A rigorous bound on the scaling of dissipation with velocity amplitude in flow past a sphere

Abstract

Abstract A rigorous bound on the energy dissipation in the flow around a sphere is derived analytically. The bound is allowed to depend on the viscosity of the fluid, the radius of the sphere, the free-stream velocity and the amplitude of the difference between the actual flow field and the irrotational flow around the sphere. The bound becomes asymptotically independent of viscosity as the Reynolds number tends to infinity. Provided that the velocity fluctuations are of the same order as the free-stream velocity, the scaling of the bound is consistent with a Reynolds-number-independent drag coefficient at high Reynolds numbers.