airy.py

# Implement functions for linear wave theory, migrated from Matlab codes in
# Dropbox/matlab/+airy

from __future__ import division

import numpy as np

import wavenumber as wn


def celerity(omega, d):
    """
    c = celerity(omega, d)
    """

    k = wn.qkfs(omega, d)
    c = omega / k
    return c


def energydens(a, rho=1025, g=9.81):
    """
    E = airy.energydens(rho, g, a)
    return energy density following Airy wave theory
    rho: water density (1025 kg/m^3 if argument is empty)
    g: gravity (9.81 m/s^2 if argument is empty)
    a: wave amplitude
    """

    return 0.5 * rho * g * a**2


def groupvel(omega, d):
    """
    # cg = airy.groupvel(omega, d)
    # return group velocity following Airy wave theory
    # omega: 2*pi/T
    # d: still water depth
    """

    k = wn.qkfs(omega, d)

    # From Paul & Amos 2011 eq 9 (and elsewhere, obviously)
    # also repeated in Lowe et al 2005 eq 5
    return 0.5 * (1 + 2 * k * d / np.sinh(2 * k * d)) * omega / k


def uorb(H, omega, d):
    """
    compute bottom orbital velocity
    H: wave height
    omega: 2*pi/T
    d: still water depth
    returns ub
    """
    k = wn.qkfs(omega, d)
    return omega * H / 2 / np.sinh(k * d)