My principal research interest is understanding the physics of long-range underwater sound propagation. Most of this work is done in a ray-theoretical context. A ray description is employed, in part, because many data sets, dating back to approximately 1980, strongly suggest that a ray-based description of the propagation physics is appropriate. Also, introduction of a ray-based description provides physical insight into the propagation physics that is difficult to obtain any other way.

Although in some ways the ray description simplifies the problem, it simultaneously leads to mathematical difficulties. Many of these difficulties stem from the observation that in environments with realistic range-dependence, ray trajectories are predominantly chaotic. In spite of this complication, recent work has shown that most features of wavefields constructed as a superposition of chaotic rays are both stable and in good agreement with measurements.

This work relies heavily on results relating to nonintegrable Hamiltonian systems. This connection is present because the ray equations have Hamiltonian form. I collaborate on this work with Javier Beron-Vera, John Colosi (WHOI), Steve Tomsovic (WSU), Mike Wolfson (APL/UW), George Zaslavsky (CIMS/NYU), Anatoly Virovlyansky (Nizhny Novgorod), and the ATOC group. This work is supported by the Office of Naval Research (ONR).

The first surface gravity problem of interest is understanding the dynamics of extreme wave events. Of particular interest is understanding whether these result from fousing (in space and/or time), or as the result of a nonlinear interaction of the Benjamin-Feir type. Focal events can be quantitatively described using a ray-based linear theory framework. Because of the relative simplicity of this type of description, it is important to understand when it can and cannot be used.

The second problem of interest is the development of a ray-based surface gravity wave prediction model that accounts for refraction, dispersion, shoaling, wave-current interactions, wind-generation, nonlinear interactions, and dissipation by breaking and bottom friction. (The model will eventually be coupled to a storm surge model and used to predict the coupled wave/surge response of a landfalling hurricane; my interest is in the wave module.) The ray-based wave model is a solution to the usual transport equation description of surface gravity wave dynamics.

There is a close mathematical connection between this work and the acoustics work in that both employ a ray-based description of the propagation physics. The ray equations in both cases have Hamiltonian form.

Hamiltonian chaos

A good starting point for the analysis of lateral transport of oceanic tracers is a model in which the velocity field is two-dimensional, incompressible and nonsteady. Fluid parcel trajectories in such a model satisfy a pair of coupled ordinary differentiated with Hamiltonian form; solutions are generally chaotic. Thus, there is a close mathematical connection between this problem and the ray-based propagation physics problems described above. Each problem, however, has special features that distinguishes it from the others. I collaborate with Javier Beron-Vera, the Langrangian Data and Modeling Group, and others on Lagrangian dynamics work.

Beron-Vera, F.J., and M.G. Brown, 2003, Travel time stability in weakly range-dependent sound channels, submitted to J. Acoust. Soc. Am..

Beron-Vera, F.J., M.J. Olascoaga, and M.G. Brown, 2003, Passive tracer patchiness and particle trajectory stability in incompressible two-dimensional flows, submitted to Nonlin. Processes in Geophys.

Beron-Vera, F.J., and M.G. Brown, 2003, Ray stability in weakly-range-dependent sound channels, J. Acoust. Soc. Am. 114, 123-130.

Beron-Vera, F.J., M.G. Brown, J.A. Colosi, S.Tomsovic, A.L. Virovlyansky, M.A. Wolfson, G.M. Zaslavsky, 2003, Ray dynamics in a long-range acoustic propagation experiment, J. Acoust. Soc. Am., in press.

Brown, M.G., J.A. Colosi, S. Tomsovic, A.L. Virovlyansky, M.A. Wolfson, G.M. Zaslavsky, 2003, Ray dynamics in long-range deep ocean sound propagation, J. Acoust. Soc. Am 113, 2533-2547.

Brown, M.G., 2001, Space-time surface gravity wave caustics: Structurally stable extreme wave events, Wave Motion 33, 117-143.

Brown, M.G., and A. Jensen, 2001, Experiments on focusing unidirectional water waves, J. Geophys. Res. 106, 16917-16928.

Brown, M.G., 2000, The Maslov integral representation of slowly-varying dispersive wavetrains in inhomogeneous moving media, Wave Motion 32, 247-266.

Brown, M.G., and J. Viechnicki, 1998, Stochastic ray theory for long-range sound propagation in deep ocean envoronments, J. Acoustic. Soc. Am. 104, 2090-2104.

Colosi, J.A., and M.G. Brown, 1998, Efficient numerical simulation of stochastic internal wave induced sound speed perturbation fields, J. Acoustic. Soc. Am. 103, 2232-2235.

Brown, M.G., 1998, Phase space structure and fractal trajectories in 1 1/2 degree of freedom Hamiltonian systems whose time-dependence is quasiperiodic, Nonlinear Processes Geophys. 5, 69-74.

Brown, M.G., 1994, A Maslov-Chapman wavefield representation for wide-angle one-way propagation, Geophys. J. Intl. 116, 513-526.

Brown, M.G., and R.M. Samelson, 1994, Particle motion in vorticity-conserving, two-dimensional incompressible flows. Physics Fluids 6, 2875-2876.

Brown, M.G., and S.T.Bauer, 1992, Empirical low-order ENSO dynamics. Geophys. Res. Lett. 19, 2055-2058.

Brown, M.G., F.D. Tappert, and S.E.R.B. Sundaram, 1991, Chaos in small amplitude surface gravity waves over slowly varying bathymetry, J. Fluid Mech. 227, 35-46.