Improving the convergence of the modal decomposition of internal waves generated by a moving dipole

Existing results on the singularities in the neighbourhood of the plane of symmetry of the wave track of the fundamental solution of the linear equati on of internal waves in Boussinesq form, obtained for exponential stratific ation are extended to cover arbitrary stratification. Use is made of well-k nown asymptotic expansions in powers of the mode number of the eigenvalues and eigenfunctions of the Sturm-Liouville problem. Apart from the principal singularity, available when using the method of "frozen coefficients", the next singularity is singled out and it is demonstrated that this is an ess ential part of the approximate calculation of the wave pattern near the pla ne of symmetry of the track. (C) 1999 Elsevier Science Ltd. All rights rese rved.