Based on MLM Slamming Model: Higher-Order Solutions Derivation

Abstract

The field of hydrodynamics has witnessed growing interest, both domestically and internationally, in optimizing slamming theory models. This shift has moved from the traditional Wagner's slamming theory towards more advanced theoretical frameworks that account for nonlinear effects. In this context, this study focuses on deriving higher-order solutions based on the Modified Logvinovich Model (MLM) slamming theory, a prominent representative within these improved paradigms. The original MLM model only incorporated the leading-order term, which, although a useful approximation, is insufficient for capturing the full range of nonlinear effects. Thus, the first-order solution derived from this leading term serves merely as an approximation and should not be considered the definitive solution governing the MLM model. The exploration of higher-order solutions and the expansion of the model's dimensionality to better account for nonlinear effects is an essential task in current hydrodynamic research. This study investigates the application of MLM slamming theory to wedge-water entry, with a particular focus on higher-order solutions. By introducing higher-order mathematical series expansions and extending the dimensional framework of the theory, we aim to enhance the accuracy and applicability of slamming predictions for objects entering water. The second-order MLM slamming solutions derived here provide a more comprehensive understanding of the slamming phenomenon. Additionally, the use of complex series superposition in the higher-order solution further improves the model’s capability to describe the behavior of wedge entry at large incline angles, offering a more precise characterization of the slamming process