T. Talipova

A Nonlinear Model of Internal Tide Transformation on the Australian North West Shelf

A numerical solution to the generalized Korteweg-de Vries (K-dV) equation, including horizontal variability and dissipation, is used to model the evolution of an initially sinusoidal long internal wave, representing an internal tide. The model shows the development of the waveform to the formation of shocks and solitons as it propagates shoreward over the continental slope and shelf. The model is run using observed hydrographic conditions from the Australian North West Shelf and results are compared to current meter and thermistor observations from the shelf-break region. It is found from observations that the coefficient of nonlinearity in the K-dV equation changes sign from negative in deep water to positive in shallow water, and this plays a major role in determining the form of the internal tide transformation. On the shelf there is strong temporal variability in the nonlinear coefficient due to both background shear flow and the large amplitude of the internal tide, which distorts the density profile over a wave period. Both the model and observations show the formation of an initial shock on the leading face of the internal tide. In shallow water, the change in sign of the coefficient of nonlinearity causes the shock to evolve into a tail of short period sinusoidal waves. After further propagation a second shock forms on the back face of the wave, followed by a packet of solitons. The inclusion of bottom friction in the model is investigated along with the dependance on initial wave amplitude and variability in the coefficients of nonlinearity and dispersion. Friction is found to be important in limiting the amplitudes of the evolving waves.

Dynamics of modulationally unstable ion-acoustic wavepackets in plasmas with negative ions

In this paper we study the propagation of nonlinear ion-acoustic waves in plasmas with negative ions. The Gardner equation governing these waves in plasmas with the negative ion concentration close to critical is derived. The weakly nonlinear theory of modulational instability based on the use of the nonlinear Schrodinger equation is discussed. The investigation of the nonlinear dynamics of modulationally unstable quasi-harmonic wavepackets is carried out by the numerical solution of the Gardner equation. The results are compared with the predictions of the weakly nonlinear theory.

A statistical analysis of extreme events in current variations due to internal waves from the Australian North West Shelf

Measurements of current fluctuations due to internal waves obtained from two fixed point moorings on the Australian North West Shelf have been analyzed with the aim of calculating the probability of short-scale, large-amplitude internal waves exceeding particular values. Such waves are generated as a result of breaking or hydrodynamical instability of the semidiurnal internal tide. The statistical stationarity of each record has been checked, and it is shown that the records can be used for the calculation of the frequency by which currents exceed a particular value for wave heights (double amplitudes) of less than 60 cm s -1 . The theoretical forms for exceedance frequency from the theory of extreme statistics have been checked, and it is shown that for one location a power asymptotic provides a slightly better descriptor of the statistics than an exponential asymptotic and for the other location an exponential asymptotic is found to provide the better fit. The exceedance frequency for internal waves near the Australian North West Shelf is found to be less than 1.3 waves per hour. The exceedance probability for each location has been calculated using Poisson statistics.

Modelling of Rogue Wave Shapes in Shallow Water

Various shapes of rogue waves are discussed within the framework of the mechanism of non-linear focusing of transient frequency modulated wave groups. A particular attention is paid to the formation of troughs in front of high crests. The conditions for appearance of the ‘three sisters’ are discussed too. It is important to emphasize that this mechanism is not too sensitive to the variation of the shape of transient frequency modulated wave groups. The variable-polarity shape of a rogue wave is more probable than only one crest or one trough, because the generation of the latter ones needs a specific phase relation between individual waves in the group.

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 nonlinear 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.

Exceedance frequency of appearance of 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.