We provide a new framework for the study of fl‡uid ‡flows presenting complex uncertain behavior. Our approach is based on the stochastic reduction and analysis of the governing equations using the dynamically orthogonal field equations. By numerically solving these equations we evolve in a fully coupled way the mean fl‡ow and the statistical and spatial characteristics of the stochastic fl‡uctuations. This set of equations is formulated for the general case of stochastic boundary conditions and allows for the application of projection methods that reduce considerably the computational cost. We analyze the transformation of energy from stochastic modes to mean dynamics, and vice-versa, by deriving exact expressions that quantify the interaction among different components of the fl‡ow. The developed framework is illustrated through specifi…c fl‡ows in unstable regimes. In particular, we consider the ‡flow behind a disk and the Rayleigh–-Bénard convection, for which we construct bifurcation diagrams that describe the variation of the response as well as the energy transfers for different parameters associated with the considered ‡flows. We reveal the low-dimensionality of the underlying stochastic attractor.

Pierre Lermusiaux is interviewed for the MGHPCC pilot project that initiated the development of a multiscale computational fluid dynamical modeling infrastructure required to make best use of the observations to be collected in the Middle Atlantic Bight and New England Shelfbreak region. This pilot project is seeding an ocean modeling collaboration that exploits opportunities provided by the Pioneer Array for longer term research and educational activities in the MIT, UMass and WHOI communities and around the region. The article and interview video can be found here.

Prof. Pierre Lermusiaux has given and been invited to give lectures at the following workshops and schools during 2013:

• 22-27 September 2013 – International Workshop on “Uncovering Transport Barriers in Geophysical Flows”, Banff, Canada.
• 8-12 July 2013 – Uncertainty Quantification in Climate Modeling and Prediction” mini-symposium, SIAM Annual Meeting, San Diego, CA.
• 24-28 June 2013 – Advanced School on Data Assimilation. University of Bologna, Italy.
• 27-29 May 2013 – 8th workshop on data assimilation methods for large models (EnKF 2013), Bergen, Norway.
• 17-22 February 2013 – International Workshop on “Probabilistic Approaches to Data Assimilation for Earth Systems”, Banff, Canada.

During naval operations, sonar performance estimates often need to be computed in-situ with limited environmental information. This calls for the use of fast acoustic propagation models. Many naval operations are carried out in challenging and dynamic environments. This makes acoustic propagation and sonar performance behavior particularly complex and variable, and complicates prediction. Using data from a field experiment, we have investigated the accuracy with which acoustic propagation loss (PL) can be predicted, using only limited modeling capabilities. Environmental input parameters came from various sources that may be available in a typical naval operation.

The outer continental shelf shallow-water experimental area featured internal tides, packets of nonlinear internal waves, and a meandering water mass front. For a moored source/receiver pair separated by 19.6 km, the acoustic propagation loss for 800 Hz pulses was computed using the peak amplitude. The variations in sound speed translated into considerable PL variability of order 15 dB. Acoustic loss modeling was carried out using a data-driven regional ocean model as well as measured sound speed profile data for comparison. The acoustic model used a two-dimensional parabolic approximation (vertical and radial outward wavenumbers only). The variance of modeled propagation loss was less than that measured. The effect of the internal tides and sub-tidal features was reasonably well modeled; these made use of measured sound speed data. The effects of nonlinear waves were not well modeled, consistent with their known three-dimensional effects but also with the lack of measurements to initialize and constrain them.