© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 Some applications of PHOENICS in the underwater environment at the Defence Science and Technology Laboratory (Dstl) Dr R P Hornby Defence Science and Technology Laboratory Winfrith, UK NASA Space Shuttle Flight STS N 111.5E 23 June 1983 This work was carried out as part of the Electronics Systems Research Programme PHOENICS European User Group Meeting, London, 30 th Nov 2006

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 Why PHOENICS? Predicting the underwater environment is a challenging problem –Vital in assessing the performance of underwater sensors and the feasibility of maritime operations Shelf Sea and Ocean models (UK Metrological Office) –Provide environmental information at relatively large scale –Not currently able to economically resolve the smaller scale processes Internal wave motions –Affect water column density structure –Produce relatively large current pulses –Enhance turbulence and mixing –These models also employ a hydrostatic approximation Restricted to processes with relatively small vertical velocities –Precludes analysis of large amplitude internal wave propagation PHOENICS –General purpose fluid flow package solving the full equations of motion Used to investigate these relatively small scale, but important, environmental effects

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 Observations of internal waves Regions of most energetic Shelf Edge internal tides –UK Shelf, Bay of Biscay –China Seas –Amazon Shelf –Northwest Australian Shelf, Timor Sea –Cape Cod Grand Banks, New York Bight, Mid Atlantic Bight –Bay of Bengal, Andaman Sea –Mid-Argentine Shelf –Pakistan/Goa Shelf, Arabian Sea –Gulf of Panama –Gulf of Alaska –North Bering Sea Regions of most energetic internal tides at straits, ridges and seamounts –Strait of Gibraltar –Strait of Messina –Strait of Malacca –Mascarene Ridge –Mid-Atlantic Ridge –Hawaian Ridge –Horseshoe seamounts (Portugal) –Hebrides Terrace, Anton Dohrn Seamounts (NW of UK) University of Delaware (US) database Luzon Strait, South China Sea UK Shelf

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 Large amplitude internal waves –Prevalent where stratified ocean is forced over bathymetry Shelf edge regions (eg UK Malin Shelf) Straits (eg Gibraltar) Ridges and seamounts Amplitudes as large as m, ‘wavelength’ ~ 1000m Phase speed ~1m/s Wave of depression Wave of elevation

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 Radar imaging of internal waves Adapted from Liu et al 1998; waves are travelling from right to left

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 UK Shelf study area Shelf Edge Study (SES) area

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 UK Shelf study area Left: Synthetic Aperture Radar image of SES study area Right: SES mooring marked with diamonds and labelled S700 to S140. Thermistor chain track shown as dotted line, th August ‘A’,’B’ mark position of lead solitons at 1136 on 20th and 21st August m B Light bands followed by dark bands

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 UK Shelf study area: internal wave profiles Malin shelf internal wave. Density (kg/m 3 ) field (left) and horizontal velocity (m/s) field (right) at t=0s. Water depth=140m.

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 Internal wave dispersal effects

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 South China Sea ASIAEX (Asian Seas International Acoustics Experiment) –ONR sponsored, 2001 Orr and Mignerey (NRL, 2003) reported in situ measurements –ADCP (Acoustic Doppler Current Profiler:200, 350kHz) Water velocity as function of depth Acoustic backscatter from plankton, zooplankton etc or turbulence to map internal wave shape –CTD (Conductivity Temperature Depth probe) Density structure –RADAR Detects internal wave at distance due to backscatter from surface ‘roughness’ induced by passage of wave Real time display allows perpendicular traverse of wave

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 Measurement site Asian Seas International Acoustics Experiment, 2001 Transformation, Mixing Luzon Strait Generation: Kuroshio, tidal Spreading Refraction Diffraction Reflection

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 Radar imaging of internal waves, South China Sea From Hsu and Liu 2000 Light bands followed by dark bandsDark bands followed by light bands as waves shoal

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 IW ship survey Orr and Mignerey, 2003 Ship track (solid line) Upslope direction (dashed line) P Mignerey, private communication

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 Acoustic backscatter Orr and Mignerey, 2003 Horizontal axis is time ~70m and 40m amplitude waves in deep water, travelling from left to right

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 Simulation approach Computational Fluid Dynamics –Unsteady 2-D equations of motion, no Coriolis force (Ro>>1), Cartesian grid 3rd order accurate spatial upwind scheme 1st order implicit in time Porosity representation for arbitrary bathymetry Grid: dx=15m, dy=2m, dt=1.25s (Determined from previous simulations) –Source term for bed friction –Two equation k,e turbulence model with buoyancy effects –Initial waveform derived from weakly non-linear theory Simulate internal wave propagation –260m to 100m over 20km range –Slope gradient 1 in 125 Malin Shelf

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 Density structure Typical temperature and salinity measurements (left) and resulting averaged density profile (right). N max ~ 17cph

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 Initial wave shape and range velocity fields 100m amplitude wave. (Left) Initial density field showing wave shape, KdV shape (dotted) and empirical KdV (solid). (Right) Initial range velocity field.

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 IW profiles (Left) CFD wave evolution for initial 70m wave and (right) 100m wave. The time interval between each profile is 1250s. The thick dashed line represents the sea bed. Elevation waves appearing in 175m to 190m depth (measurements record 150m to 180m depth)

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 IW phase speed Variation of wave phase speed with on shelf propagation. The solid curve represents the 100m amplitude initial wave and the dashed curve the 70m amplitude initial wave. ASIAEX measurements (coloured) ; Mignerey, private communication Blue Purple Green Red Yellow ADCP record (Mignerey, private communication) marked with features used to determine wave phase speeds Cyan

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 IW shape CFD (left) wave profile predictions for the 100m initial wave at t=21250s compared with observations (right, Orr and Mignerey, 2003) from ADCP backscatter intensity. Waves are travelling from left to right.

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 IW velocity field CFD(left) range velocity comparison for the 100m initial wave at t=21250s with ADCP (right, Orr and Mignerey private communication) range velocity measurements

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 IW kinetic energy – upslope component Kinetic energy per unit crest length in a control volume centred on the leading wave and extending 2.5km in the upstream and downstream directions (from 22.4m below the surface to 24m above the bottom). Square symbols – 7 th May, triangles 8 th May. ADCP upslope ke: Mignerey, private communication. GM Total ke from ADCP Upslope ke from ADCP Simulation (upslope) Estimates (with error bar) from ADCP for just lead soliton and elevation wave

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 Turbulent dissipation rate (Left) Log10 of the rate of dissipation of turbulent kinetic energy per unit mass at t=11250s (scale range is –9.05 to –3.79). Density contours relative to 1000 kg/m 3 are superimposed to illustrate the wave shape in relation to the dissipation predictions. (Right) Gradient Richardson number plot.

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 Turbulent dissipation rate (Left) Log10 of the rate of dissipation of turbulent kinetic energy per unit mass at t=21250s (scale range is –9.05 to –3.84). Density contours relative to 1000 kg/m 3 are superimposed to illustrate the wave shape in relation to the dissipation predictions. (Right) Gradient Richardson number plot.

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 Turbulent dissipation rate – elevation waves Peak dissipation rate levels ~10 -4 W/kg predicted in the elevation waves

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 Turbulence levels Turbulent kinetic energy integrated over a control volume 2.5km upstream and downstream of leading wave Energy dissipation rate by turbulence in a control volume 2.5km upstream and downstream of leading wave Energy dissipation rate and turbulence levels peak as elevation waves form

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 Ambient turbulence Open literature, various sources Dstl Mixed Layer Model Shelf sea - vertical profiler (UW) Oregon coast – J Moum Elevation wave prediction

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 Bottom shear stress A bed stress ~ 2N/m**2 would lift sand type particles with diameter < ~0.1mm (Shields criterion) Bed shear stress after formation of elevation wave (note change in sign due to flow reversal) Typical shear stress distribution Flow distribution Maximum bed stress with range

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 Bottom sediment transport – passive scalar (Left) Concentration distribution at t=20000s+1250s from an initial slope line source between 15km and 16.5km range. (Right) Concentration distribution at t=20000s+2500s. Wave position at t=20000s shown with dashed line. Current wave position shown as solid line.

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015 Summary PHOENICS simulations have produced satisfactory results Reasonable agreement for ASIAEX programme –Phase speeds –Evolving wave shape and flow structure –Kinetic energy in wave Results show strong horizontal and vertical flows and highest levels of turbulence as the wave of depression transforms into waves of elevation –Turbulence results need validating against measurements Improvements to quality and computing time can be achieved –Second order accurate time discretisation (Ochoa et al PHOENICS J 2004) –PARSOL for variable bathymetry (Palacio et al PHOENICS J 2004) Adaptive formulation?

© Dstl 2006 Dstl is part of the Ministry of Defence 02 June 2015