Scouring of granular beds by jet-driven axisymmetric turbulent cauldrons

We study a sustained, jet-driven, axisymmetric turbulent cauldron that scours a pothole in a cohesionless granular bed. We focus on the energetics of the turbulent cauldron and use dimensional analysis and similarity methods to derive (up to a multiplicative constant) a formula for the equilibrium depth of the pothole. To that end, we assume that the power of the jet is stationary and that under equilibrium conditions no air or granular material from the bed is entrained in the cauldron. The resulting formula contains a single similarity exponent, which we show can be determined via the phenomenological theory of turbulence. Our method of analysis may prove useful in developing a theoretical understanding of mine burial, bridge pier-induced erosion, and other applications in which a localized turbulent flow interacts with a granular bed.