Entrainment, Mixing, Their Parameterization, and the

1
Entrainment, Mixing, Their Parameterization, and
the Vertical Structure of Gravity
Currents Hartmut Peters RSMAS/MPO, University of
Miami CPT Gravity Currents Workshop, Boulder, CO,
Dec. 2-3, 2003
2

• 2001 Red Sea Outflow Experiment (REDSOX).
• Detail of analysis elsewhere (preprints, 2004
  Ocean Sciences Meeting).
• Analysis still incomplete.
• References
• H. Peters, W. E. Johns, A. S. Bower and D. M.
  Fratantoni Mixing and Entrainment in the Red
  Sea Outflow Plume. I. Plume Structure. Submitted
  to JPO Oct. 8, 2003 (http//www.rsmas.miami.edu/p
  ersonal/h.peters/rsmix.pdf)
• H. Peters, W. E. Johns and A. S. Bower Mixing
  and Entrainment in the Red Sea Outflow Plume. II.
  Turbulence Characteristics. Manuscript in
  preparation. (http//www.rsmas.miami.edu/personal
  /h.peters/rsmix2.pdf)
• A. S. Bower, D. M. Fratantoni, W. E. Johns and H.
  Peters Gulf of Aden Eddies and their Impact on
  Red Sea Water. Geophys. Res. Lett., 29, 21,
  2025, doi 10.1029/2002GL015342

3
Red Sea outflow channels
4

• Redsox, Northern Channel
• Narrow channel, 120 km long to water depth of 800
  m, a few km wide
• ? Coriolis force negligible
• Slope 1/3 degree on average
• Less steep than the initial slope at Gibraltar,
  but comparable to the lower slope just west of
  the Strait

5
(No Transcript)
6
Red Sea outflow, seasonality w/ winter maximum
summer minimum
7

• Red Sea plume
• thick (O(100m))
• vertical structure
• interfacial layer (IL)
• stratified sheared
• thicker
• bottom layer (BL)
• mixed
• topvelocity maximum
• less thick

8
IL
BL
9
Application of entrainment concepts not
unproblematic..
Price Baringer, 1994
H ?? dr ?? Frb ??
10

• In the Northern Channel of REDSOX
• bulk Froude number Frb 0.8.
• The interfacial layer
• is mixing intensely (correlated with Frb),
• this mixing produces the entrainment,
• dilution of plume mostly in the IL, less in the
  BL
• IL is thicker than the bottom layer,
• carries the bulk of the transport
• fraction of total transport in IL increases
  downstream.

11
Redsox-1, Northern Channel small Frb strong
mixing in IL
12
Correlation of mixing in the IL with Frb
13
Redsox-1, fraction of (local) transport carried
by the bottom layer decreasing with distance.
14
Mixing / dilution / entrainment are not uniform
vertically. The IL carries the bulk of the
entrainment. ? Relatively undiluted water is
delivered to relatively great depth in the BL. ?
The gravity current and the waters it carries to
depth spread vertically. ? The gravity current
has an extra degree of freedom.
15
Dilution of the whole plume twice that of the
bottom layer
16
REDSOX 1, Northern Channel Little dilution in
BL over 120 km distance.
17
an extra degree of freedom
18
At the velocity maximum - minimum shear, maximum
Richardson number - minimum in mixing, i.e.
dissipation rate (Johnson et al., Med
Outflow) - ? local minimum in vertical
turbulent fluxes of mass and momentum ?
Separation of mixing between IL and BL,
non-uniform entrainment.
19
Johnson et al., 1994b Minimum dissipation _at_
velocity maximum
20

• Redsox, Northern Channel (sparse data) ( lower
  slope at Gibraltar)
• Bottom stress interfacial stress

21

• Discussion Physics of mixing, of turbulence
  production
• Mixing in the bottom layer
• Related to the bottom boundary layer (TKE
  production u3 V3).
• Mixing in the interfacial layer
• Stable stratification shelters the IL from direct
  influence of the bottom boundary layer.
• Production of TKE by local shear instability.
• Stratified, turbulent shear flow.
• Similar to other stratified shear flows, e.g. the
  equatorial undercurrent?
• Role of internal waves in the IL?

22

• Discussion Parameterization
• No physical basis for Kraus-Turner-type recipes.
• Application of entrainment formulas to mixing in
  the interfacial layer of gravity currents appears
  ad-hoc
  (at least in models with
  more than one layer / grid point within the
  gravity current).
• Generic parameterization for stratified shear
  flows (Ri ¼) turbulence closures
  (2-equation).
• Do turbulence closures work for gravity currents?
• Are closure schemes desirable, affordable,
  compatible with models?

23

• Conclusions
• Red Sea Outflow Gravity current in gently
  inclined, narrow channel
• Low bulk Froude number intense mixing in the
  interfacial layer (IL)
• Vertical structure - IL bottom layer (BL)
• Separation between IL BL
• Fairly little dilution entrainment in BL
• IL carries - most of the transport
• - most of the entrainment
• Funded by NSF. Team of REDSOX PIs W.E. Johns,
  A.S. Bower, D.M. Fratantoni H.P.