1. Connecting Observations With Theory
Ocean Dynamics
Turbulence
Connecting Observations With Theory

2. Mathematical Framework
Navier-Stokes equations are deterministic, but they describe turbulence
Statistical approach required
Mathematical framework: Random Processes
e.g., Brownian motion
Turbulence is non-stationary:
mean, variance, etc - vary in time
How to make non-stationary data stationary?
take differences
Therefore, natural variables are increments

3. The 2/3 law (Kolmogorov 1941) Universality Hypothesis
In the inertial range, small-scale statistical properties are uniquely and universally determined by scale r and mean energy dissipation .
This suggests…
Apply dimensional analysis…

4. Deriving the Kolmogorov Equation
Write Navier-Stokes equations at two points
(1)
(2)
Eq. (3) = (1) - (2) — and equation for
Eq. (4) =
— an equation for kinetic energy
Next ensemble average:
use
and apply assumption of homogeneity

5. Kolmogorov Equation
In terms of the velocity component in the direction of
the separation vector r
In the inertial range (neglect second term on right)
The four-fifths law
(most fundamental result in turbulence theory)

6. Turbulence predictions 2D and 3D

7. An Ongoing Debate… Is Atmospheric KE transferred…
Down-scale? (as in 3D turbulence)
Up-scale?
(as in 2D turbulence)

8. SeaWinds-on-QuikSCAT
Satellite Winds
Scatterometer winds…
At the bottom of the marine boundary layer
SeaWinds-on-QuikSCAT
(1999 – 2009)
ASCAT-on-MetOp-A
(2007 – present)

9. SeaWinds
Ku-band
~2 cm
13.4 GHz
Wind vectors degraded by rain
Complicated
geometry
But no nadir gap
(1800 km wide swath)

10. ASCAT
C-band
~5 cm
5 GHz
Unaffected
by rain !
Simple geometry
Has nadir gap

11. SeaWinds
Ku-band
~2 cm
13.4 GHz
Wind vectors degraded by rain
Complicated
geometry
But no nadir gap
(1800 km wide swath)
ASCAT
C-band
~5 cm
5 GHz
Unaffected
by rain !
Simple geometry
Has nadir gap

12. SeaWinds/QuikSCAT
ASCAT

13. Tropical Pacific

14. Study Area Study Period Nov 2008 – October 2009
(both QuikSCAT and ASCAT operational)