conatus.problems.channel_evp¶
- conatus.problems.channel_evp(*, N, Re, alpha)[source]¶
Orr–Sommerfeld EVP of plane Poiseuille flow U = 1 - y^2 (2D modes).
Normal modes v(y) exp(i alpha (x - c t)) of the wall-normal velocity, eigenvalue the complex wave speed c (growth rate alpha Im c):
(D^2 - alpha^2)^2 v / (i alpha Re) - U (D^2 - alpha^2) v + U'' v + c (D^2 - alpha^2) v = 0, v = v' = 0 at y = -1, +1.
Units as in
channel()(h = 1, U_c = 1, Re = U_c h / nu). Chebyshev(y, N, (-1, 1)), dealias 1 (a linear problem has no product to dealias; the NCC U is exact at N >= 3).nccholds U; pass it to discretize. Spurious (tau) modes appear at large |c|: select the physical ones (|c| < 2, or a drift test between two N; tutorial t01).Validation reference: Orszag (1971), J. Fluid Mech. 50, 689, Table 3: at Re = 10000, alpha = 1, the least-stable mode is c = 0.23752649 + 0.00373967i; Re_c = 5772.22 at alpha_c = 1.02056 (tests/problems/test_problems_shear.py: c to 1e-8 at N = 64).
- Parameters:
N (int)
Re (float)
alpha (float)
- Return type: