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Register a new userTracking breather dynamics in irregular sea state conditions
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Authors
A. Chabchoub
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Breather solutions of the nonlinear Schrodinger equation (NLSE) are known to be considered as backbone models for extreme events in the ocean as well as in Kerr media. These exact determinisitic rogue wave (RW) prototypes on a regular background describe a wide-range of modulation instability configurations. Alternatively, oceanic or electromagnetic wave fields can be of chaotic nature and it is known that RWs may develop in such conditions as well. We report an experimental study confirming that extreme localizations in an irregular oceanic JONSWAP wave field can be tracked back to originate from exact NLSE breather solutions, such as the Peregrine breather. Numerical NLSE as well as modified NLSE simulations are both in good agreement with laboratory experiments and highlight the significance of universal weakly nonlinear evolution equations in the emergence as well as prediction of extreme events in nonlinear dispersive media.
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Solitons are coherent structures that describe the nonlinear evolution of wave localizations in hydrodynamics, optics, plasma and Bose-Einstein condensates. While the Peregrine breather is known to amplify a single localized perturbation of a carrier wave of finite amplitude by a factor of three, there is a counterpart solution on zero background known as the degenerate two-soliton which also leads to high amplitude maxima. In this study, we report several observations of such multi-soliton with doubly-localized peaks in a water wave flume. The data collected in this experiment confirm the distinctive attainment of wave amplification by a factor of two in good agreement with the dynamics of the nonlinear Schrodinger equation solution. Advanced numerical simulations solving the problem of nonlinear free water surface boundary conditions of an ideal fluid quantify the physical limitations of the degenerate two-soliton in hydrodynamics.
Plane Couette flow presents a regular oblique turbulent-laminar pattern over a wide range of Reynolds numbers R between the globally stable base flow profile at low R<R_g and a uniformly turbulent regime at sufficiently large R>R_t. The numerical simulations that we have performed on a pattern displaying a wavelength modulation show a relaxation of that modulation in agreement with what one would expect from a standard approach in terms of dissipative structures in extended geometry though the structuration develops on a turbulent background. Some consequences are discussed.
A system of simplified equations is proposed to govern the feedback interactions of large-scale flows present in laminar-turbulent patterns of transitional wall-bounded flows, with small-scale Reynolds stresses generated by the self-sustainment process of turbulence itself modeled using an extension of Waleffes approach (Phys. Fluids 9 (1997) 883-900), the detailed expression of which is displayed as an annex to the main text.
We introduce a general decomposition of the stress tensor for incompressible fluids in terms of its components on a tensorial basis adapted to the local flow conditions, which include extensional flows, simple shear flows, and any type of mixed flows. Such a basis is determined solely by the symmetric part of the velocity gradient and allows for a straightforward interpretation of the non-Newtonian response in any local flow conditions. In steady homogeneous flows, the material functions that represent the components of the stress on the adapted basis generalize and complete the classical set of viscometric functions used to characterize the response in simple shear flows. Such a general decomposition of the stress is effective in coherently organizing and interpreting rheological data from laboratory measurements and computational studies in non-viscometric steady flows of great importance for practical applications. The decomposition of the stress in terms with clearly distinct roles is also useful in developing constitutive models.
The evolution of crossing sea states and the emergence of rogue waves in such systems are studied via numerical simulations performed using a higher order spectral method to solve the free surface Euler equations with a flat bottom. Two classes of crossing sea states are analysed: one using directional spectra from the Draupner wave crossing at different angles, another considering a Draupner-like spectra crossed with a narrowband JONSWAP state to model spectral growth between wind sea and swell. These two classes of crossing sea states are constructed using the spectral output of a WAVEWATCH III hindcast on the Draupner rogue wave event. We measure ensemble statistical moments as functions of time, finding that although the crossing angle influences the statistical evolution to some degree, there are no significant third order effects present. Additionally, we pay particular attention to the mean sea level measured beneath extreme crest heights, the elevation of which (set up or set down) is shown to be related to the spectral content in the low wavenumber region of the corresponding spectrum.
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