigorodskii factor (Kitaigorodskii et al. (1975)) approximation.

compute_donelan_normalization(γ, fp)

Numerical normalization for the Donelan shape.

compute_ochi_component(f, Hs, fp, λ)

Calculates the f-based density for a single Ochi component. Formula: S(f) = [ (λ + 1/4) * fp^4 ]^λ / Γ(λ) * [ Hs^2 / 4 * f^(4λ+1) ] * exp[ -(λ + 1/4) * (fp/f)^4 ]

estimate_Hs(Tp, γ=3.3)

Estimation of Hs, given Tp and gamma

estimate_Tp(Hs, γ=3.3)

Estimation of Tp, given Hs and gamma

estimate_γ(Hs, Tp)

Estimation of γ, given Hs and Tp

get_Hs(s::AbstractSpectrum)

Returns the significant wave height Hs [m] of the spectrum.

get_Hs(s::RegularWave)

Returns the wave height (H) for the regular wave.

get_Tp(s::AbstractSpectrum)

Returns the peak period Tp [s] of the spectrum.

get_Tp(s::RegularWave)

Returns the wave period (T) for the regular wave.

get_alpha(s::JONSWAP)

Estimation of α, given JONSWAP parameters

get_cumulative_energy(s::AbstractSpectrum, f::Real, npoints, method=:symbol, order)

Compute the CDF of abstract spectrum at frequency f, using npoints-1 bins and the selected method of integration.

get_density(s::AbstractSpectrum, f::Real)

Returns the spectral density S(f) in [m²s]. Must be implemented by all subtypes.

get_density(s::Bretschneider, f::Real)

Returns the spectral density S(f) [m²s]. Formula: S(f) = (1.25/4) * (Hs²/fp) * (f/fp)⁻⁵ * exp(-1.25 * (f/fp)⁻⁴)

get_density(s::Donelan, f::Real)

Returns the spectral density S(f). Note the f⁻⁴ dependency.

get_density(s::JONSWAP, f::Real)

Returns the spectral density S(f) in [m²s]. Assumes s.Ag is the normalization factor for the f-based JONSWAP.

get_density(s::OchiHubble, f::Real)

Returns the spectral density S(f) [m²s] by summing the two components.

get_density(s::RegularWave, f::Real)

Returns the spectral density S(f) for the regular wave. Implements a Dirac delta: returns H^2/8 at f = 1/T, 0 elsewhere.

get_fmax(s::AbstractSpectrum; multiplier=5.0)

Returns a recommended maximum frequency for numerical integration based on the peak frequency: fmax = multiplier * fp. According to literature, fmax between 3 to 5 times fp is sufficient to capture more than 99% of the energy.

get_γ_exponent(s::JONSWAP, fr::Real)

Returns the γ exponent b for a given relative frequency fr = f/fp.

integrate(s::AbstractSpectrum, fmin, fmax; npoints, method=:symbol, order)

Returns the numeric integral of the spectrum between fmin and fmax, using npoints-1 bins and the selected method of integration