Scaling properties of the velocity turbulent field from micro-structure profiles in the ocean Xavier Sanchez Martin Elena Roget Armengol Jesus Planella Morato Physics Department University of Girona VIENNA EGU 2012APRIL 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 Measure instrument: MSS micro-structure profiler Lozovatsky, 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. Free sinking MSS Profiler: FROZEN FIELD HYPOTHESIS: p-order Structure functions: ENSEMBLE OF OVERLAPPED SEGMENTS:

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) K41a: Hypothesis of similarity K41c: 4/5 th law. Exact relation Negative skewness Kolmogorov 1962 (K62): Refined similarity hypothesis Intermittent behavior of the dissipation: Anomalous scaling Cascade α model for ε intermittency. Schertzer and Lovejoy, JGR 92, Non intermittent K41:

4. Second order statistics: spectrum. 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.

5. Measured anomalous scaling. 4/5th law

5. Measured anomalous scaling. EXAMPLE: VERY HIGH REYNOLDS NUMBER SEGMENT: NON NATURAL PRODUCTION

IR to IS: Lohse et al., 1995, Physical review letters 74,10: DIRECT SCALINGSELF-SCALING: ESS EXAMPLE: VERY HIGH REYNOLDS NUMBER SEGMENT: NON NATURAL PRODUCTION 5. Measured anomalous 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 anomalous 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 anomalous scaling.

EXAMPLE: MODERATE REYNOLDS NUMBER SEGMENT WHERE IR AND L ARE NOT DEFINED 5. Measured anomalous 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 anomalous 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: 1)It’s needed to develop methodology to detect segments where the structure functions show a well defined scaling (ESS or direct). 2)Confirm if the intermittency depends on the Reynolds number or on the stratification. 3)The intermittency analysis will be extended to the temperature, salinity, and chlorophyll.

THANKS