def energy_dissipation_rate(self, H, U):
'''
c_ub = 100 = dimensionless empirical coefficient to correct
for non-Law-of-the-Wall results (Umlauf and Burchard, 2003)
u_c = water friction velocity (m/s)
sqrt(rho_air / rho_w) * u_a ~ .03 * u_a
u_a = air friction velocity (m/s)
z_0 = surface roughness (m) (Taylor and Yelland)
c_p = peak wave speed for Pierson-Moskowitz spectrum
w_p = peak angular frequency for Pierson-Moskowitz spectrum (1/s)
TODO: This implementation should be in a utility function.
It should not be part of the Waves management object itself.
'''
if H is 0 or U is 0:
return 0
c_ub = 100
c_p = PiersonMoskowitz.peak_wave_speed(U)
w_p = PiersonMoskowitz.peak_angular_frequency(U)
z_0 = 1200 * H * ((H / (2*np.pi*c_p)) * w_p)**4.5
u_a = .4 * U / np.log(10 / z_0)
u_c = .03 * u_a
eps = c_ub * u_c**3 / H
return eps
def test_delvigne_sweeney():
wind_speed = 10.0
T_w = PiersonMoskowitz.peak_wave_period(wind_speed)
assert np.isclose(DelvigneSweeney.breaking_waves_frac(wind_speed, 10.0),
0.016)
assert np.isclose(DelvigneSweeney.breaking_waves_frac(wind_speed, T_w),
0.0213333)
def test_delvigne_sweeney():
wind_speed = 10.0
T_w = PiersonMoskowitz.peak_wave_period(wind_speed)
assert np.isclose(DelvigneSweeney.breaking_waves_frac(wind_speed, 10.0),
0.016)
assert np.isclose(DelvigneSweeney.breaking_waves_frac(wind_speed, T_w),
0.0213333)
def peak_wave_period(self, time):
'''
:param time: the time you want the wave data for
:type time: datetime.datetime object
:returns: peak wave period (s)
'''
U = self.wind.get_value(time)[0]
return PiersonMoskowitz.peak_wave_period(U)
def peak_wave_period(self, time):
'''
:param time: the time you want the wave data for
:type time: datetime.datetime object
:returns: peak wave period (s)
'''
U = self.wind.get_value(time)[0]
return PiersonMoskowitz.peak_wave_period(U)
def peak_wave_period(self, points, time):
'''
:param time: the time you want the wave data for
:type time: datetime.datetime object
:returns: peak wave period (s)
'''
U = self.get_wind_speed(points, time) # only need velocity
return PiersonMoskowitz.peak_wave_period(U)
def test_ding_farmer():
wind_speed = 10.0 # m/s
rdelta = 200.0 # oil/water density difference (kg / m^3)
droplet_diameter = 0.0002 # 200 microns
wave_height = PiersonMoskowitz.significant_wave_height(wind_speed)
wave_period = PiersonMoskowitz.peak_wave_period(wind_speed)
f_bw = DelvigneSweeney.breaking_waves_frac(wind_speed, wave_period)
k_w = Stokes.water_phase_xfer_velocity(rdelta, droplet_diameter)
assert np.isclose(DingFarmer.calm_between_wave_breaks(0.5, 10), 15.0)
assert np.isclose(DingFarmer.calm_between_wave_breaks(f_bw, wave_period),
347.8125)
assert np.isclose(DingFarmer.refloat_time(wave_height, k_w), 386.0328)
assert np.isclose(
DingFarmer.water_column_time_fraction(f_bw, wave_period, wave_height,
k_w), 1.0)
def calm_between_wave_breaks(self, model_time, time_step,
time_spent_in_wc=0.0):
wind_speed = max(.1, self.waves.wind.get_value(model_time)[0])
wave_period = PiersonMoskowitz.peak_wave_period(wind_speed)
f_bw = DelvigneSweeney.breaking_waves_frac(wind_speed, wave_period)
T_calm = DingFarmer.calm_between_wave_breaks(f_bw, wave_period)
return np.clip(T_calm, 0.0, float(time_step) - time_spent_in_wc)
def water_column_time_fraction(self, points, model_time,
water_phase_xfer_velocity):
wave_height = self.waves.get_value(points, model_time)[0]
wind_speed = np.clip(self.get_wind_speed(points, model_time), 0.01,
None)
wave_period = PiersonMoskowitz.peak_wave_period(wind_speed)
f_bw = DelvigneSweeney.breaking_waves_frac(wind_speed, wave_period)
return DingFarmer.water_column_time_fraction(
f_bw, wave_period, wave_height, water_phase_xfer_velocity)
def water_column_time_fraction(self, model_time,
water_phase_xfer_velocity):
wave_height = self.waves.get_value(model_time)[0]
wind_speed = max(.1, self.waves.wind.get_value(model_time)[0])
wave_period = PiersonMoskowitz.peak_wave_period(wind_speed)
f_bw = DelvigneSweeney.breaking_waves_frac(wind_speed, wave_period)
return DingFarmer.water_column_time_fraction(f_bw,
wave_period,
wave_height,
water_phase_xfer_velocity)
def water_column_time_fraction(self,
points,
model_time,
water_phase_xfer_velocity):
wave_height = self.waves.get_value(points, model_time)[0]
wind_speed = np.clip(self.get_wind_speed(points, model_time), 0.01, None)
wave_period = PiersonMoskowitz.peak_wave_period(wind_speed)
f_bw = DelvigneSweeney.breaking_waves_frac(wind_speed, wave_period)
return DingFarmer.water_column_time_fraction(f_bw,
wave_period,
wave_height,
water_phase_xfer_velocity)
def test_ding_farmer():
wind_speed = 10.0 # m/s
rdelta = 0.2 # oil/water density difference
droplet_diameter = 0.0002 # 200 microns
wave_height = PiersonMoskowitz.significant_wave_height(wind_speed)
wave_period = PiersonMoskowitz.peak_wave_period(wind_speed)
f_bw = DelvigneSweeney.breaking_waves_frac(wind_speed, wave_period)
k_w = Stokes.water_phase_xfer_velocity(rdelta, droplet_diameter)
assert np.isclose(DingFarmer.calm_between_wave_breaks(0.5, 10),
15.0)
assert np.isclose(DingFarmer.calm_between_wave_breaks(f_bw, wave_period),
347.8125)
assert np.isclose(DingFarmer.refloat_time(wave_height, k_w),
385.90177)
assert np.isclose(DingFarmer.water_column_time_fraction(f_bw,
wave_period,
wave_height,
k_w),
1.1095)
def percent_whitecap_coverage(cls, wind_speed):
'''
percent whitecap coverage
drag coefficient reduces linearly with wind speed
for winds less than 2.4 m/s
'''
if wind_speed is 0:
return 0
if wind_speed > 2.4:
C_D = .0008 + .000065 * wind_speed
else:
C_D = (.0008 + 2.4 * .000065) * wind_speed / 2.4
visc_air = 1.5 * 10**(-5) # m2/s
peak_ang_freq = PiersonMoskowitz.peak_angular_frequency(wind_speed)
R_Bw = C_D * wind_speed**2 / (visc_air * peak_ang_freq)
Wc = 3.88 * 10**(-5) * R_Bw**(1.09)
return Wc
def test_pierson_moskowitz():
assert np.isclose(PiersonMoskowitz.significant_wave_height(10.0), 2.24337)
assert np.isclose(PiersonMoskowitz.peak_wave_period(10.0), 7.5)
def test_pierson_moskowitz():
assert np.isclose(PiersonMoskowitz.significant_wave_height(10.0), 2.24337)
assert np.isclose(PiersonMoskowitz.peak_wave_period(10.0), 7.5)
