The Beavers--Joseph Interface Boundary Condition is Well Approximated by the Beavers--Joseph--Saffman--Jones Interface Boundary Condition

We prove that the difference between the solutions to the Stokes--Darcy system derived using the Beavers-Joseph or Beavers--Joseph--Saffman--Jones interfacial conditions is of the order of the Darcy number assuming the Reynolds number is below an explicit threshold value. Hence, the Beavers--Joseph--Saffman--Jones interface boundary condition is an excellent approximation of the classical Beavers-Joseph interface boundary condition in the physically important small Darcy number regime.