conatus.problems.taylor_couette

conatus.problems.taylor_couette(*, Nphi, Nr, Nz, Lz, Re, eta, mu, dealias)[source]

Taylor–Couette flow between rotating cylinders: perturbation u of circular Couette flow U0 = V(r) e_phi, V = A r + B / r, incompressible Navier–Stokes, IVP:

dt(u) + U0.grad(u) + u.grad(U0) + grad(p) - lap(u)/Re = -u.grad(u),   div(u) = 0,
u = 0 at r = r_i and r = r_o (the wall motion is carried by U0).

Units: gap d = r_o - r_i = 1, inner wall speed Omega_i r_i = 1, Re = Omega_i r_i d / nu; radius ratio eta = r_i / r_o, rotation ratio mu = Omega_o / Omega_i. Bases: RealFourier(phi, Nphi) x AnnulusBasis(r, Nr, (r_i, r_o)) x ComplexFourier(z, Nz, (0, Lz)); two taus lifted in the derivative basis of order 2 (lam=2), the radial part of the second one also into continuity (dot(rvec, lift(t2, br, -1, lam=1)): the plain second-order form of tutorial t08 is singular in the group m = 0, k_z = 0); pressure gauge tp. ncc holds U0 and rvec = r e_r. The linearized pencil in a group (m, k) has the spectrum of taylor_couette_evp() (tests/problems/test_problems_cylinders.py).

Validation reference: linear onset, taylor_couette_evp(): eta = 0.5, outer cylinder at rest (mu = 0), axisymmetric modes: Re_c = 68.19 at k_c = 3.16 (Recktenwald, Luecke & Mueller 1993, Phys. Rev. E 48, 4444, Table I).

Parameters:

  • Nphi (int)

  • Nr (int)

  • Nz (int)

  • Lz (float)

  • Re (float)

  • eta (float)

  • mu (float)

  • dealias (float)

Return type:

Ready