Influence of lock aspect ratio upon the evolution of an axisymmetric intrusion

Through theory and numerical simulations in an axisymmetric geometry, we examine evolution of a symmetric intrusion released from a cylindrical lock in stratified fluid as it depends upon the ambient interface thickness, h, and the lock aspect ratio Rc/H, in which Rc is the lock radius and H is the ambient depth. Whereas self-similarity and shallow-water theory predicts that intrusions, once established, should decelerate shortly after release from the lock, we find that the intrusions rapidly accelerate and then enter a constant-speed regime that extend between 2Rc and 5Rc from the gate, depending upon the relative interface thickness δh ≡ h/H. This result is consistent with previously performed laboratory experiments. Scaling arguments predict that the distance, Ra, over which the lock fluid first accelerates increases linearly with Rc if Rc/H 1 and Ra/H approaches a constant for high aspect ratios. Likewise in the constant-speed regime, the speed relative to the rectilinear speed, U/U∞, increases linearly with Rc/H if the aspect ratio is small and is of order unity if Rc/H 1. Beyond the constant-speed regime, the intrusion front decelerates rapidly, with powerlaw exponent as large as 0.7 if the relative ambient interface thickness, δh . 0.2. For intrusions in uniformly stratified fluid (δh = 1), the power-law exponent is close to 0.2. Except in special cases, the exponents differ significantly from the 1/2 power predicted from self-similarity and the 1/3 power predicted for intrusions from partialdepth lock releases.