Exact Beltrami flows in a spherical shell

Abstract Exact flows of an incompressible fluid satisfying the Beltrami equation inside a spherical shell are constructed in Cartesian coordinates terms elementary functions. Two scale-invariant equations defining two infinite series eigenvalues λ n and λ ̃ m ${\tilde {\lambda }}_{m}$ operator curl with nonpenetration boundary conditions on spheres derived. The corresponding eigenfields presented explicit form their symmetries investigated. Asymptotics at , m → ∞ obtained.