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float_advection_routines.py
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float_advection_routines.py
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# -*- coding: utf-8 -*-
"""
Created on Thu Dec 11 14:27:01 2014
Advection routines.
@author: jc3e13
"""
import numpy as np
from scipy.integrate import odeint
import gsw
import gravity_waves as gw
import utils
def U_const(z):
"""Constant velocity of 50 cm s-1."""
return 0.5
def U_shear(z):
"""Default shear of 20 cm s-1 over 1500 m."""
return 1.3333e-4*z + 5e-1
default_params = {
'Ufunc': U_const,
'f': gsw.f(-57.5),
'N': 1.8e-3,
'w_0': 0.17,
'Wf_pvals': np.polyfit([0., 0.06], [0.14, 0.12], 1),
'dt': 10.,
't_1': 15000.,
'x_0': 0.,
'y_0': 0.,
'z_0': -1500,
'print': False
}
def drdt(r, t, phi_0, Ufunc, Wf_pvals, k, l, m, om, N, f=0., phase_0=0.):
x = r[0]
y = r[1]
z = r[2]
Wf_g = Wf_pvals[0]
Wf_0 = Wf_pvals[1]
U = Ufunc(z)
dxdt = U + gw.u(x, y, z, t, phi_0, k, l, m, om, f=f, U=U, phase_0=phase_0)
dydt = gw.v(x, y, z, t, phi_0, k, l, m, om, f=f, U=U, phase_0=phase_0)
dzdt = (Wf_0 + gw.w(x, y, z, t, phi_0, k, l, m, om, N, U=U, phase_0=phase_0))/(1 - Wf_g)
return np.array([dxdt, dydt, dzdt])
def model_basic(phi_0, X, Y, Z, phase_0=0., oparams=default_params):
Ufunc = oparams['Ufunc']
f = oparams['f']
N = oparams['N']
# Float change in buoyancy with velocity.
Wf_pvals = oparams['Wf_pvals']
# Wave parameters
k = 2*np.pi/X
l = 2*np.pi/Y
m = 2*np.pi/Z
om = gw.omega(N, k, m, l, f)
args = (phi_0, Ufunc, Wf_pvals, k, l, m, om, N, f, phase_0)
# Integration parameters.
dt = oparams['dt']
t_0 = 0.
t_1 = oparams['t_1']
t = np.arange(t_0, t_1, dt)
# Initial conditions.
x_0 = oparams['x_0']
y_0 = oparams['y_0']
z_0 = oparams['z_0']
r_0 = np.array([x_0, y_0, z_0])
# This integrator calls FORTRAN odepack to solve the problem.
r = odeint(drdt, r_0, t, args)
uargs = (phi_0, Ufunc(r[:, 2]), k, l, m, om, N, f, phase_0)
u = gw.wave_vel(r, t, *uargs)
u[:, 0] += Ufunc(r[:, 2])
b = gw.buoy(r, t, *uargs)
return t, r, u, b
def model_leastsq(params, z, sub, var_name, oparams=default_params):
""" Return individual variables given by var_name.
Subtract data given by 'sub' to return residual.
"""
phi_0, X, Y, Z, phase_0 = params
__, r, u, b = model_basic(phi_0, X, Y, Z, phase_0, oparams)
u[:, 0] -= oparams['Ufunc'](r[:, 2])
# Variable to return.
var_dict = {'w': u[:, 2], 'u': u[:, 0], 'v': u[:, 1], 'b': b}
var = var_dict[var_name]
ivar = np.interp(z, r[:, 2], var)
return ivar - sub
def model_pymc(zf, phi_0, X, Y, Z, phase_0=0., bscale=250., oparams=default_params):
"""Return a stack of all velocity components and buoyancy."""
__, r, u, b = model_basic(phi_0, X, Y, Z, phase_0, oparams)
u[:, 0] -= oparams['Ufunc'](r[:, 2])
um = np.interp(zf, r[:, 2], u[:, 0])
vm = np.interp(zf, r[:, 2], u[:, 1])
wm = np.interp(zf, r[:, 2], u[:, 2])
bm = bscale*np.interp(zf, r[:, 2], b)
return np.hstack((um, vm, wm, bm))
def model_verbose(phi_0, X, Y, Z, phase_0=0., oparams=default_params):
"""Return loads and loads of info."""
t, r, u, b = model_basic(phi_0, X, Y, Z, phase_0, oparams)
Ufunc = oparams['Ufunc']
f = oparams['f']
N = oparams['N']
# Float change in buoyancy with velocity.
Wf_pvals = oparams['Wf_pvals']
# Wave parameters
w_0 = oparams['w_0']
k = 2*np.pi/X
l = 2*np.pi/Y
m = 2*np.pi/Z
om = gw.omega(N, k, m, l, f)
u_0 = gw.U_0(phi_0, k, l, om, f)
v_0 = gw.V_0(phi_0, k, l, om, f)
w_0 = gw.W_0(phi_0, m, om, N)
b_0 = gw.B_0(phi_0, m, om, N)
if oparams['print']:
print("N = {:1.2E} rad s-1.\n"
"om = {:1.2E} rad s-1.\n"
"u_0 = {:1.2E} m s-1.\n"
"v_0 = {:1.2E} m s-1.\n"
"w_0 = {:1.2E} m s-1.\n"
"phi_0 = {:1.2E} m2 s-2.\n"
"b_0 = {:1.2E} m s-2.\n"
"X = {:1.0f} m.\n"
"k = {:1.2E} rad m-1.\n"
"Y = {:1.0f} m.\n"
"l = {:1.2E} rad m-1.\n"
"Z = {:1.0f} m.\n"
"m = {:1.2E} rad m-1.\n"
"".format(N, om, u_0, v_0, w_0, phi_0, b_0, X, k, Y, l, Z, m))
output = utils.Bunch(Ufunc=Ufunc,
U=Ufunc(r[:, 2]),
f=f,
N=N,
Wf_pvals=Wf_pvals,
w_0=w_0,
k=k,
l=l,
m=m,
om=om,
phi_0=phi_0,
u_0=u_0,
v_0=v_0,
b_0=b_0,
t=t,
z_0=oparams['z_0'],
r=r,
u=u,
b=b,
oparams=oparams)
return output