Transcript file ppt
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. 2. 3. 4. University of Arizona Lebedev Institute for Physics Landau Institute for Theoretical Physics Waves and Solitons LLC, W. Sereno Dr., Gilbert, AZ, 85233, USA Let ( r , t ) elevation of ocean surface. In the first approximation this is quasistationary, quasi homogeneous random process, close to Gaussian. 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 dissipation and 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 Evolution of the surface waves spectra is described by the Hasselmann kinetic equation N k S in S nl S diss t Here S nl nothing but the standart quantum kinetics equation for Boson-type Quasiparticles in the limit of large occupation numbers. Sin - nothing but the standart quantum kinetics equation for Boson-type quasiparticles in the limit of large occupation numbers. S diss - dissipation due to wave breaking. To find Sin we should have an adequate theory of atmospheric boundary layer over ocean. This boundary layer is badly turbulent. To find S diss we need the theory of wave breaking. It is not developed yet. But we can perform a numerical experiment k R i ( R /U RU / ) k R t V i (UV / RB / ) g ( R 1) kV t should be the same in both equations. The instability growth rate was k Magnified surface shape Y(x) for time t=2994 (start of run-off) 0.025 0.02 0.015 0.01 0.005 0 -0.005 -0.01 -0.015 -4 -3 -2 -1 0 1 2 3 4 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) 0.00018 0.00016 0.00014 0.00012 0.0001 8e-05 6e-05 4e-05 2e-05 0 0 5000 10000 15000 20000 25000 30000 35000 Steepness μ(t), smoothed 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0 5000 10000 15000 20000 25000 30000 35000 H (t ) t Particular experiment 0 -2e-12 -4e-12 -6e-12 -8e-12 -1e-11 -1.2e-11 -1.4e-11 -1.6e-11 -1.8e-11 -2e-11 0 5000 10000 15000 20000 t 25000 30000 35000 Approximation of function: H ( 0 ) H 0 0.02 : f ( x) 6 106 4 102 x 2 0 0.02 : f ( x) 2 105 5 107 x8 (numerical values obtained by least squares method) 0.00025 0.0002 0.00015 0.0001 5e-05 0 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 Program Development of these experiments will make possible to determine way and improve essentially quality of wave-forecasting models. S diss in a reliable Then from comparison with experimental data we will be able to estimate which model of Sin is closer to reality.