Nonlinear mechanism of tsunami wave generation by atmospheric disturbances

International audienceThe problem of tsunami wave generation by variable meteo-conditions is discussed. The simplified linear and nonlinear shallow water models are derived, and their analytical solutions for a basin of constant depth are discussed. The shallow-water model describes well the properties of the generated tsunami waves for all regimes, except the resonance case. The nonlinear-dispersive model based on the forced Korteweg-de Vries equation is developed to describe the resonant mechanism of the tsunami wave generation by the atmospheric disturbances moving with near-critical speed (long wave speed). Some analytical solutions of the nonlinear dispersive model are obtained. They illustrate the different regimes of soliton generation and the focusing of frequency modulated wave packets

Numerical modeling of rogue waves in coastal waters

Spatio-temporal evolution of rogue waves measured in Taiwanese coastal waters is reconstructed by means of numerical simulations. Their lifetimes are up to 100 s. The time series used for reconstructions were measured at dimensionless depths within the range of <i>kh</i> = 1.3&ndash;4.0, where <i>k</i> is the wave number and <i>h</i> is the depth. All identified rogue waves are surprisingly weakly nonlinear. The variable-coefficient approximate evolution equations, which take into account the shoaling effect, allow us to analyze the abnormal wave evolution over non-uniform real coastal bathymetry. The shallowest simulated point is characterized by <i>kh</i> &approx; 0.7. The reconstruction reveals an interesting peculiarity of the coastal rogue events: though the mean wave amplitudes increase as waves travel onshore, rogue waves are likely to occur at deeper locations, but not closer to the coast

Strongly nonlinear steepening of long interfacial waves

International audienceThe transformation of nonlinear long internal waves in a two-layer fluid is studied in the Boussinesq and rigid-lid approximation. Explicit analytic formulation of the evolution equation in terms of the Riemann invariants allows us to obtain analytical results characterizing strongly nonlinear wave steepening, including the spectral evolution. Effects manifesting the action of high nonlinear corrections of the model are highlighted. It is shown, in particular, that the breaking points on the wave profile may shift from the zero-crossing level. The wave steepening happens in a different way if the density jump is placed near the middle of the water bulk: then the wave deformation is almost symmetrical and two phases appear where the wave breaks

Exceedance frequency of appearance of the extreme internal waves in the World Ocean

Statistical estimates of internal waves in different regions of the World Ocean are discussed. It is found that the observed exceedance probability of large-amplitude internal waves in most cases can be described by the Poisson law, which is one of the typical laws of extreme statistics. Detailed analysis of the statistical properties of internal waves in several regions of the World Ocean has been performed: tropical part of the Atlantic Ocean, northwestern shelf of Australia, the Mediterranean Sea near the Egyptian coast, and the Yellow Sea.</p

The modified Korteweg - de Vries equation in the theory of large - amplitude internal waves

International audienceThe propagation of large- amplitude internal waves in the ocean is studied here for the case when the nonlinear effects are of cubic order, leading to the modified Korteweg - de Vries equation. The coefficients of this equation are calculated analytically for several models of the density stratification. It is shown that the coefficient of the cubic nonlinear term may have either sign (previously only cases of a negative cubic nonlinearity were known). Cubic nonlinear effects are more important for the high modes of the internal waves. The nonlinear evolution of long periodic (sine) waves is simulated for a three-layer model of the density stratification. The sign of the cubic nonlinear term influences the character of the solitary wave generation. It is shown that the solitary waves of both polarities can appear for either sign of the cubic nonlinear term; if it is positive the solitary waves have a zero pedestal, and if it is negative the solitary waves are generated on the crest and the trough of the long wave. The case of a localised impulsive initial disturbance is also simulated. Here, if the cubic nonlinear term is negative, there is no solitary wave generation at large times, but if it is positive solitary waves appear as the asymptotic solution of the nonlinear wave evolution

Морфологические и физико-химические свойства наноструктурированной целлюлозы, полученной химическим и биологическим способами

The authors obtained samples of chemically pure, crystalline, microand nanostructured cellulose of various modifications using two approaches – biological and chemical. They studied these cellulose samples via scanning electron microscopy (SEM), thermogravimetric analysis, and infrared (IR) spectroscopy. To prepare cellulose microcrystals, they used the mild acid treatment method based on glycerolacid mixtures for treating cotton fibers. They showed that the chemical processing of cotton fiber ensured its dispersion with generation of microcrystals surrounded by a partially preserved amorphous shell. The authors produced bacterial cellulose (BC) films using the Komagataeibacter xylinus C3 strain in surface cultivation conditions. With a view of obtaining higher-quality SEM images, they applied chemical fixation of lipids and proteins with critical drying to fix the process of nanofiber synthesis by bacterial cells. The two-step fixation method helped find the fibrillar structure of a cellulose film, while the morphology of bacterial cells was not deformed. The authors made a comparative analysis of the IR spectroscopy results between chemically synthesized cellulose microcrystals and BC. The obtained cellulose samples do not contain lignin and hemicellulose, both samples are highly crystalline. The BC has an ordered structure, higher crystallinity and gets carbonized when exposed to air pyrolysis. A thermogravimetric analysis of the samples shows the absence of thermally stable impurities. Both cellulose samples of biological and chemical origin are thermally stable, and the initial decomposition temperature is high enough for cellulose materials. These results show that the authors have managed to create nanocellulose materials that might be potentially applied in various industries, such as pharmaceuticals, functional composites, engineering, etc

Kinematic parameters of internal waves of the second mode in the South China Sea

Spatial distributions of the main properties of the mode function and kinematic and non-linear parameters of internal waves of the second mode are derived for the South China Sea for typical summer conditions in July. The calculations are based on the Generalized Digital Environmental Model (GDEM) climatology of hydrological variables, from which the local stratification is evaluated. The focus is on the phase speed of long internal waves and the coefficients at the dispersive, quadratic and cubic terms of the weakly non-linear Gardner model. Spatial distributions of these parameters, except for the coefficient at the cubic term, are qualitatively similar for waves of both modes. The dispersive term of Gardner's equation and phase speed for internal waves of the second mode are about a quarter and half, respectively, of those for waves of the first mode. Similarly to the waves of the first mode, the coefficients at the quadratic and cubic terms of Gardner's equation are practically independent of water depth. In contrast to the waves of the first mode, for waves of the second mode the quadratic term is mostly negative. The results can serve as a basis for expressing estimates of the expected parameters of internal waves for the South China Sea

Fourier spectrum and shape evolution of an internal Riemann wave of moderate amplitude

The nonlinear deformation of long internal waves in the ocean is studied using the dispersionless Gardner equation. The process of nonlinear wave deformation is determined by the signs of the coefficients of the quadratic and cubic nonlinear terms; the breaking time depends only on their absolute values. The explicit formula for the Fourier spectrum of the deformed Riemann wave is derived and used to investigate the evolution of the spectrum of the initially pure sine wave. It is shown that the spectrum has exponential form for small times and a power asymptotic before breaking. The power asymptotic is universal for arbitrarily chosen coefficients of the nonlinear terms and has a slope close to &ndash;8/3

Estimations of the nonlinear properties of the internal wave field off the Israel coast

International audienceThe measurements of the vertical structure of hydrological fields and internal waves on the Levantine Sea's polygon in the Mediterranean, obtained in the 27-th cruise of the RV "Professor Kolesnikov" in 1991, have been used to estimate the kinematic and nonlinear characteristics of the internal wave field. Statistical and spatial distributions of the vertical profiles of the Brunt-Vaisala frequency are described. They have been used to calculate the coefficients of the Korteweg - de Vries equation. This equation forms the main model for nonlinear parameters. It is shown that the variations of the long wave speed propagation and the dispersion parameter are relatively small in comparison with the variation of the nonlinear parameter. Estimations of the nonlinear properties of the internal waves, being measured, based on the calculation of the local Ursell parameter are given. This method can be used for investigation of the internal wave transformation processes in oceanic regions with horizontal variability of the hydrophysical fields (temperature, salinity) and sloped sea floor