Numerical implementation and validation of the Neumann–Michell theory of ship waves

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

“…In particular, numerical predictions (of the sinkage, trim, and drag experienced by several ship hulls, and of wave profiles along the hulls, for a range of Froude numbers) based on the Hogner approximation are found in [28,30] to be consistent with experimental measurements as well as numerical predictions given by the more accurate Neumann-Michell theory. The slender-ship approximations given in [24,25] and the related Michell thin-ship approximation [29] are considerably simpler than the Neumann-Michell or Neumann-Kelvin theories because they explicitly define the flow created by a ship in terms of the Froude number F (i.e.…”

“…The Hogner approximation [24] is considered here. Thus, the flow around a ship hull is represented via a distribution of sources with density n x , in accordance with [24,28,30].…”

Farfield waves created by a monohull ship in shallow water

“…One then has kd L /F 2 → ∞ and t ≡ tanh(kd L /F 2 ) ∼ 1 as F → ∞. Thus, the interference relation (19) yields t intrf ≈ 1 and k intrf ≈ π 2 F 4 /ℓ 2 as F → ∞. (20) Moreover, one has kd L /F 2 ≡ kd V → ∞ and expression (10) for a d yields a d → 0 as F → ∞.…”

“…Expressions (19) and (10) for t and a d yield 1 − t < 0.01 ≪ 1 and a d < 0.03 ≪ 1 if 3 ≤ k intrf d L /F 2 . The high Froude number approximation (20) for k intrf holds if the deep-water condition 3 ≤ k intrf d L /F 2 is satisfied.…”

“…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.…”