def calc_velocity(self, nonlinear=True):
"""
Return the velocity components
u = d \psi /dz
w = -d \psi /dx
"""
psi = self.calc_streamfunction(nonlinear=nonlinear)
#us, ws = np.gradient(psi)
#return -us/self.dZ[np.newaxis,...], -ws/self.dx_s
u = grad_z(psi, self.Z, axis=0)
w = -1 * grad_z(psi, self.X, axis=1)
return u.T, w.T
def get_Lw(rho, z, z0=None, Nz=400, mode=1, omega=2 * np.pi / (12.42 * 3600)):
"""
A function to calculate the wavelength of a specific vertical mode for a specific frequency given stratification conditions.
z0 is the final depth. Will interpolate there if necessary.
"""
if z0 is None:
z0 = max(z)
Z = -np.linspace(0, 1, Nz) * z0
dZ = np.abs(Z[1] - Z[0])
# Interpolate the density profile onto all points
Fi = interp1d(z, rho, axis=0, fill_value='extrapolate')
rhoZ = Fi(Z)
drho_dz = grad_z(rhoZ, Z, axis=0)
N2 = -GRAV * drho_dz / RHO0
phi, c = isw.iwave_modes(N2, dZ)
phi_n = phi[:, mode]
c_n = c[mode]
k = omega / c_n
Lw = 2 * np.pi / k
return Lw
def calc_N2(self):
"""
Calculate the buoyancy frequency
"""
#drho_dz = np.gradient(self.rhoz, -np.abs(self.dz))
drho_dz = grad_z(self.rhoz, self.z, axis=0)
N2 = -GRAV * drho_dz
if not self.nondim:
N2 /= RHO0
return N2
def calc_buoyancy_h99(self, nonlinear=True):
"""
Use the Holloway et al 99 version of the eqn's
"""
dN2_dz = grad_z(self.N2, self.Z, axis=0)
# Linear term
b = self.B[np.newaxis, :] * self.phi_1 * self.N2
#alpha = self.r10/(2*self.c1) ??
#alpha = -2*self.c1*self.r10
alpha = self.Alpha
# nonlinear terms
if nonlinear:
b -= alpha / (
2 * self.c1) * self.B[np.newaxis, :] * self.phi_1 * self.N2
b -= 0.5 * dN2_dz * self.B[np.newaxis, :]**2. * self.phi_1**2.
# Cubic nonlinearity
#b += self.c1*self.B[:,np.newaxis]**2. *self.N2 * self.T10
return b.T
def calc_N2(self):
drho_dz = grad_z(self.rhoZ, self.Z, axis=0)
return -GRAV * drho_dz / RHO0