Scaling properties of the velocity turbulent field from micro-structure profiles in the ocean
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Transcript of Scaling properties of the velocity turbulent field from micro-structure profiles in the ocean
Scaling properties of the velocity turbulent field from micro-structure profiles in the ocean
Xavier Sanchez MartinElena Roget ArmengolJesus Planella Morato
Physics DepartmentUniversity of Girona
VIENNA EGU 2012 APRIL 2012
1. Scope of the work.
Experimental data: Oceanic profiles Cruise: 54N from America to Europe. Ship: Akademik Ioffe. P.P. Shirshov Institute of Oceanology. Data: April 1999. Measure instrument: MSS micro-structure profilerLozovatsky, I., M. Figueroa, E. Roget, H. J. S. Fernando, and S. Shapovalov, 2005: Observations and scaling of the upper mixed layer in the North Atlantic. Journal of Geophysical Research-Oceans, 110
Objectives:a) Development of a methodology for the determination of the transverse
Kolmogorov structure functions (SF) with the spatial series measured with a shear airfoil installed in a free sinking profiler.
b) Comparison of the measured transverse anomalous scaling of the SF (intermittency) in the inertial range (IR) with previous works, with longitudinal and transverse SF. Has the transverse SF a different scaling that the longitudinal?
c) Does the anomalous scaling (intermittence) depend on the Re number?. Or alternatively, is this scaling universal?
d) Comparison of the self-scaling or ESS (extended self-similarity) with the direct scaling. Do they fit for high Re number?
2. Structure functions from oceanic profiles.
tWz p
Free sinking MSS Profiler: FROZEN FIELD HYPOTHESIS:
constWp
)(zuT
pT
pT urS )()(
p-order Structure functions:
L0
1/ prms WuI
r
z)( rzuT
)(zuT ENSEMBLE OF OVERLAPPED SEGMENTS:
)()(),( zurzurzu TTT
)( TuP
3lawLur
3. K41 and the anomalous scaling.
INERTIAL RANGE SCALING OF THE STRUCTURE FUNCTION: From K41 to the intermittency and the anomalous scaling measures.
Kolmogorov 1941 (K41)
pLpL urS )()(
3/)( )( ppL rrS
K41a: Hypothesis of similarity
1)3(
54)( rrSL K41c: 4/5th law. Exact relationNegative skewness
Kolmogorov 1962 (K62):
Refined similarity hypothesis
Intermittent behavior of the dissipation:
r
)(qKqr r
3Llaw
r ur
3/)3/()()( )()(
ppKprrS
L
ppL
L
Anomalous scaling
3/0)( If pqK Non intermittent K41:
4. Second order statistics: spectrum
.
3/12 kFkSsh
3/513/212
Sanchez, X., E. Roget, J. Planella, and F. Forcat, 2011: Small-Scale Spectrum of a Scalar Field in Water: The Batchelor and Kraichnan Models. J.Phys.Oceanogr., 41.
2 when ??)()( scaling) anomalous (small 3/27.0)2()2(isotropy
ppp LT
LT
3/2)2( )3/4)(76.0/( rCST 3/53/2)55/24( kCFT (exp.) 6.1C
5. Measured anom
alous scaling.
p 0)()( pL
pL urS
odd is p if 0)()( pT
pT urS
pT
pT urS )()(
symmetric Tu
skewness) (negative asymmetric Lu
)()3()(
)()3()(
)()(
)()(
:(ESS) scaling-self
:scalingdirect
: measured
pT
pT
pL
pL
ppT
ppL
T
L
T
L
SS
SS
rS
rS
4/5th law
?
5. Measured anom
alous scaling.
EXAMPLE: VERY HIGH REYNOLDS NUMBER SEGMENT: NON NATURAL PRODUCTION
IR to IS: Lohse et al., 1995, Physical review letters 74,10:
DIRECT SCALING SELF-SCALING: ESS
2/2)2( )/(1/ LrCrS
EXAMPLE: VERY HIGH REYNOLDS NUMBER SEGMENT: NON NATURAL PRODUCTION
5. Measured anom
alous scaling.
5. Measured anom
alous scaling.
Lozovatsky, I., E. Roget, J. Planella, H. J. S. Fernando, and Z. Liu, 2010: Intermittency of near-bottom turbulence in tidal flow on a shallow shelf. Journal of Geophysical Research-Oceans, 115
Scaling exponents are very close to previous measures, for direct and ESS scaling.
EXAMPLE: VERY HIGH REYNOLDS NUMBER SEGMENT: NON NATURAL PRODUCTION
5. Measured anom
alous scaling.
Symmetry of the probability for the transverse velocity increments:
EXAMPLE: VERY HIGH REYNOLDS NUMBER SEGMENT: NON NATURAL PRODUCTION
EXAMPLE: MODERATE REYNOLDS NUMBER SEGMENT WHERE IR AND L ARE NOT DEFINED
5. Measured anom
alous scaling.
EXAMPLE: MODERATE REYNOLDS NUMBER SEGMENT WHERE IR AND L ARE NOT DEFINED
5. Measured anom
alous scaling.
IR AND INTEGRAL SCALE NOT WELL DEFINED
SELF SCALING WELL DEFINED
EXAMPLE: MODERATE REYNOLDS NUMBER SEGMENT: natural production
THE DIRECT SCALING DOES NOT FOLLOW THE CLASSICAL SCALINGS: NOT DEFINED IR.THE ESS SCALING FOLLOWS CLASSICAL SCALING FOR LONGITUDINAL STRUCT. FUNCT.
5. Measured anom
alous scaling.
6. Conclusions and future research.
CONCLUSIONS:1) Anomalous scaling of the transverse SF has been measured with a
profiler in the ocean. It is the first time until our knowledge. 2) Anomalous scaling of the transverse SF in fluid areas with very high
Reynolds number give results very similar to some of the previous measures in field and laboratory with longitudinal and transverse measures. It should be tested with more data before a definitive conclusion.
3) The anomalous scaling at relatively low Reynolds number give values of the anomalous scaling from ESS in concordance with previous measures. In this cases, the direct scaling deviates from classical values when the order of p increases. It should be tested with more data.
FUTURE RESEARCH:4) It’s needed to develop methodology to detect segments where the
structure functions show a well defined scaling (ESS or direct).5) Confirm if the intermittency depends on the Reynolds number or on
the stratification.6) The intermittency analysis will be extended to the temperature,
salinity, and chlorophyll.
THANKS