Multifractal Thermal Structure in the Western Philippine Sea Upper Layer with Internal Wave Propagation
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1 Multifractal Thermal Structure in the Western Philippine Sea Upper Layer with Internal Wave Propagation Peter C Chu and C.-P. Hsieh Naval Postgraduate School Monterey, CA pcchu@nps.edu 39 th International Liege Colloquium on Ocean Dynamics (7-11 May 2007) TURBULENCE REVISTED
2 Upper Ocean Dynamics from
3 What is the upper ocean thermal structure with internal wave propagation? An observational study in the western Philippine Sea is taken as an example for illustration.
4 Philippine Sea in World Oceans
5 Geology and Topography East China Sea ASIAEX ASIAEX South China Sea NAVO Philippine Sea
6
7 Internal Waves and Solitons near Taiwan (Liu et al., 1998)
8 MODIS (bands 1,3,4) 250-m resolution visible image over the East China Sea August 3, 2003 at 0235 UTC (Alpers et al. 2004)
9 Internal Waves/Solitons in the South China Sea (Liu and Hsu, 2007) width ~ 0.8 km ESA 4/26/2000 RADARSAT 4/22/2000
10 Data Observation Coastal Monitoring Buoy (CMB) - U.S. Naval Oceanographic Office - July 28 - August 7, Ocean data 1,3,5,18, and 20 m Surface atmospheric data - Record intervals - 10 min Thermistors -SBE 39 - Attached at 15 depths from 25 to 140 m. - Records intervals - 15 s.
11 Latitude N N Longitude E E Distance Km Velocity m/ 15s
12
13 Taylor Hypothesis for Drifting Buoy Measurements Difference between measurements at some time t and a later time t + acts as a proxy for the difference between measurements made at two points x and x + l. T(t 1 ), T(t 2 ),, T(t n ) temporal interval T(x 1 ), T(x 2 ),, T(x n ), spatial interval l
14 High-Order Structure Function Here, r is the lag, q is the order of the structure function. S(r, 1) is the commonly used structure function. S(1,1) is the mean gradient.
15 Scale-Invariance H is the scaling exponent, or called the Hurst exponent. In 1941, Kolmogorov suggested that the velocity increment in high-reynolds number turbulent flows should scale with the mean (time-averaged) energy dissipation and the separation length scale. The Hurst exponent H is equal to 1/3.
16 Simple self-similarity Multifractal behavior
17 Three Types (a) Internal Wave -turbulence (IW-T) ( GMT July 29) (b) Internal Soliton - turbulence (IS-T) ( GMT July 30) (c) Turbulence-dominated (T) ( GMT August 1)
18 Isopycnal Displacement (Desaubles and Gregg, 1981,JPO)
19 (a) IW-T type ( GMT July 29) (b) IS-T type ( GMT July 30) (c) T- type ( GMT August 1)
20 Isopycnal Displacement IW-T (10-15 GMT July 29)
21 Isopycnal Displacement IS-T (07-12 GMT July 30) Frequency is around 4 CPH
22 Isopycnal Displacement turbulence-dominated (00-05 GMT Aug 1)
23 Power Spectrum Stationary Nonstationary with stationary increments Nonstationary with nonstationary increments
24 IW-T T IS-T IW-T and T have similar multi scaling characteristics with around 0.4 (stationary) for low wavenumbers and nearly 5/3 (non-stationary with stationary increment) for high wave numbers. 60 m depth
25 Structure Function (Power Law) IW-T type
26 Structure Function (Power Law) T type
27 Structure Function IS-T type Power law breaks at 8 min, near half period (4 CPH) of the internal solitons
28 Possible Reason for Preservation of the Power Law in IW-T Type Using the Hamitonian formulation, Lvov and Tabak (2001) modified the Garrett-Munk spectrum into which represents both internal waves and wave turbulence.
29 Possible Reason for Break of the Power Law in IS-T Type The internal solitary waves are a class of nonsinusoidal, nonlinear, more-or-less isolated waves of complex shape that maintain their coherence. Their energy spectrum is totally different from the internal wave spectrum.
30 Conclusions (1) Three types of thermal variability (IW-T, IS-T, and T) are identified. (2) Multifractal structures are found in the upper layer of the western Philippine Sea. (3) Power law preserves in structure function with multifractal characteristics for the IW-T and T types, but not for the IS-T type. (4) The internal waves increase the power of the structure function especially for high moments. (5) The internal solitons destroy the multifractal characteristics of the structure function at the lag of 8 min, which is nearly half period of the IS (with frequency of 4 CPH).
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