Intermodal Interactions Research Articles

Nonlinear three-mode interactions in a developing mixing layer

A formulation based on the integral energy method is presented for the nonlinear interaction problem between three large-scale coherent modes in a developing, laminar, free shear layer. Both binary and three-mode nonlinear, modal energy and phase interactions are included. The modal evolution and the development of the mean flow are very sensitive to the initial energy contents and phases of the participating modes. A strong nonlinear coupling of the modal phase variations with the variations of the modal energies is shown to exist and is responsible for the rapid reversal of the intermodal energy interactions in favor of the occasionally declining mode. This nonlinear mechanism preserves the higher frequency modes far downstream and is shown to contribute to the appearance of mean flow contraction observed in experiments through local collective return of energy to the mean by all modes. Depending on initial conditions, our results support the arguments of R. A. Petersen and R. C. Clough [“The influence of higher harmonics on vortex pairing in an axisymmetric mixing layer,” J. Fluid Mech. 239, 81 (1992)] and M. R. Hajj, R. W. Miksad, and E. J. Powers [“Subharmonic growth by parametric resonance,” ibid. 236, 35 (1992)] according to which three-mode resonances are more efficient than the binary ones. Two cases relevant to situations where the first and second subharmonics of the most amplified mode are forced involving the 3/2 harmonic and 2/3 subharmonic, respectively, are examined. Comparisons of the calculations with experimental results indicate good qualitative agreement.

Temporal codes within a typology of cooperation between modalities

The Human-Machine Communication Department of LIMSI (LIMSI Report 1994), a laboratory of the French National Scientific Research Agency (CNRS), conducts research in the field of Pattern Recognition, Artificial Intelligence and Pattern Generation. Several approaches are currently investigated there for studying interactions between modalities: studies about the cognitive processes involved in human intermodal tasks (Denis and Cocude 1992; Gryl 1994; Daniel et al. 1994), image and language interactions for learning (Bordeaux 1993), human factors (Castaing and True 1993), symbolic approaches for designing multimodal human-computer interfaces (Bellik and Teil 1993; Bares et al. 1992), spatial reasoning (Ligozat 1992; Briffault 1992).

Excitonic interaction in the fluorene dimer

The fluorene van der Waals dimer exhibits a complex origin spectrum. This region has been studied by resonance two-photon ionization and by fluorescence excitation spectroscopies. The spectra can be interpreted on the basis of intermediate strength exciton coupling, in which the electronic interaction is comparable to the van der Waals vibrational energies. The spectra are reasonably well described by two distorted adiabatic potential surfaces, which correspond to the two excitonic components of the origin system. A single Franck–Condon active intermolecular mode provides a reasonable description of the system, however the potentials have significant cubic and quartic contributions. Non-Born–Oppenheimer nuclear momentum coupling is present and intermodal (IVR) interactions are observed, even for intermolecular modes as low as v=1. The results are remarkably different from prior observations of excitonic structure in other systems, providing a detailed picture of coupling between electronic and intermolecular motion in a van der Waals dimer.

Rossby wave interactions and instabilities in a rotating, two-layer fluid on a beta-plane. Part I: Resonant interactions

Abstract Triads of Rossby waves in a two-layer fluid on a β-plane can interact resonantly at the second order. In contrast to the single layer case, three possible triads may occur in situations of geophysical interest, namely (a) pure mode barotropic, (b) pure mode baroclinic, and (c) mixed mode baroclinic-barotropic-baroclinic types. The geometrical conditions for two baroclinic waves to form a triad with a given barotropic wave [case (c)] are determined, and it is shown that there exists a range of barotropic waves which cannot take part in such mixed triads; in the mid-latitude deep ocean these waves are characterized by periods of less than about 100 days. The direction of energy transfer within the mixed triads is discussed and found to depend upon the ordering of a new quantity, the pseudowavenumber, which is defined for each mode as the square root of the sum of the square of the wavenumber and the inverse square of the radius of deformation of the mode; in particular, the “unstable” member of the triad is the wave which possesses the intermediate pseudowavenumber. This last result is in contrast to Fjortoft's conclusion that the direction of energy transfer in a homogeneous two-dimensional fluid is to larger and smaller wavenumbers. It is also shown that Hasselmann's criterion appears to hold for mixed mode Rossby wave resonant triads. With regards to geophysical applications, it is suggested that such intermodal interactions as discussed here can be extended to multi-layer systems, and indeed, to continuously stratified fluids, and provides a mechanism for altering the depth structure of such phenomena as the mid-ocean eddies.