def test_depth_kwarg(self):
nz = 100
zN2 = 0.5*nz**-1 + np.arange(nz, dtype=np.float64)/nz
zU = 0.5*nz**-1 + np.arange(nz+1, dtype=np.float64)/nz
N2 = np.full(nz, 1.)
f0 = 1.
#beta = 1e-6
beta = 0.
Nx = 1
Ny = 1
dx = .1
dy = .1
k = fft.fftshift( fft.fftfreq(Nx, dx) )
l = fft.fftshift( fft.fftfreq(Ny, dy) )
ubar = np.zeros(nz+1)
vbar = np.zeros(nz+1)
etax = np.zeros(2)
etay = np.zeros(2)
with self.assertRaises(ValueError):
z, growth_rate, vertical_modes = modes.instability_analysis_from_N2_profile(
zN2, N2, f0, beta, k, l, zU, ubar, vbar, etax, etay, depth=zN2[-5]
)
# no error expected
z, growth_rate, vertical_mode = modes.instability_analysis_from_N2_profile(
zN2, N2, f0, beta, k, l, zU, ubar, vbar, etax, etay, depth=1.1
)
def test_Eady(self, atol=5e-2, nz=20, Ah=0.):
""" Eady setup
"""
###########
# prepare parameters for Eady
###########
nz = nz
zin = np.arange(nz+1, dtype=np.float64)/nz
N2 = np.full(nz, 1.)
f0 = 1.
beta = 0.
Nx = 10
Ny = 1
dx = 1e-1
dy = 1e-1
k = fft.fftshift( fft.fftfreq(Nx, dx) )
l = fft.fftshift( fft.fftfreq(Ny, dy) )
vbar = np.zeros(nz+1)
ubar = zin
etax = np.zeros(2)
etay = np.zeros(2)
z, growth_rate, vertical_modes = \
modes.instability_analysis_from_N2_profile(
.5*(zin[1:]+zin[:-1]), N2, f0, beta, k, l,
zin, ubar, vbar, etax, etay, depth=1., sort='LI', num=2
)
self.assertEqual(nz+1, vertical_modes.shape[0],
msg='modes array must be in the right shape')
self.assertTrue(np.all( np.diff(
growth_rate.reshape((growth_rate.shape[0], len(k)*len(l))).imag.max(axis=1) ) <= 0.),
msg='imaginary part of modes should be descending')
mode_amplitude1 = (np.absolute(vertical_modes[:, 0])**2).sum(axis=0)
self.assertTrue(np.allclose(1., mode_amplitude1),
msg='mode1 should be normalized to amplitude of 1 at all horizontal wavenumber points')
mode_amplitude2 = (np.absolute(vertical_modes[:, 1])**2).sum(axis=0)
self.assertTrue(np.allclose(1., mode_amplitude2),
msg='mode2 should be normalized to amplitude of 1 at all horizontal wavenumber points')
#########
# Analytical solution for Eady growth rate
#########
growthEady = np.zeros(len(k))
for i in range(len(k)):
if (k[i]==0) or ((np.tanh(.5*k[i])**-1 - .5*k[i]) * (.5*k[i] - np.tanh(.5*k[i])) < 0):
growthEady[i] = 0.
else:
growthEady[i] = ubar.max() * np.sqrt( (np.tanh(.5*k[i])**-1 - .5*k[i]) * (.5*k[i] - np.tanh(.5*k[i])) )
self.assertTrue( np.allclose(growth_rate.imag[0, 0, :], growthEady, atol=atol),
msg='The numerical growth rates should be close to the analytical Eady solution' )
def test_depth_kwarg(self):
nz = 100
zN2 = 0.5 * nz**-1 + np.arange(nz, dtype=np.float64) / nz
zU = 0.5 * nz**-1 + np.arange(nz + 1, dtype=np.float64) / nz
N2 = np.full(nz, 1.)
f0 = 1.
#beta = 1e-6
beta = 0.
Nx = 1
Ny = 1
dx = .1
dy = .1
k = fft.fftshift(fft.fftfreq(Nx, dx))
l = fft.fftshift(fft.fftfreq(Ny, dy))
ubar = np.zeros(nz + 1)
vbar = np.zeros(nz + 1)
etax = np.zeros(2)
etay = np.zeros(2)
with self.assertRaises(ValueError):
z, growth_rate, vertical_modes = modes.instability_analysis_from_N2_profile(
zN2,
N2,
f0,
beta,
k,
l,
zU,
ubar,
vbar,
etax,
etay,
depth=zN2[-5])
# no error expected
z, growth_rate, vertical_mode = modes.instability_analysis_from_N2_profile(
zN2, N2, f0, beta, k, l, zU, ubar, vbar, etax, etay, depth=1.1)
def test_OCCA_GulfStream(self, atol=1e-8):
""" Actual profiles in the Gulf Stream region
(@ 39.5N, 299.5E)
"""
###########
# prepare parameters for Gulf Stream region in OCCA
###########
z_u = np.array([5.00000000e+00, 1.50000000e+01, 2.50000000e+01,
3.50000000e+01, 4.50000000e+01, 5.50000000e+01,
6.50000000e+01, 7.50050049e+01, 8.50250015e+01,
9.50950012e+01, 1.05309998e+02, 1.15870003e+02,
1.27150002e+02, 1.39739990e+02, 1.54470001e+02,
1.72399994e+02, 1.94735001e+02, 2.22710007e+02,
2.57470001e+02, 2.99929993e+02, 3.50679993e+02,
4.09929993e+02, 4.77470001e+02, 5.52710022e+02,
6.34735046e+02, 7.22400024e+02, 8.14470093e+02,
9.09740112e+02, 1.00715503e+03, 1.10590503e+03,
1.20553503e+03, 1.30620508e+03, 1.40914990e+03,
1.51709497e+03, 1.63417480e+03, 1.76513477e+03,
1.91414990e+03, 2.08403491e+03, 2.27622510e+03,
2.49125000e+03, 2.72925000e+03, 2.99025000e+03,
3.27425000e+03, 3.58125000e+03, 3.91125000e+03,
4.26425000e+03, 4.64025000e+03, 5.03925000e+03,
5.46125000e+03, 5.90625000e+03])
z_N2 = -np.array([-10.00006115, -20.00006114, -30.00006113, -40.00006112,
-50.0000611 , -60.00006109, -70.00256358, -80.01506451,
-90.06006328, -100.20256308, -110.5900682 , -121.51007976,
-133.44509256, -147.10512803, -163.43519352, -183.5678012 ,
-208.72298023, -240.09073926, -278.70109317, -325.30655719,
-380.30712264, -443.70276088, -515.09343642, -593.72659767,
-678.57216844, -768.44015906, -862.11055267, -958.45325725,
-1056.53586028, -1155.72595435, -1255.87608991, -1357.68378579,
-1463.12934261, -1575.64299213, -1699.66489761, -1839.65538686,
-1999.10931291, -2180.15155508, -2383.76440293, -2610.28273438,
-2859.78914881, -3132.29607118, -3427.80347989, -3746.3113517 ,
-4087.81966191, -4452.32838443, -4839.83749199, -5250.34695635,
-5683.85674858])
ubar = np.array([0.24113144, 0.20566152, 0.18566666, 0.17763813, 0.17248898,
0.16799432, 0.16402273, 0.16024273, 0.15672079, 0.1532983 ,
0.15058691, 0.1480111 , 0.14513075, 0.14221466, 0.13825534,
0.13390785, 0.12829159, 0.12135932, 0.11275966, 0.10259634,
0.09075638, 0.07769765, 0.06402871, 0.05062123, 0.0384005 ,
0.02791209, 0.01922886, 0.01237531, 0.00755318, 0.00470483,
0.00328818, 0.00261901, 0.00221545, 0.00182732, 0.0013118 ,
0.00058111, -0.00035143, -0.0013624 , -0.00230507, -0.00308389,
-0.00365073, -0.00393951, -0.00386523, -0.00344036, -0.00277483,
-0.00189117, -0.00060206, 0.00060187, np.nan, np.nan])
vbar = np.array([0.03732778, 0.03306238, 0.03844519, 0.04393799, 0.04580961,
0.04673327, 0.04731352, 0.04768672, 0.04787091, 0.04791058,
0.0476704 , 0.04725287, 0.04666282, 0.04587267, 0.04479391,
0.04350807, 0.04190299, 0.03983596, 0.03736874, 0.03421749,
0.03057165, 0.02645037, 0.02181544, 0.01715759, 0.01278938,
0.00886511, 0.00544434, 0.00260065, 0.00052863, -0.00065227,
-0.00111283, -0.00120176, -0.00119863, -0.00122544, -0.00130761,
-0.00143906, -0.00161413, -0.00183596, -0.00210659, -0.00240779,
-0.002703 , -0.00296008, -0.00314709, -0.00320451, -0.00309561,
-0.0028392 , -0.00253795, 0. , np.nan, np.nan])
N2 = np.array([4.49013733e-05, 1.32619531e-04, 1.67213349e-04,
1.39980381e-04, 1.08620176e-04, 8.89353316e-05,
7.59696940e-05, 6.85660114e-05, 6.13053056e-05,
4.96623307e-05, 4.26153730e-05, 3.83933836e-05,
3.33244718e-05, 3.14573673e-05, 2.74780120e-05,
2.50869570e-05, 2.35907064e-05, 2.26047540e-05,
2.06309696e-05, 1.93499569e-05, 1.85802260e-05,
1.73887368e-05, 1.49995125e-05, 1.25945779e-05,
1.06210281e-05, 9.69791903e-06, 9.18845407e-06,
7.56655382e-06, 5.00383224e-06, 2.83633215e-06,
1.67170878e-06, 1.19350982e-06, 9.87252978e-07,
9.54096555e-07, 1.05979705e-06, 1.18957478e-06,
1.23432375e-06, 1.22190029e-06, 1.20084648e-06,
1.18287498e-06, 1.14801849e-06, 1.08643614e-06,
9.36511867e-07, 6.17342678e-07, 3.35507108e-07,
3.19646379e-07, 2.60733349e-07, np.nan,
np.nan])
Rd = 25787.38588424
f0 = 9.27671062527e-05
beta = 1.76637107718e-11
Nx = 100; dx = 4e3
k = np.array([-1.88495559e-04, -1.72787596e-04, -1.57079633e-04, -1.41371669e-04,
-1.25663706e-04, -1.09955743e-04, -9.42477796e-05, -7.85398163e-05,
-6.28318531e-05, -4.71238898e-05, -3.14159265e-05, -1.57079633e-05])
l = np.array([0.])
etax = np.zeros(2)
etay = np.zeros(2)
z, growth_rate, vertical_modes = \
modes.instability_analysis_from_N2_profile(
z_N2, N2, f0, beta, k, l,
z_u, ubar, vbar, etax, etay, num=2
)
self.assertEqual(len(z), vertical_modes.shape[0],
msg='modes array must be in the right shape')
self.assertTrue(np.all( np.diff(
growth_rate.reshape((growth_rate.shape[0],
len(k)*len(l))).imag.max(axis=1) ) <= 0.),
msg='imaginary part of modes should be descending')
mode_amplitude1 = (np.absolute(vertical_modes[:, 0])**2).sum(axis=0)
self.assertTrue(np.allclose(1., mode_amplitude1),
msg='mode1 should be normalized to amplitude of 1 at all horizontal wavenumber points')
mode_amplitude2 = (np.absolute(vertical_modes[:, 1])**2).sum(axis=0)
self.assertTrue(np.allclose(1., mode_amplitude2),
msg='mode2 should be normalized to amplitude of 1 at all horizontal wavenumber points')
##########
# Row corresponding to l=0 of growth mode (Ah=0)
##########
w_sol = np.array([1.04641026e-06, 8.55850224e-07, 6.56131690e-07, 4.40205651e-07,
2.22218418e-07, 1.07589996e-07, 9.46591756e-08, 4.64407815e-08,
1.29096295e-07, 6.74206451e-08, 5.74783413e-07, 6.86202530e-08])
self.assertTrue( np.allclose(growth_rate.imag[0, 0], w_sol, atol=atol),
msg='The OCCA numerical growth rates should be close to the solution with Ah=0' )
z, growth_rate, vertical_modes = \
modes.instability_analysis_from_N2_profile(
z_N2, N2, f0, beta, k, l,
z_u, ubar, vbar, etax, etay, Ah=1e1, num=2
)
##########
# Row corresponding to l=0 of growth mode (Ah=10.)
##########
w_sol = np.array([3.15410778e-06, 2.82584613e-06, 2.47671069e-06, 2.10243465e-06,
1.69802277e-06, 1.26121608e-06, 8.09682819e-07, 4.13752221e-07,
1.43811161e-07, 7.84288795e-08, 5.93310629e-07, 6.33544320e-08])
self.assertTrue( np.allclose(growth_rate.imag[0, 0], w_sol, atol=atol),
msg='The OCCA numerical growth rates should be close to the solution with Ah=10' )
def test_linear_instability_args(self):
nz = 10
N2 = np.zeros(nz)
depth = np.arange(nz)
ubar = 1e-2 * np.ones(nz+1)
vbar = 1e-2 * np.ones(nz+1)
beta = 1e-6
etax = np.array([1e-1*beta, beta])
etay = np.array([1e-1*beta, beta])
Nx = 1
Ny = 1
dx = .1
dy = .1
k = fft.fftshift( fft.fftfreq(Nx, dx) )
l = fft.fftshift( fft.fftfreq(Ny, dy) )
###########
# check for unequal lengths of arrays
###########
with self.assertRaises(ValueError):
_, _, _ = modes.instability_analysis_from_N2_profile(
depth[1:], N2, 1., beta, k, l, depth, ubar, vbar, etax, etay
)
with self.assertRaises(ValueError):
_, _, _ = modes.instability_analysis_from_N2_profile(
depth, N2[1:], 1., beta, k ,l, depth, ubar, vbar, etax, etay
)
with self.assertRaises(ValueError):
_, _, _ = modes.instability_analysis_from_N2_profile(
-depth, N2, 1., beta, k ,l, np.append(depth, float(nz+1)), ubar, vbar, etax, etay
)
with self.assertRaises(ValueError):
_, _, _ = modes.instability_analysis_from_N2_profile(
depth, N2[1:], 1., beta, k ,l, -np.append(depth, float(nz+1)), ubar, vbar, etax, etay
)
depth_non_monotonic = depth
depth_non_monotonic[0] = 5
depth_non_monotonic[1] = 5
# check for non-monotonic profile
Nx = 50
Ny = 50
dx = 1e-1
dy = 1e-1
k = fft.fftshift( fft.fftfreq(Nx, dx) )
l = fft.fftshift( fft.fftfreq(Ny, dy) )
with self.assertRaises(ValueError) as cm:
_, _, _ = modes.instability_analysis_from_N2_profile(
depth_non_monotonic[1:], N2, 1., beta, k, l, depth, ubar, vbar, etax, etay
)
N2 = np.append(N2, [1.,1.]) #N2 has longer length than u
with self.assertRaises(ValueError):
_, _, _ = modes.instability_analysis_from_N2_profile(
depth, N2, 1., beta, k ,l, depth, ubar, vbar, etax, etay
)
N2 = np.zeros(nz)
depth = np.arange(nz+1)
ubar = np.zeros(nz+1)
vbar = np.zeros(nz+1)
etax = np.zeros(2)
etay = np.zeros(2)
beta = 0.
with warnings.catch_warnings(record=True) as w:
# Trigger a warning
_, _, _ = modes.instability_analysis_from_N2_profile(
depth[:-1], N2, 0., beta, k ,l, depth, ubar, vbar, etax, etay
)
# Verify some things
self.assertTrue( issubclass(w[-1].category, RuntimeWarning) )
self.assertEqual("The matrix is ill-conditioned or singular", str(w[-1].message))
def test_OCCA_GulfStream(self, atol=1e-8):
""" Actual profiles in the Gulf Stream region
(@ 39.5N, 299.5E)
"""
###########
# prepare parameters for Gulf Stream region in OCCA
###########
z_u = np.array([
5.00000000e+00, 1.50000000e+01, 2.50000000e+01, 3.50000000e+01,
4.50000000e+01, 5.50000000e+01, 6.50000000e+01, 7.50050049e+01,
8.50250015e+01, 9.50950012e+01, 1.05309998e+02, 1.15870003e+02,
1.27150002e+02, 1.39739990e+02, 1.54470001e+02, 1.72399994e+02,
1.94735001e+02, 2.22710007e+02, 2.57470001e+02, 2.99929993e+02,
3.50679993e+02, 4.09929993e+02, 4.77470001e+02, 5.52710022e+02,
6.34735046e+02, 7.22400024e+02, 8.14470093e+02, 9.09740112e+02,
1.00715503e+03, 1.10590503e+03, 1.20553503e+03, 1.30620508e+03,
1.40914990e+03, 1.51709497e+03, 1.63417480e+03, 1.76513477e+03,
1.91414990e+03, 2.08403491e+03, 2.27622510e+03, 2.49125000e+03,
2.72925000e+03, 2.99025000e+03, 3.27425000e+03, 3.58125000e+03,
3.91125000e+03, 4.26425000e+03, 4.64025000e+03, 5.03925000e+03,
5.46125000e+03, 5.90625000e+03
])
z_N2 = -np.array([
-10.00006115, -20.00006114, -30.00006113, -40.00006112,
-50.0000611, -60.00006109, -70.00256358, -80.01506451,
-90.06006328, -100.20256308, -110.5900682, -121.51007976,
-133.44509256, -147.10512803, -163.43519352, -183.5678012,
-208.72298023, -240.09073926, -278.70109317, -325.30655719,
-380.30712264, -443.70276088, -515.09343642, -593.72659767,
-678.57216844, -768.44015906, -862.11055267, -958.45325725,
-1056.53586028, -1155.72595435, -1255.87608991, -1357.68378579,
-1463.12934261, -1575.64299213, -1699.66489761, -1839.65538686,
-1999.10931291, -2180.15155508, -2383.76440293, -2610.28273438,
-2859.78914881, -3132.29607118, -3427.80347989, -3746.3113517,
-4087.81966191, -4452.32838443, -4839.83749199, -5250.34695635,
-5683.85674858
])
ubar = np.array([
0.24113144, 0.20566152, 0.18566666, 0.17763813, 0.17248898,
0.16799432, 0.16402273, 0.16024273, 0.15672079, 0.1532983,
0.15058691, 0.1480111, 0.14513075, 0.14221466, 0.13825534,
0.13390785, 0.12829159, 0.12135932, 0.11275966, 0.10259634,
0.09075638, 0.07769765, 0.06402871, 0.05062123, 0.0384005,
0.02791209, 0.01922886, 0.01237531, 0.00755318, 0.00470483,
0.00328818, 0.00261901, 0.00221545, 0.00182732, 0.0013118,
0.00058111, -0.00035143, -0.0013624, -0.00230507, -0.00308389,
-0.00365073, -0.00393951, -0.00386523, -0.00344036, -0.00277483,
-0.00189117, -0.00060206, 0.00060187, np.nan, np.nan
])
vbar = np.array([
0.03732778, 0.03306238, 0.03844519, 0.04393799, 0.04580961,
0.04673327, 0.04731352, 0.04768672, 0.04787091, 0.04791058,
0.0476704, 0.04725287, 0.04666282, 0.04587267, 0.04479391,
0.04350807, 0.04190299, 0.03983596, 0.03736874, 0.03421749,
0.03057165, 0.02645037, 0.02181544, 0.01715759, 0.01278938,
0.00886511, 0.00544434, 0.00260065, 0.00052863, -0.00065227,
-0.00111283, -0.00120176, -0.00119863, -0.00122544, -0.00130761,
-0.00143906, -0.00161413, -0.00183596, -0.00210659, -0.00240779,
-0.002703, -0.00296008, -0.00314709, -0.00320451, -0.00309561,
-0.0028392, -0.00253795, 0., np.nan, np.nan
])
N2 = np.array([
4.49013733e-05, 1.32619531e-04, 1.67213349e-04, 1.39980381e-04,
1.08620176e-04, 8.89353316e-05, 7.59696940e-05, 6.85660114e-05,
6.13053056e-05, 4.96623307e-05, 4.26153730e-05, 3.83933836e-05,
3.33244718e-05, 3.14573673e-05, 2.74780120e-05, 2.50869570e-05,
2.35907064e-05, 2.26047540e-05, 2.06309696e-05, 1.93499569e-05,
1.85802260e-05, 1.73887368e-05, 1.49995125e-05, 1.25945779e-05,
1.06210281e-05, 9.69791903e-06, 9.18845407e-06, 7.56655382e-06,
5.00383224e-06, 2.83633215e-06, 1.67170878e-06, 1.19350982e-06,
9.87252978e-07, 9.54096555e-07, 1.05979705e-06, 1.18957478e-06,
1.23432375e-06, 1.22190029e-06, 1.20084648e-06, 1.18287498e-06,
1.14801849e-06, 1.08643614e-06, 9.36511867e-07, 6.17342678e-07,
3.35507108e-07, 3.19646379e-07, 2.60733349e-07, np.nan, np.nan
])
Rd = 25787.38588424
f0 = 9.27671062527e-05
beta = 1.76637107718e-11
Nx = 100
dx = 4e3
k = np.array([
-1.88495559e-04, -1.72787596e-04, -1.57079633e-04, -1.41371669e-04,
-1.25663706e-04, -1.09955743e-04, -9.42477796e-05, -7.85398163e-05,
-6.28318531e-05, -4.71238898e-05, -3.14159265e-05, -1.57079633e-05
])
l = np.array([0.])
etax = np.zeros(2)
etay = np.zeros(2)
z, growth_rate, vertical_modes = \
modes.instability_analysis_from_N2_profile(
z_N2, N2, f0, beta, k, l,
z_u, ubar, vbar, etax, etay, num=2
)
self.assertEqual(len(z),
vertical_modes.shape[0],
msg='modes array must be in the right shape')
self.assertTrue(np.all(
np.diff(
growth_rate.reshape((growth_rate.shape[0], len(k) *
len(l))).imag.max(axis=1)) <= 0.),
msg='imaginary part of modes should be descending')
mode_amplitude1 = (np.absolute(vertical_modes[:, 0])**2).sum(axis=0)
self.assertTrue(
np.allclose(1., mode_amplitude1),
msg=
'mode1 should be normalized to amplitude of 1 at all horizontal wavenumber points'
)
mode_amplitude2 = (np.absolute(vertical_modes[:, 1])**2).sum(axis=0)
self.assertTrue(
np.allclose(1., mode_amplitude2),
msg=
'mode2 should be normalized to amplitude of 1 at all horizontal wavenumber points'
)
##########
# Row corresponding to l=0 of growth mode (Ah=0)
##########
w_sol = np.array([
1.04641026e-06, 8.55850224e-07, 6.56131690e-07, 4.40205651e-07,
2.22218418e-07, 1.07589996e-07, 9.46591756e-08, 4.64407815e-08,
1.29096295e-07, 6.74206451e-08, 5.74783413e-07, 6.86202530e-08
])
self.assertTrue(
np.allclose(growth_rate.imag[0, 0], w_sol, atol=atol),
msg=
'The OCCA numerical growth rates should be close to the solution with Ah=0'
)
z, growth_rate, vertical_modes = \
modes.instability_analysis_from_N2_profile(
z_N2, N2, f0, beta, k, l,
z_u, ubar, vbar, etax, etay, Ah=1e1, num=2
)
##########
# Row corresponding to l=0 of growth mode (Ah=10.)
##########
w_sol = np.array([
3.15410778e-06, 2.82584613e-06, 2.47671069e-06, 2.10243465e-06,
1.69802277e-06, 1.26121608e-06, 8.09682819e-07, 4.13752221e-07,
1.43811161e-07, 7.84288795e-08, 5.93310629e-07, 6.33544320e-08
])
self.assertTrue(
np.allclose(growth_rate.imag[0, 0], w_sol, atol=atol),
msg=
'The OCCA numerical growth rates should be close to the solution with Ah=10'
)
def test_Eady(self, atol=5e-2, nz=20, Ah=0.):
""" Eady setup
"""
###########
# prepare parameters for Eady
###########
nz = nz
zin = np.arange(nz + 1, dtype=np.float64) / nz
N2 = np.full(nz, 1.)
f0 = 1.
beta = 0.
Nx = 10
Ny = 1
dx = 1e-1
dy = 1e-1
k = fft.fftshift(fft.fftfreq(Nx, dx))
l = fft.fftshift(fft.fftfreq(Ny, dy))
vbar = np.zeros(nz + 1)
ubar = zin
etax = np.zeros(2)
etay = np.zeros(2)
z, growth_rate, vertical_modes = \
modes.instability_analysis_from_N2_profile(
.5*(zin[1:]+zin[:-1]), N2, f0, beta, k, l,
zin, ubar, vbar, etax, etay, depth=1., sort='LI', num=2
)
self.assertEqual(nz + 1,
vertical_modes.shape[0],
msg='modes array must be in the right shape')
self.assertTrue(np.all(
np.diff(
growth_rate.reshape((growth_rate.shape[0], len(k) *
len(l))).imag.max(axis=1)) <= 0.),
msg='imaginary part of modes should be descending')
mode_amplitude1 = (np.absolute(vertical_modes[:, 0])**2).sum(axis=0)
self.assertTrue(
np.allclose(1., mode_amplitude1),
msg=
'mode1 should be normalized to amplitude of 1 at all horizontal wavenumber points'
)
mode_amplitude2 = (np.absolute(vertical_modes[:, 1])**2).sum(axis=0)
self.assertTrue(
np.allclose(1., mode_amplitude2),
msg=
'mode2 should be normalized to amplitude of 1 at all horizontal wavenumber points'
)
#########
# Analytical solution for Eady growth rate
#########
growthEady = np.zeros(len(k))
for i in range(len(k)):
if (k[i] == 0) or ((np.tanh(.5 * k[i])**-1 - .5 * k[i]) *
(.5 * k[i] - np.tanh(.5 * k[i])) < 0):
growthEady[i] = 0.
else:
growthEady[i] = ubar.max() * np.sqrt(
(np.tanh(.5 * k[i])**-1 - .5 * k[i]) *
(.5 * k[i] - np.tanh(.5 * k[i])))
self.assertTrue(
np.allclose(growth_rate.imag[0, 0, :], growthEady, atol=atol),
msg=
'The numerical growth rates should be close to the analytical Eady solution'
)
def test_linear_instability_args(self):
nz = 10
N2 = np.zeros(nz)
depth = np.arange(nz)
ubar = 1e-2 * np.ones(nz + 1)
vbar = 1e-2 * np.ones(nz + 1)
beta = 1e-6
etax = np.array([1e-1 * beta, beta])
etay = np.array([1e-1 * beta, beta])
Nx = 1
Ny = 1
dx = .1
dy = .1
k = fft.fftshift(fft.fftfreq(Nx, dx))
l = fft.fftshift(fft.fftfreq(Ny, dy))
###########
# check for unequal lengths of arrays
###########
with self.assertRaises(ValueError):
_, _, _ = modes.instability_analysis_from_N2_profile(
depth[1:], N2, 1., beta, k, l, depth, ubar, vbar, etax, etay)
with self.assertRaises(ValueError):
_, _, _ = modes.instability_analysis_from_N2_profile(
depth, N2[1:], 1., beta, k, l, depth, ubar, vbar, etax, etay)
with self.assertRaises(ValueError):
_, _, _ = modes.instability_analysis_from_N2_profile(
-depth, N2, 1., beta, k, l, np.append(depth, float(nz + 1)),
ubar, vbar, etax, etay)
with self.assertRaises(ValueError):
_, _, _ = modes.instability_analysis_from_N2_profile(
depth, N2[1:], 1., beta, k, l,
-np.append(depth, float(nz + 1)), ubar, vbar, etax, etay)
depth_non_monotonic = depth
depth_non_monotonic[0] = 5
depth_non_monotonic[1] = 5
# check for non-monotonic profile
Nx = 50
Ny = 50
dx = 1e-1
dy = 1e-1
k = fft.fftshift(fft.fftfreq(Nx, dx))
l = fft.fftshift(fft.fftfreq(Ny, dy))
with self.assertRaises(ValueError) as cm:
_, _, _ = modes.instability_analysis_from_N2_profile(
depth_non_monotonic[1:], N2, 1., beta, k, l, depth, ubar, vbar,
etax, etay)
N2 = np.append(N2, [1., 1.]) #N2 has longer length than u
with self.assertRaises(ValueError):
_, _, _ = modes.instability_analysis_from_N2_profile(
depth, N2, 1., beta, k, l, depth, ubar, vbar, etax, etay)
N2 = np.zeros(nz)
depth = np.arange(nz + 1)
ubar = np.zeros(nz + 1)
vbar = np.zeros(nz + 1)
etax = np.zeros(2)
etay = np.zeros(2)
beta = 0.
with warnings.catch_warnings(record=True) as w:
# Trigger a warning
_, _, _ = modes.instability_analysis_from_N2_profile(
depth[:-1], N2, 0., beta, k, l, depth, ubar, vbar, etax, etay)
# Verify some things
self.assertTrue(issubclass(w[-1].category, RuntimeWarning))
self.assertEqual("The matrix is ill-conditioned or singular",
str(w[-1].message))
