Penetration Depth of a Plunging Jet: From Microjets to Cascades

When a liquid jet impacts a pool of the same liquid, a bubble cloud is generated below the surface: we address here the question of the vertical size of this bubble cloud. We have measured this size on experiments spanning a large range of scales, from 0.3 to 210 mm in jet diameter, and from 0.2 to 9.5 m in height of fall. We show that a simple model based on a balance of forces at the scale of the bubble cloud is able to account for all experimental results over this wide range of scales and types of jets. We derive from this model a simple expression for the prediction of the bubble cloud penetration depth.