Freak Waves and Wave Breaking - Catastrophic Events in Ocean V.E. Zakharov [1,2,3,4] in collaboration with Alexander Dyachenko [3,4], Andrey Pushkarev.

Freak Waves and Wave Breaking -Catastrophic Events in Ocean

V.E. Zakharov [1,2,3,4]

in collaboration with Alexander Dyachenko [3,4], Andrey Pushkarev [2,4], Alexander Prokofiev [3,4] and Alexander Korotkevich [1,3]

1. University of Arizona2. Lebedev Institute for Physics3. Landau Institute for Theoretical Physics4. Waves and Solitons LLC, W. Sereno Dr., Gilbert,

AZ, 85233, USA

Let elevation of ocean surface. In the first approximation this is quasi-stationary, quasi homogeneous random process, close to Gaussian.

),( tr

There are two types of rare catastrophic events on the ocean surface:

1. Freak waves (major catastrophic event) 2. Wave breaking (minor catastrophic event)

Freak waves are responsible for ship-wreaking, loss of boats, cargo and lives.Wave breaking is the most important mechanism of wave energy dissipationand for transport of momentum from wind to ocean.

Analytic theory is for both of these are not developed

“New Year” wave – 1995 year

Extreme wave in the Black sea – 2002 year

Freak waves – program for future.

We are planning to perform massive numerical simulation of different stationary wave spectra to determine dependence of probability of freak wave formation on energy spectrum.

Measuring of energy spectrum is a relatively easy problem. It will Make possible to estimate a danger of freak wave appearance in a given place in a given time…

Wave breaking

dissnlink SSSt

N

nlS

inS

Evolution of the surface waves spectra is described by the Hasselmann kinetic equation

Here nothing but the standart quantum kinetics equation for Boson-type Quasiparticles in the limit of large occupation numbers.

- nothing but the standart quantum kinetics equation for Boson-type quasiparticles in the limit of large occupation numbers.

dissS - dissipation due to wave breaking.

To find inS we should have an adequate theory of atmospheric boundary layer

over ocean. This boundary layer is badly turbulent.

dissS

k

RRUURit

Rk

)( //

VRgRBUVit

Vk

)1()( //

k

To find we need the theory of wave breaking. It is not developed yet.

But we can perform a numerical experiment

should be the same in both equations. The instability growth rate was

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.025

-4 -3 -2 -1 0 1 2 3 4

Magnified surface shape Y(x) for time t=2994 (start of run-off)

Surface shape Y(x) for time t=2994 Similar scale for both axes

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0 0.2 0.4 0.6 0.8 1

H(t)

0

2e-05

4e-05

6e-05

8e-05

0.0001

0.00012

0.00014

0.00016

0.00018

0 5000 10000 15000 20000 25000 30000 35000

Steepness μ(t), smoothed

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0 5000 10000 15000 20000 25000 30000 35000

-2e-11

-1.8e-11

-1.6e-11

-1.4e-11

-1.2e-11

-1e-11

-8e-12

-6e-12

-4e-12

-2e-12

0

0 5000 10000 15000 20000 25000 30000 35000

t

tH

)(

Particular experiment

t

Approximation of function:

0

5e-05

0.0001

0.00015

0.0002

0.00025

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

H

H )( 0

8750

2260

105102)(:02.0

104106)(:02.0

xxf

xxf

(numerical values obtained by least squares method)

ProgramdissSDevelopment of these experiments will make possible to determine in a reliable

way and improve essentially quality of wave-forecasting models.

inSThen from comparison with experimental data we will be able to estimate which model of is closer to reality.