Using fully nonlinear simulations of the two-dimensional Navier-Stokes equations at large Reynolds number ͑Re͒, we bracket a threshold amplitude above which a perturbed Gaussian monopole will relax to a quasi-steady, rotating tripole, and below which will relax to an axisymmetric monopole. The resulting quasi-steady structures are robust to small perturbations. We propose a means of measuring the decay rate of disturbances to asymptotic vortical structures wherein streamlines and lines of constant vorticity correspond in some rotating or translating frame. These experiments support the hypothesis that small or moderate deviations from asymptotic structures decay through inviscid and viscous mixing.

In this paper it is argued ~hat a two-dimensional axisymmetric large Reynolds number (Re) monopole when perturbed will return to an axisymmetric state on a time scale (Re l / 3 ) that is much faster t~an the visc?us evolution time scale (Re). It is shown that an arbitrary perturbation can be broken .1~to three pIeces; first, an axisymmetric piece corresponding to a slight radial redistribution of vorhc~t~; second, a translational piece which corresponds to a small displacement of the center of the ongmal vortex; and finally, a nonaxisymmetric perturbation which decays on the Rel/ 3 time scale due to a shear/diffus~on averaging mechanism studied by Rhines and Young [J. Fluid Mech. 133, 13~ (19~3)] f~r a passIve .scalar and Lundgren [Phys. Fluids 25,2193(1982] for vorticity. This mechamsm IS ~erified num:flcally for the canonical example of a Lamb monopole. This result suggests a phYSIcal explanatiOn for the persistence of monopole structures in large Reynolds flows such as decaying turbulence.'

Various parabolic equations for advected acoustic waves have been derived based on the assumptions of small Mach number and narrow propagation angles, which are of limited validity in atmospheric acoustics. A parabolic equation solution that does not require these assumptions is derived in the weak shear limit, which is appropriate for frequencies of about 0.1 Hz and above for atmospheric acoustics. When the variables are scaled appropriately in this limit, terms involving derivatives of the sound speed, density, and wind speed are small but can have significant cumulative effects. To obtain a solution that is valid at large distances from the source, it is necessary to account for linear terms in the first derivatives of these quantities [A. D. Pierce, J. Acoust. Soc. Am. 87, 2292-2299 (1990)]. This approach is used to obtain a scalar wave equation for advected waves. Since this equation contains two depth operators that do not commute with each other, it does not readily factor into outgoing and incoming solutions. An approximate factorization is obtained that is correct to first order in the commutator of the depth operators.

Time reversal mirrors have been applied to focus energy at probe source locations and point scatterers in inhomogeneous media. In this paper, we investigate the application of a time reversal mirror to rough interface reverberation processing in a waveguide. The method is based on the decomposition of the time reversal operator which is computed from the transfer matrix measured on a source-receiver array [Prada et al., J. Acoust. Soc. Am. 99, 2067-2076 (1996)]. In a similar manner, reverberation data collected on a source-receiver array can be filtered through an appropriate temporal window to form a time reversal operator. The most energetic eigenvector of the time reversal operator focuses along the interface at the range corresponding to the filter delay. It is also shown that improved signal-to-noise ratio measurement of the time reversal operator can be obtained by ensonifying the water column with a set of orthogonal array beams. Since these methods do not depend upon a priori environmental information, they are applicable to complex shallow water environments. Numerical simulations with a Pekeris waveguide demonstrate this method.

This paper examines the interaction of an axisymmetric vortex monopole, such as a Lamb vortex, with a background irrotational liow. At leading order, the monopole is advected with the background flow velocity at the center of vorticity. However, inhomogeneities of the llow will cause the monopole to distort. It is shown that a shear-diffusion mechanism, familiar from the study of mixing of passive scalars, plays an important role in the evolution of the vorticity distribution. Through this mechanism, nonaxisymmetric vorticity perturbations which do not shift the center of vorticity are homogenized along streamlines on a Ren3 time scale, much faster than the Re decay time scale of an axisymmetric monopole. This separation of time scales leads to the quasisteady evolution of a monopole in a slowly varying flow. The asymptotic theory is verified by numerically computing the linear response of a Lamb monopole to a time-periodic straining flow and it is shown that a large amplitude, @(Ren3), distortion results when the monopole is forced at its resonant frequency. 6