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

Abstract 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 ${R}_{c} / H$ , in which ${R}_{c} $ 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 $2{R}_{c} $ and $5{R}_{c} $ from the gate, depending upon the relative interface thickness ${\delta }_{h} \equiv h/ H$ . This result is consistent with previously performed laboratory experiments. Scaling arguments predict that the distance, ${R}_{a} $ , over which the lock fluid first accelerates increases linearly with ${R}_{c} $ if ${R}_{c} / H\ll 1$ and ${R}_{a} / H$ approaches a constant for high aspect ratios. Likewise in the constant-speed regime, the speed relative to the rectilinear speed, $U/ {U}_{\infty } $ , increases linearly with ${R}_{c} / H$ if the aspect ratio is small and is of order unity if ${R}_{c} / H\gg 1$ . Beyond the constant-speed regime, the intrusion front decelerates rapidly, with power-law exponent as large as $0. 7$ if the relative ambient interface thickness, ${\delta }_{h} \lesssim 0. 2$ . For intrusions in uniformly stratified fluid ( ${\delta }_{h} = 1$ ), 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 partial-depth lock releases.

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