def coth(x):
return cosh(x) / sinh(x)
# set theta_pert
def coth(x):
return cosh(x)/sinh(x)
def Z(z):
return Bu*((z/H)-0.5)
def n():
return Bu**(-1)*sqrt((Bu*0.5-tanh(Bu*0.5))*(coth(Bu*0.5)-Bu*0.5))
a = -4.5
Bu = 0.5
theta_exp = a*theta_surf/g*sqrt(Nsq)*(-(1.-Bu*0.5*coth(Bu*0.5))*sinh(Z(z))*cos(pi*(x-L)/L)
- n()*Bu*cosh(Z(z))*sin(pi*(x-L)/L))
theta_pert = Function(Vt).interpolate(theta_exp)
# set theta0
theta0.interpolate(theta_b + theta_pert)
# calculate hydrostatic Pi
piparams = {'pc_type': 'fieldsplit',
'pc_fieldsplit_type': 'schur',
'ksp_type': 'gmres',
'ksp_rtol': 1.e-8,
'ksp_atol': 1.e-8,
'ksp_max_it': 100,
'ksp_gmres_restart': 50,
'pc_fieldsplit_schur_fact_type': 'FULL',
return cosh(x) / sinh(x)
def Z(z):
return Bu * ((z / H) - 0.5)
def n():
return Bu**(-1) * sqrt(
(Bu * 0.5 - tanh(Bu * 0.5)) * (coth(Bu * 0.5) - Bu * 0.5))
a = -4.5
Bu = 0.5
b_exp = a * sqrt(Nsq) * (
-(1. - Bu * 0.5 * coth(Bu * 0.5)) * sinh(Z(z)) * cos(pi * (x - L) / L) -
n() * Bu * cosh(Z(z)) * sin(pi * (x - L) / L))
b_pert = Function(Vb).interpolate(b_exp)
# set total buoyancy
b0.project(b_b + b_pert)
# calculate hydrostatic pressure
p_b = Function(Vp)
incompressible_hydrostatic_balance(state, b_b, p_b)
incompressible_hydrostatic_balance(state, b0, p0)
# set x component of velocity
dbdy = parameters.dbdy
u = -dbdy / f * (z - H / 2)
# buoyancy perturbation
def coth(x):
return cosh(x)/sinh(x)
def Z(z):
return Bu*((z/H)-0.5)
def n():
return Bu**(-1)*sqrt((Bu*0.5-tanh(Bu*0.5))*(coth(Bu*0.5)-Bu*0.5))
a = -4.5
Bu = 0.5
b_exp = a*sqrt(Nsq)*(-(1.-Bu*0.5*coth(Bu*0.5))*sinh(Z(z))*cos(pi*(x-L)/L)
- n()*Bu*cosh(Z(z))*sin(pi*(x-L)/L))
b_pert = Function(Vb).interpolate(b_exp)
# set total buoyancy
b0.project(b_b + b_pert)
# calculate hydrostatic pressure
p_b = Function(Vp)
incompressible_hydrostatic_balance(state, b_b, p_b)
incompressible_hydrostatic_balance(state, b0, p0)
# set x component of velocity
dbdy = parameters.dbdy
u = -dbdy/f*(z-H/2)