# Cavity Formation during Asymmetric Water Entry of Rigid Bodies
## 1 Introduction  
The phenomenon of a structure impacting on the water generally implies large forces due to the massive fluid volume displaced in a small time. The duration of the slamming event is in the order of milliseconds. These loads might damage the structure or, because of their short duration, excite a dynamic response of the local structure of the hull and cause vibrations. Non-symmetric impacts might further introduce a tilting moment and influence the impact dynamics and structural stability. The first analytical solution to solve the impact dynamics of rigid bodies entering the water was presented by [PERSON] [1], who developed a formula capable of predicting the maximum force acting on a rigid body entering the water, to make a stress analysis on the members connecting the fuselage with the floats of a seaplane. Many analytical methods have been proposed to extend [PERSON]'s method to different shapes (e.g., [2, 3, 4, 5, 6, 7]) and most of them are very effective in predicting the water entry of simple-shaped structures impacting the surface with pure vertical velocity. Some of these solutions are even capable of accounting for oblique impacts (e.g., [8, 9, 10, 11, 12]). It is reported that particular conditions of entry velocity, deadrise angle, and tilt angle might lead the fluid to detach at the wedge apex, introducing difficulties in evaluating the pressure at the interface by analytical formulations. A typical water entry event that largely deviates from a symmetric case is ditching [13, 14, 15], where fluid detachment and cavitation arise if the advancing velocity is sufficiently large. Another area of interest for asymmetric impacts is the analysis of the response of planing hulls during the maneuvering operation since, depending on the conditions, restoring or capsizing moments can take place [16]. [PERSON] [17] defined two types of asymmetric impact. Type A flow is the one when there is small asymmetry and the flow moves outward along the contour on both sides of the vertex. Type B flow occurs when there is large asymmetry and the flow detaches from the body contour at the vertex onone side. [PERSON] [18] concluded that there was only one unique combination of wedge angle and impact angle at which no separation of flow from the vertex would occur. For a given wedge shape and impact direction, any other impact angle would force separation. Defining \(U\) as the horizontal velocity and \(V\) as the vertical velocity, the advancing ratio \(U/V\) at which the flow separation appears is less for bodies of larger deadrise angles. For small asymmetry impacts, the cavity flow during the water-entry is limited to a very small region. Furthermore, the flow that separates from the apex quickly re-attaches to the wedge. A symmetric body impacting with horizontal velocity will produce a flow similar to asymmetric impact with only vertical velocity when a tilting motion is not permitted. [PERSON] et al. [8] performed experiments on wedges where asymmetry and horizontal impact velocity were present and compared the results with an analytical solution, showing good agreement for low angles of asymmetry and small advancing ratios. [PERSON] et al. [17] observed that the pressure near the tip of asymmetric wedges might attain negative values with respect to the gauge pressure, and hence be lower than the ambient pressure. They also observed that the peak pressure increases with the horizontal velocity, and with it, an increase in the wave elevation on the upstream side and a decrease on the downstream one. However, the simulations are based on the assumption of attached flow. In this work, we also consider the eventual detachment at the wedge tip, similarly to that described in [19] but utilizing a different numerical scheme. [PERSON] [20] studied the effect of the horizontal component of the entry velocity for various wedge orientations.