Influence of Froude number and submergence depth on wave patterns

Abstract

Abstract The Kelvin–Havelock–Peters farfield approximation is applied to illustrate the influence of the Froude number F based on a ship length L , and – for a body below the free surface – the influence of the Froude number F Δ based on the submergence depth Δ , on a ship wave pattern in deep water. The influence of the Froude number F is illustrated for a free-surface piercing monohull ship; and the influence of the Froude number F Δ is illustrated for a point source submerged at a depth Δ below the free surface. The influences of F and of the submergence depth Δ ∕ L , which is related to F Δ and is used instead of F Δ , are illustrated for a fully-submerged body. These numerical illustrations show that a ship wave pattern – which does not depend on L and Δ within Kelvin’s classical analysis for a ship modeled as a 1-point wavemaker – in fact is greatly influenced by the Froude numbers F and F Δ . In particular, at high Froude numbers, e.g. at F = 1 . 5 , a ship wave pattern mostly contains divergent waves that are most apparent well inside the cusps of the Kelvin wake due to interferences between the dominant waves created by the bow and the stern of the ship, as was previously explained. A very different wave pattern is obtained at low Froude numbers, e.g. at F = 0 . 2 , for which the dominant waves are found outside the cusps of the Kelvin wake. Indeed, the wave patterns created by surface-piercing or submerged bodies can differ greatly from Kelvin’s classical pattern of transverse and divergent waves found inside a 39° wedge aft of a ship.