A steady approach flow around a circular cylinder is investigated by using a large eddy simulation (LES) with the Smagorinsky subgrid-scale model. A second-order accurate in time fractional-step method and a combined finite-difference/spectral approximation are employed to solve the filtered three-dimensional incompressible Navier-Stokes equations. To demonstrate the viability and accuracy of the method, we present results at Reynolds numbers of 100, 3 × 103, 2 × 104, and 4.42 × 104. At Re = 100, the physical flow is two-dimensional and the calculation is done without use of the LES method. For the higher values of Re, the flow in the wake is three-dimensional and turbulent and the LES method is necessary to describe the flow accurately. Calculated values of lift and drag coefficients and Strouhal number are in good agreement with the experimentally determined values at all of the Reynolds numbers for which calculation was done.

The starting point for the derivation of a new set of approaches for predicting both the wavefield at depth in an unknown medium and transmission data from measured reflection data is the inverse scattering series. We present a selection of these maps that differ in order ͑i.e., linear or nonlinear͒, capability, and data requirements. They have their roots in the consideration of a data format known as the T-matrix and have direct applicability to the data construction techniques motivating this special issue. Of particular note, one of these, a construction of the wavefield at any depth ͑includ-ing the transmitted wavefield͒, order-by-order in the measured reflected wavefield, has an unusual set of capabilities ͑e.g., it does not involve an assumption regarding the minimum-phase nature of the data and is accomplished with processing in the simple reference medium only͒ and requirements ͑e.g., a suite of frequencies from surface data are required to compute a single frequency of the wavefield at depth when the subsurface is unknown͒. An alternative reflection-to-transmission data mapping ͑which does not require a knowledge of the wavelet, and in which the component of the unknown medium that is linear in the reflection data is used as a proxy for the component of the unknown medium that is linear in the transmission data͒ is also derivable from the inverse scattering series framework.