How Do Breaking Waves Show Up In Low-Grazing Angle Backscatter and Ocean Wave Spectra?

William J. Plant, APL/UW, SoMaR, July 14, 2015

VV = Solid HH = Dashed

X-Band7 m/s

Plant, JGR, 1997

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Detrended o (dB): Antenna 2

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Det Vel (NaN at low SNR) (m/s): Antenna 2

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o Spectrum: Antenna 2

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Velocity Spectrum: Antenna 2

File No. 1660

Ant Look to 333 degT

Wind Vel 7.5 m/s from 333 degT

Ship Vel 0.5 m/s to 346 degT

Current 0.45 m/s from 346 degT

Vel Sprd Threshold 0 m/s-0.4 -0.2 0 0.2 0.4-0.5

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Distance East, m

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Surface Displacement in m at t = 0 (White is cut along x = 82 m.)

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Space/Time Image of Velocity in m/s Along Northerly Cut

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Spectrum of Velocities in the Space/Time Image (dBm3s-1)

Ks_rng = -1 to 2 (Unidirectional)

kw_rng = 1 to 16; phi_rng = 1 to 31

fetch = 500 km; Wind Speed = 7.5 m/s

Inc = 80 deg, Breaking slope = 13 deg, <Vbr> = 2 m/s

<Min Slope> = -19.375 Deg

Wind waves: A = 0.33 m, = 63 m from 360

Swell: A = 0 m, = 95 m from -90 deg

Speed of dominant wind wave = 9.9 m/s

Speed of modulation pattern in x/t image = 3.6 m/s

Speed from linear spectral feature = 3.2 m/s-0.4 -0.2 0 0.2 0.4

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Data SimulationWith Breaking

Distance East, m

Dis

tanc

e N

orth

, m

Surface Displacement in m at t = 0 (White is cut along x = 82 m.)

0 50 100 150 200 2500

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-1

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Distance North, m

Tim

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Space/Time Image of Velocity in m/s Along Northerly Cut

0 50 100 150 200 2500

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Wavenumber, rad/m

Fre

quen

cy,

Hz

Spectrum of Velocities in the Space/Time Image (dBm3s-1)

Ks_rng = -1 to 2 (Unidirectional)

kw_rng = 1 to 16; phi_rng = 1 to 31

fetch = 500 km; Wind Speed = 7.5 m/s

Inc = 80 deg, Breaking slope = 45 deg, <Vbr> = 2 m/s

<Min Slope> = -19.2824 Deg

Wind waves: A = 0.33 m, = 63 m from 360

Swell: A = 0 m, = 95 m from -90 deg

Speed of dominant wind wave = 9.9 m/s

Speed of modulation pattern in x/t image = 4.3 m/s

Speed from linear spectral feature = -4.5 m/s-0.4 -0.2 0 0.2 0.4

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SimulationWithout Breaking

Plant, GRL, 2012

o o

o Ding and Farmer Acoustic Tracking

So far I believe the material presented to be pretty well established.

Now I begin to speculate

From Trokhimovski, JTech, 2000

Trokhimovski, Radiometer

Hwang et al., Tank, 1993

Hwang et al., Field, 1996

Friction Velocity about 25 cm/s

Speculation:

This peak in B is caused by the breakers moving at the speed of the downwind interference pattern.

Plant, JGR, 2015

Combine f-k Spectra with Speeds of Breakers4 m/s 2 m/s 4 m/s 2 m/s

8 40 200 800

From Hwang and Wang, GRL, 2004

Dissipation Rate:“In the middle range (about 3<k<40 rad/m or0.16<λ<2.1 m), the dependence [of dissipation on wavenumber] is as strong as B10, approaching a delta function.”

Contour plots of constant spectral density from Banner et al. (JFM, 1989), their figures 6 and 7. Left: Wind speed 5.5 m/s from the right (East). Right: Wind speed 13.3 m/s from the left (West) . The short lines in the fourth quadrant give the confidence intervals

From Yueh et al., TGRS, 2013 L-Band, Inc = 29-46 degkb ≈ 41 rad/m

0.6 rad/m to 40 rad/m 100 rad/m to 800 rad/m

Speeds match those of downwind interference pattern if advection by orbital velocities in

taken into account.

Peak of X-band Low-Grazing-Angle HH Doppler spectra match those of downwind

interference pattern

Greatly increased dissipation rates according to Hwang and Wang (2004).

Curvature spectrum peaks in this range.

Group speeds match those in the higher range

Group speeds match those in the lower range.

At low wind speeds, crosswind spectra are larger than downwind ones

Upwind spectra always larger than downwind ones.

Much wave breaking Unexplained Roughness

SPECTRAL FEATURES, MANY UNUSUAL

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L XC

1450

Ka

Ku K( Bragg Wavenumber at 10o Grazing )

VV = Solid HH = Dashed

X-Band7 m/s

Plant, JGR, 1997

Plant, GRL, 2012, Figure 4b