Some applications of PHOENICS in the underwater environment at the Defence Science and Technology Laboratory (Dstl)

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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
This work was carried out as part of
the Electronics Systems Research Programme
NASA Space Shuttle Flight STS-7 18.5N 111.5E 23
June 1983
PHOENICS European User Group Meeting, London,
30th Nov 2006
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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

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Observations of internal waves
University of Delaware (US) database

• 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

Luzon Strait, South China Sea
UK Shelf
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Large amplitude internal waves

• 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 100-150m, wavelength
  1000m
• Phase speed 1m/s
• Wave of depression
  Wave of elevation

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Radar imaging of internal waves
Adapted from Liu et al 1998 waves are travelling
from right to left
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UK Shelf study area
Shelf Edge Study (SES) area
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UK Shelf study area
Light bands followed by dark bands
B
300m

• Right SES mooring marked with diamonds and
  labelled S700 to S140. Thermistor chain track
  shown as dotted line, 0000-0200 19th August 1995.
  A ,B mark position of lead solitons at 1136
  on 20th and 21st August 1995.

• Left Synthetic Aperture Radar image of SES study
  area

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UK Shelf study area internal wave profiles

• Malin shelf internal wave. Density (kg/m3)
  field (left) and horizontal velocity (m/s) field
  (right) at t0s. Water depth140m.

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Internal wave dispersal effects
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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 Profiler200,
  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

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Measurement site
Asian Seas International Acoustics Experiment,
2001 Transformation, Mixing
Luzon Strait Generation Kuroshio, tidal
Spreading Refraction Diffraction Reflection
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Radar imaging of internal waves, South
China Sea
Light bands followed by dark bands
Dark bands followed by light bands as waves shoal
From Hsu and Liu 2000
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IW ship survey
Orr and Mignerey, 2003
Upslope direction (dashed line)
Ship track (solid line)
P Mignerey, private communication
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Acoustic backscatter
Orr and Mignerey, 2003 Horizontal axis is time
70m and 40m amplitude waves in deep water,
travelling from left to right
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Simulation approach

• Computational Fluid Dynamics
• Unsteady 2-D equations of motion, no Coriolis
  force (Rogtgt1), Cartesian grid
• 3rd order accurate spatial upwind scheme
• 1st order implicit in time
• Porosity representation for arbitrary bathymetry
• Grid dx15m, dy2m, dt1.25s (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
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Density structure
Nmax 17cph
Typical temperature and salinity measurements
(left) and resulting averaged density profile
(right).
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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.

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IW profiles
Elevation waves appearing in 175m to 190m depth
(measurements record 150m to 180m depth)
(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.
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IW phase speed
Green
Cyan
Purple
Red
Yellow
Blue
ADCP record (Mignerey, private communication)
marked with features used to determine wave phase
speeds
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
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IW shape
CFD (left) wave profile predictions for the 100m
initial wave at t21250s compared with
observations (right, Orr and Mignerey, 2003) from
ADCP backscatter intensity. Waves are travelling
from left to right.
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IW velocity field
CFD(left) range velocity comparison for the 100m
initial wave at t21250s with ADCP (right, Orr
and Mignerey private communication) range
velocity measurements
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IW kinetic energy upslope component
Total ke from ADCP
Upslope ke from ADCP
Estimates (with error bar) from ADCP for just
lead soliton and elevation wave
GM
Simulation (upslope)

• 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 7th May, triangles 8th
  May. ADCP upslope ke Mignerey, private
  communication.

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Turbulent dissipation rate
(Left) Log10 of the rate of dissipation of
turbulent kinetic energy per unit mass at
t11250s (scale range is 9.05 to 3.79). Density
contours relative to 1000 kg/m3 are superimposed
to illustrate the wave shape in relation to the
dissipation predictions. (Right) Gradient
Richardson number plot.
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Turbulent dissipation rate
(Left) Log10 of the rate of dissipation of
turbulent kinetic energy per unit mass at
t21250s (scale range is 9.05 to 3.84). Density
contours relative to 1000 kg/m3 are superimposed
to illustrate the wave shape in relation to the
dissipation predictions. (Right) Gradient
Richardson number plot.
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Turbulent dissipation rate elevation waves

• Peak dissipation rate levels 10-4 W/kg
  predicted in the elevation waves

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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

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Ambient turbulence
Dstl Mixed Layer Model
Shelf sea -vertical profiler (UW)
Oregon coast J Moum
Dstl Mixed Layer Model
Open literature, various sources
Elevation wave prediction
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Bottom shear stress
Typical shear stress distribution
Flow distribution
Maximum bed stress with range

• A bed stress 2N/m2 would lift sand type
  particles with diameter lt 0.1mm (Shields
  criterion)

Bed shear stress after formation of elevation
wave (note change in sign due to flow reversal)
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Bottom sediment transport passive scalar
(Left) Concentration distribution at
t20000s1250s from an initial slope line source
between 15km and 16.5km range . (Right)
Concentration distribution at t20000s2500s.
Wave position at t20000s shown with dashed line.
Current wave position shown as solid line.
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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?

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