def pv1_calc(v,b,x,z,w = None):
"""pv1_calc(dgl) calculates pv1 from vz and b_x"""
zlen = len(z)
vz = n2_calc(v,z) #This is below the v-point
vz = 0.5*(np.roll(vz,1,axis=1) + vz) #This is at the lower-left cell corner
bx = mit.ddx(b,x) #This is on u-points
bx = 0.5*(bx[:,:,0:zlen-1] + bx[:,:,1:zlen]) #This is below u-points
bx = 0.5*(np.roll(bx,1,0) + bx) #This is at the lower-left cell corner
w_exists = isinstance(w, np.ndarray)
if not w_exists:
pv1 = (-vz)*bx
else:
wy = mit.ddy(w,y) #This is below tracer points
wy = mit.four_cell_average(wy) #This is at the lower-left cell corner
pv1 = (wy-vz)*bx
return pv1
def pv2_calc(u,b,y,z,w = None):
"""pv2(dgl) calculates pv2 from uz and b_y"""
zlen = len(z)
uz = n2_calc(u,z) #This is below u-points
uz = 0.5*(np.roll(uz,1,0) + uz) #This is at the lower-left cell corner
by = mit.ddy(b,y) #This is at v-points
by = 0.5*(by[:,:,0:zlen-1] + by[:,:,1:zlen]) #This is below v-points
by = 0.5*(np.roll(by,1,1) + by) #This is at the lower-left cell corner
w_exists = isinstance(w, np.ndarray)
if not w_exists:
pv2 = (uz)*by
else:
wx = mit.ddx(w,x) #This is below the lower-left hand corner
pv2 = (uz-wx)*by
return pv2
def rib_calc(b,f,x,y,z):
"""rib_calc(b,f,xy,,z) caclulate the balanced Richardson number fN^2 |/nabla b|^2/f"""
zlen = len(z)
n2 = n2p(b,z) #This is at the lower-left cell corner
bx = mit.ddx(b,x) #This is on u-points
bx = 0.5*(bx[:,:,0:zlen-1] + bx[:,:,1:zlen]) #This is below u-points
bx = 0.5*(np.roll(bx,1,0) + bx) #This is at the lower-left cell corner
by = mit.ddy(b,y) #This is at v-points
by = 0.5*(by[:,:,0:zlen-1] + by[:,:,1:zlen]) #This is below v-points
by = 0.5*(np.roll(by,1,1) + by) #This is at the lower-left cell corner
#import matplotlib.pyplot as plt
#fig, ax = plt.subplots()
#cm = ax.pcolormesh(n2[:,0,:])
#cbar = plt.colorbar(cm)
plt.show()
grad_b_squared = bx**2 + by**2
rib = (f**2) * n2/grad_b_squared
return rib
