The Neumann–Michell theory of ship waves

Farfield waves created by a monohull ship in shallow water

“…(20) Moreover, one has kd L /F 2 ≡ kd V → ∞ and expression (10) for a d yields a d → 0 as F → ∞. The relations (18) and (20) then show that the 'largest-waves' ray angle ψ max is given by…”

“…Moreover, in the shallow-water regime d V ≤ 1, one has k min = 0 ≤ k intrf and no transverse waves can exist, but interference between divergent waves occurs. In either case, the largest divergent waves are found along the ray angles ψ = ±ψ diverg with ψ diverg defined by (11) as (18) and the wake angle ψ max is given by ψ max = ψ diverg . .…”

“…Within the framework of the theory of linear inviscid waves, the flow around a ship hull can be represented by means of a distribution of sources and sinks over the ship hull surface, e.g. as specified by the Neumann-Michell theory [18,19] or the related Hogner approximation. Thus, longitudinal interference occurs between the waves created by the sources and the sinks distributed over the bow and stern (fore and aft) regions of a ship hull, and lateral interference occurs between the sources (or sinks) distributed over the port and starboard sides of the bow (or stern) regions of the hull.…”

Interference effects on the Kelvin wake of a monohull ship represented via a continuous distribution of sources

“…The density of the distribution of sources over the ship hull surface in the linear potential flow theory of ship waves is explicitly specified in terms of the hull geometry in the approximate theories associated with the classical Hogner approximation [24] or the similar slender-ship approximation given in [25]. Alternatively, the source density can be determined numerically via the Neumann-Kelvin theory [26,27] or the related Neumann-Michell theory [28]. The Hogner approximation [24] and the approximation given in [25] are shown in [28,25] to correspond to approximate solutions of the Neumann-Michell or Neumann-Kelvin theories given in [28] or [26,27], respectively.…”

FEM SUPG stabilisation of mixed isoparametric BEMs: Application to linearised free surface flows

“…For these reasons, several methods have been developed for the solution of the linearised free surface potential problem. Among others, in [21,23], the authors studied the possibility to employ ad hoc Green functions, called Kelvin sources, which automatically satisfy the linearised condition and suppress unphysical waves propagating upstream. Although this approach leads to good results, its numerical implementation is rather cumbersome.…”