A numerical model based on the incompressible two-dimensional Navier–Stokes equations in the Boussinesq approximation is used to study mode-2 internal solitary waves propagating on a pycnocline between two deep layers of different densities. Numerical experiments on the collapse of an initially mixed region reveal a train of solitary waves with the largest leading wave enclosing an intrusional ‘bulge’. The waves gradually decay as they propagate along the horizontal direction, with a corresponding reduction in the size of the bulge. When the normalized wave amplitude, a, falls below the critical value ac=1.18, the wave is no longer able to transport mixed fluid as it propagates away from the mixed region, and a sharp-nosed intrusion is left behind. The wave structure is studied using a Lagrangian particle tracking scheme which shows that for small amplitudes the bulges have a well-defined elliptic shape. At larger amplitudes, the bulge entrains and mixes fluid from the outside while instabilities develop in the rear part of the bulge. Results are obtained for different wave amplitudes ranging from small-amplitude ‘regular’ waves with a=0.7 to highly nonlinear unstable waves with a=3.8. The dependence of the wave speed and wavelength on amplitude is measured and compared with available experimental data and theoretical predictions. Consistent with experiments, the wave speed increases almost linearly with amplitude at small values of a. As a becomes large, the wave speed increases with amplitude at a smaller rate, which gradually approaches the asymptotic limit for a two-fluid model. Results show that in the parameter range considered the wave amplitude decreases linearly with time at a rate inversely proportional to the Reynolds number. Numerical experiments are also conducted on the head-on collision of solitary waves. The simulations indicate that the waves experience a negative phase shift during the collision, in accordance with experimental observations. Computations are used to determine the dependence of the phase shift on the wave amplitude.

A robust method for detecting periodicity and measuring fundamental frequency in speech and other signals is proposed.The method is based on concepts originally developed for analyzing chaotic time-series. A signal segment is transformed into trajectory in m-dimensional state space by using embedding procedure. Close pairs of points on the trajectory with the distance between them less than prescribed neighborhood radius are found and their time separations are computed. A periodicity histogram for the distribution of computed time separations is characterized by distinct peaks corresponding to pitch period and its multiples for periodic regions, and by the absence of such peaks fot aperiodic regions. The proposed method does not suffer from the limitations of other short-term pitch-estimation techniques. Updated information and demo software can be found at www .soundmathtech.comlpitch.

The collapse of an axisymmetric mixed region in a continuously stratified pycnocline is analyzed using direct simulation of the Navier–Stokes equations in the Boussinesq limit. Attention is focused on cylindrical mixed regions of size comparable to the thickness of the pycnocline, which lies between two deep layers of different densities. Computed results show that the collapse leads to the formation of a cylindrical internal gravity wave that encloses a concentrated toroidal vortex. The vortex roll-up is related to the strain-induced intensification of vorticity and is found to be most pronounced for “tall” and horizontally compact mixed regions. The wave and vortex gradually decay as they spread radially in the pycnocline. After significant decay has occurred, the vortex disintegrates but the wave continues to propagate away from the mixed region. A sharp-nosed intrusion is left in the wake of the wave, which is no longer able to transport fluid. A Lagrangian particle scheme is used to visualize and quantify the wave structure. Analysis of particle distributions shows that the toroidal vortices entrain ambient stratified fluid into their cores. It is found that the speed of the cylindrical solitary wave is lower than the two-dimensional (2D) weakly-nonlinear prediction. In addition, unlike the 2D case, the wave speed does not appear to be a simple function of the wave amplitude. The vortex decay is finally analyzed in terms of a simplified model on the viscous cancellation of the two strained vortices of opposite sign. An approximate qualitative agreement between model predictions and computations is found. The comparison highlights the role of viscous diffusion of vorticity as well as the contributions of entrainment and baroclinic vorticity generation to the vortex decay.

A new robust nonlinear method for determination of fundamental frequency (F0) was recently proposed with application to speech pitch detection [Terez, Proc. ICASSP 1, 345–348 (2002)]. The method uses state-space embedding technique originally introduced for analyzing chaotic signals. The new method has been generalized and tested on different types of speech signals, as well as on a variety of other acoustic signals. In addition, some artificially generated nonstationary and complex wave forms have been used to test the limits of the method in comparison with other known (short-term) F0-estimation techniques (e.g., correlation, spectrum or cepstrum-based methods). Evaluation results demonstrate a unique combination of properties distinguishing the new method from conventional techniques. In particular, reliable and accurate F0 estimates can be obtained for clean periodic signals using signal segments slightly longer than one complete fundamental period. Other properties include immunity to speech formants and robust performance on noisy and band-limited speech signals. Some improvements are introduced to reduce the number of required computations and to achieve higher (subsample) accuracy. The method waused to implement a robust pitch-tracking algorithm for speech processing applications. Further information and demo software can be found at http://www.soundmathtech.com/pitch.

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