  In chaotic systems, such as turbulent flows, the solutions to tangent and
adjoint equations exhibit an unbounded growth in their norms. This behavior
renders the instantaneous tangent and adjoint solutions unusable for
sensitivity analysis. The Lea-Allen-Haine ensemble sensitivity (ES) estimates
provide a way of computing meaningful sensitivities in chaotic systems by
utilizing tangent/adjoint solutions over short trajectories. In this paper, we
analyze the feasibility of ES computations under optimistic mathematical
assumptions on the flow dynamics. Furthermore, we estimate upper bounds on the
rate of convergence of the ES method in numerical simulations of turbulent
flow. Even at the optimistic upper bound, the ES method is computationally
intractable in each of the numerical examples considered.
