Mean and Fluctuating Quantities Ocean Surface 3 D

Mean and Fluctuating Quantities Ocean Surface 3 D Turbulence Current Meter Mean Flow Fluctuating Flow One Dimensional Measurement time

Three Types of Averages Ensemble Time Space Ergodic Hypothesis: Replace ensemble average by either a space or time average

Concept of Correlation Function Auto Correlation Function Cross Correlation Function

Concept of Spatial Homogeneity and Temporal Stationarity Time or Space Correlation Function R

Homogeneous/Stationary I D Correlation Function

Velocity Cross Correlation Function Auto Covariance Function

1 r x r=0 Time or Space Axis

Concept of Structure Function Microscale Integral scale

Taylor’s Microscale Temporal case Spatial case

How to Calculate Correlation Functions from Data x, t L, T

Concept of Spectrum Temporal Spectrum

Spatial Spectra Terminology

Normalized Correlation Function and Spectra Integral Scale = Area under curve You can show that: r x

3 D + Time Spectra

Gradient Spectra

Spatial Spectra Gradient Spectra

Use of the Log-Log plot Linear Plot Log-Log Plot p=-2 100 p=-2 20 10 p=2 0 1 2 20 10

Spectra Area under curve Interpret k as eddy of size Gradient Spectra Area under curve

is the area under w Consider Model Correlation Function

From F we create a simulation of and

Calculation of Spectra = Decomposition of Variance into contributions by sines/cosines L

Calculation of Spectra of u’ Dx L 1. Choose Sampling Dx (digitizing) 2. Calculate f the DFT (Discrete Fourier Transform) of sections of u’ 3. Estimate Spectra by where 1 & 2 3 n

The Uncertainty Principle

Developing the Concept of an Eddy Real(u) f

The Eddy

Q

k. Q

k. Q