Lecture 10 Tidal Variations in Stratification

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Lecture 10 Tidal Variations in Stratification

• Outline
• Tidal StrainingSIPS
• Modeling SIPS with Potential Energy Anomaly
• The Horizontal Richardson Number
• Lateral Straining Mechanisms
• Implications of Tidal Straining

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Tidal Straining
During ebb, straining enhances stratification
Damps Turbulence
EBB
saltier
fresher
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During flood, straining reduces or eliminates
stratification
Enhances Turbulence
saltier
fresher
FLOOD
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Convective mixing?
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Modeling Tidal Straining with Potential Energy
Anomaly
By definition
1st order salt (density) balance
Assuming density gradient is constant (in z and t)
Common approach is to assume velocity profile of
this form
Where a 1.15 and b 0.425 see Bowden and
Fairbain (1952)
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See Simpson et al. (1990) for details
Plug in expression for u
Evaluating Integral gives
This is a periodic function that reverses sign
Strain-Induced Periodic Stratification (SIPS)
Stratification will develop during the Ebb tide
when Tidal Straining exceeds Tidal Mixing
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Simple Model for Estuarine Stratification
Straining vs. Mixing
Ignores wind and surface heating.
Est. Circulation vs. Mixing
Estuarine circulation
Tidal mixing
straining
days
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ROMS Simulations of Hudson River
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Alternative Approach
Stacey et al. (1999) define a Horizontal
Richardson Number (Rix)
Stratification wont develop as long as mixing
equals straining
Assume log-layer shear and integrate twice
Log-layer Turbulent Production uwdu/dz

• Rix is analogous to the Rf. It is the ratio of
  Buoyancy flux due to straining to shear
  production.
• Also ratio of baroclinic P.G to bed stress

Caution This scaling does not account for the
increase in shear caused by the presence of
stratification.
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Scaling for Stratified Boundary Layer Height
(hbbl)
Vertical location at which stratification
develops. This should occur where mixing cannot
over come straining. (i.e. Rf0.2)
Horizontal Richardson Number and Potential Energy
Anomaly Approach are consistent
straining
mixing
Periodic Stratification will develop when RiX gt
0.2 to 1.
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But what about the terms we have ignored?
Lateral Salinity Distribution-Hudson River,
October 2006
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Lateral Circulation from the Hudson River
(October 2006)
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• Implications of Tidal Straining
• Increased Stratification during ebbs damps
  turbulence relative to flood tide.
• As a result of increased turbulence during flood
  tides, there is greater sediment resuspension
  resulting in landward flux of sediment.
• More shear during ebb relative to the flood tide
  may have implications for residual circulation
  (tidal asymmetrynon-linearity in eddy
  viscosity).
• Phytoplankton residence time in the photic zone.

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Stratification in the York River
Scully and Friedrichs (2003)
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Implications for Sediment Flux
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Internal Tidal Asymmetry
From Jay and Musiak, JGR, 1994.