  Many physical questions in fluid dynamics can be recast in terms of norm
constrained optimisation problems; which in-turn, can be further recast as
unconstrained problems on spherical manifolds. Due to the nonlinearities of the
governing PDEs, and the computational cost of performing optimal control on
such systems, improving the numerical convergence of the optimisation procedure
is crucial. Borrowing tools from the optimisation on manifolds community we
outline a numerically consistent, discrete formulation of the direct-adjoint
looping method accompanied by gradient descent and line-search algorithms with
global convergence guarantees. We numerically demonstrate the robustness of
this formulation on three example problems of relevance in fluid dynamics and
provide an accompanying library SphereManOpt
