Simulation of Internal Wave Wakes and Comparison with Observations J.K.E. Tunaley London Research and Development Corporation, 114 Margaret Anne Drive, Ottawa, Ontario K0A 1L0, Tel:

Outline Objectives Modelling Loch Linnhe Trials Hull Designs Simulations Discussion

Objectives Towards an evaluation of use of internal wave wakes in wide area maritime surveillance Towards understanding their generation from surface ships – Start with simplest scenario – Surface ship with stationary wake (in ship frame) The effect of hull form on the wake

Georgia Strait: ERS1

Modelling Layer models – Discrete (e.g. loch, fjord) – Diffuse Internal wave wake model – Linearized – Far wake

Loch Linnhe Trials Trials from 1989 to 1994 in Scotland Ship displacements from 100 to 30,000 tonnes Shallow layer Ship speeds typically 2 to 4 m/s Wake angles 10 to 20º Airborne synthetic aperture radars From Watson et al, 1992

Wigley Hull Canoe shaped: Parabolic in 2-D, constant draft Useful theoretical model but block coefficient is 4/9

Wigley Offsets

Practical Hulls Taylor Standard Series – Twin screw cruiser David Taylor Model Basin Series 60 – Single screw merchant National Physical Laboratory – Round bilge, high speed displacement hulls Maritime Administration (MARAD) Series – Single screw merchant, shallow water British Ship Research Association Series – Single screw merchant

DTMB Offsets C B = 0.60

Taylor Offsets SternBow

Sir Tristram, 2m/s From Watson, Chapman and Apel, 1992

Sir Tristram Parameters Ship Length, L (m)136 Ship Beam, B (m)17 Ship Draft, T (m)3.9 Estimated Block Coefficient, C B 0.59 Ship Speed, U (m/s)2.0 Layer Depth, h (m)3.0 Layer Strength, δ0.004 Pixel size (m 2 )4x4

Simulated Wake

Observed Surface Velocity From Watson et al, 1992

Simulated Surface Velocity Wigley: h=5.0 m, δ= Wigley: h=3.0 m, δ=0.004)

Simulated Surface Velocity Taylor C B =0.48DTMB C B =0.6 Taylor C B =0.7 DTMB C B =0.8

Effect of Hull Model In this application: – Minor changes to velocity profile as a function of hull model – Minor changes to velocity profile as a function of C B – Shifts shoulder downwards in plots as C B increases

Olmeda (cf Stapleton, 1997) Length = 180 m Beam = 26 m Draft = 9.2 m Speed = 2.2 m/s Wake Angle 18º Layer: h = 3 m, δ = Taylor C B =0.7

Conclusions Simulations are reasonably consistent with observations Sir Tristram observed maximum water velocity at sensor is about 3 cm/s; same as simulations Olmeda observed maximum velocity at sensor is about 5 cm/s; same as simulations Wake determined mainly by block coefficient Structure in first cycle appears to be similar in observations and simulations