conatus.expert.parallel_shear_flow

conatus.expert.parallel_shear_flow(U, *, kx, kz, Re, walls, bounds=(-1.0, 1.0))

Linearized Navier–Stokes around U(y) e_x, mode e^{i(kx x + kz z)}, primitive variables.

dt u = (Δ/Re − i kx U) u − U’ v − i kx p dt v = (Δ/Re − i kx U) v − ∂y p dt w = (Δ/Re − i kx U) w − i kz p, 0 = i kx u + ∂y v + i kz w,

Δ = ∂y² − kx² − kz². U is a sympy expression in conatus.nonmodal.Y (real). walls is mandatory (no default); only “no-slip” (u = v = w = 0 at both walls) is implemented. Energy: ½ ∫ (|u|² + |v|² + |w|²) dy (weights 1). kz = 0 keeps w (it decouples: Squire); the reduction is not applied silently.

Parameters:

• kx (float)

• kz (float)

• Re (float)

• walls (str)

• bounds (tuple[float, float])

Return type:

ModalSystem