AESOP Energetics of internal tides in Monterey Bay

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AESOPEnergetics of internal tides in Monterey
Bay

• Ph.D. work of S. M. Jachec
• O. B. Fringer, M. Gerritsen, R. L. Street
• Environmental Fluid Mechanics Laboratory
• Department of Civil and Environmental Engineering
  
• Stanford University
• 1 March 2007

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Internal wave-induced velocity field
North-South velocity at transect 1
-15 cm/s
15 cm/s
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Depth-integrated Energy Flux ltp'u'gt

• LWS (Large Wave Simulation)
• OTIS Tidal forcing
• No turbulence model
• Constant horizontal and vertical eddy viscosity
  (20.0 0.001 m2/s)
• Density field Average of 50 CTD casts from
  11/89-12/92 (Rosenfeld et al., 1994).
• What about ltr' g z u'gt and other terms?

Model Blue Data Red (Kunze, 2002)
Figure courtesy of J. Girton
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There are 14 terms in the energy flux!
Advection of kinetic energy
Barotropic energy flux
Baroclinic energy flux
Advection of available potential energy
Nonhydrostatic energy flux
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log10(W/m2)
52 MW
52 MW/100 km of coastline 520 W/m Hawaiian
ridge 10 GW/1200 km 8300 W/m
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Tidal energy budgets

• Internal tidal generation in Monterey Bay 520
  W/m ? 5.8 GW scaled to NA West Coast
• North American West Coast
• Total tidal dissipation 14 GW (Egbert Ray,
  JGR 2001)
• 8.2 GW dissipated locally (59)
• 5.8 GW radiates away as internal waves (41)
• Hawaii Ocean Ridge (Rudnick et al., Science
  2003)
• Total tidal dissipation 20.6 GW
• 51 dissipates locally (10.6 GW)
• 49 radiates away as internal waves (10 GW)

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AESOP Million Dollar Questions

• Can we calculate the other terms in the internal
  wave energy budget from field data?
• Are the other terms important to assess feedback
  of energy into larger-scale models?
• What resolution do we need in order to assess
  finer scale parameterizations for wave breaking
  and mixing?
• What are the effects of mesoscale currents on the
  internal wave energetics?
• What are the effects of the internal waves on the
  mesoscale currents?

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Barotropic Tide
Internal tide generation in Monterey Bay
59
41
Interaction with bathymetry
?
?
?
Reflection
Transmission
Dissipation
Radiation into open ocean.
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Boluses propagating onshore
Incident first-mode internal gravity wave
Transmitted first, second-mode internal bolus
g/s 1, FrU0/c0.33
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Effect of Fr U0/c when g/s1
Density contours
Linear case Fr0.056
Nonlinear case Fr0.783
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Control volume analysis of the shelf break
Total energy dissipated within control volume
Net onshelf (transmitted) flux of internal wave
energy
Net offshelf (incidentreflected) flux of
internal wave energy
Total change in energy (EkEp) within the control
volume over the time period of interest
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Differentiating reflected from incident energy
offshelf
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Effect of Fr on transmission for g/s1
High Fr leads to waves that lose too much energy
on the slope due to breaking and turbulent
mixing.
Low Fr leads to linear waves that dissipate
on the slope and do not form nonlinear boluses.
Peak transmission of ET/EI0.41 occurs in a Fr
range that leads to bolus formation without
significant onslope mixing and dissipation.
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Summary I

• An analysis of the internal wave field in
  Monterey Bay indicates that internal wave energy
  radiates from the region at a rate of 52 MW.
  When scaled to the North American West Coast,
  this accounts for roughly 41 of the tidal
  dissipation, while the rest is dissipated
  locally.
• This is consistent with the HOME findings, which
  indicate that roughly half of the tidal
  dissipation is in the form of internal wave
  radiation.

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Summary II

• While internal wave energy radiates from Monterey
  Bay at a rate of 52 MW, the actual internal wave
  energy that is generated must be much larger,
  since as much as 40 of internal wave energy
  incident on a shelf break is transmitted onshelf,
  and this energy is likely lost to dissipation and
  mixing.

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Summary III

• There exists a Froude number range in which
  onshelf transmission of internal wave energy is
  maximized for critical slopes. Within this
  range, a significant portion of the transmitted
  energy is in the form of nonlinear boluses.
• For low Fr, linear incident waves do not form
  nonlinear boluses that propagate onshelf, while
  for large Fr the incoming wave energy is so
  energetic that it dissipates most of its energy
  on the slope.