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