conatus.problems.rotating_shell_convection_evp

conatus.problems.rotating_shell_convection_evp(*, Nr, Lmax, m, eta, Ra, E, Pr)

Linear onset of rotating shell convection: normal modes exp(i m phi + s t) about the conduction state, equations and units of rotating_shell_convection() multiplied back by E:

E (s u - lap u) + 2 e_z x u + grad p - (Ra / r_o) T r e_r = 0,   div u = 0,
s T + u.grad(T0) - lap(T)/Pr = 0,   u = T = 0 at r_i and r_o.

Eigenvalue s in viscous units (Im s / (1/E) = drift frequency in units of Omega). Only the group m is meaningful: the phi basis is ComplexFourier(phi, 2|m| + 4) (structural: large enough to hold m); SphereBasis(theta, Lmax + 1), ShellBasis(r, Nr), dealias 1 (linear). Use plan.group(m); e_z couples all degrees l of one m.

Validation reference: eta = 0.35, E = 1e-3, Pr = 1: m_c = 4, Ra_c = 55.904299, omega_c = -0.0230918 Omega at (Nr, Lmax) = (32, 48) (run Skene & Tobias 2024 Table 1: 55.9, 4, -0.0231; Barik et al. 2023: 55.904296).

Parameters:

• Nr (int)

• Lmax (int)

• m (int)

• eta (float)

• Ra (float)

• E (float)

• Pr (float)

Return type:

Ready