Turbulent jets are known to support large-scale vortical wave packets traveling downstream. We show that a propagating helical wave represents a common form of the "optimal" eigenfunction tracking these structures from the near to the far field of a round jet issuing from a pipe. Two first mirror-symmetric modes containing around 5% of the total turbulent kinetic energy capture all significant large-scale events and accurately replicate the full shear-layer dynamics of the azimuthal wave number m=1. A family of the most energy-containing traveling waves represents low wave numbers and is described in terms of "empirical" dispersion laws.

This paper introduces a virtual boundary method for compressible viscous fluid flow that is capable of accurately representing moving bodies in flow and aeroacoustic simulations. The method is the compressible extension of the boundary data immersion method (BDIM, Maertens & Weymouth (2015), [18]). The BDIM equations for the compressible Navier–Stokes equations are derived and the accuracy of the method for the hydrodynamic representation of solid bodies is demonstrated with challenging test cases, including a fully turbulent boundary layer flow and a supersonic instability wave. In addition we show that the compressible BDIM is able to accurately represent noise radiation from moving bodies and flow induced noise generation without any penalty in allowable time step.

Direct numerical simulation data of supersonic axisymmetric wakes are analysed for the existence of large coherent structures. Wakes at Ma = 2.46 are considered with results being presented for cases at Reynolds numbers Re_D = 30, 000 and 100,000. Criteria for identification of coherent structures in free-shear flows found in the literature are compiled and discussed, and the role of compressibility is addressed. In particular, the ability and reliability of visualisation techniques intended for incompressible shear-flows to educe meaningful structures in supersonic wakes is scrutinised. It is shown that some of these methods retain their usefulness for identification of vortical structures as long as the swirling rate is larger than the local compression and expansion rates in the flow field. As a measure for the validity of this condition in a given flow the 'vortex compressibility parameter' is proposed which is derived here. Best 'visibility' of coherent structures is achieved by employing visualisation techniques and proper orthogonal decomposition in combination with the introduction of artificial perturbations (forcing of the wake). The existence of both helical and longitudinal structures in the shear layer and of hairpin-like structures in the developing wake is demonstrated. In addition, elongated tubes of streamwise vorticity are observed to emanate from the region of recirculating flow.

Drag reduction by means of flow control is investigated for supersonic base flows at M = 2.46 using direct numerical simulations and the flow simulation methodology. The objective of the present work is to understand the evolution of coherent structures in the flow and how flow control techniques can modify these structures. For such investigations, simulation methods that capture the dynamics of the large turbulent structures are required. Direct numerical simulations are performed for transitional base flows at Re_D = 30,000. Because of the drastically increased computational cost of direct numerical simulations at higher Reynolds numbers, a hybrid methodology (flow simulation methodology) is applied to simulate base flows with flow control at Re_D = 100,000. Active and passive flow control techniques that alter the near wake by introducing axisymmetric and longitudinal perturbations are investigated. A detailed analysis of the dynamics of the resulting turbulent structures is presented.

A flow simulation Methodology (FSM) is presented for computing the time-dependent behavior of complex compressible turbulent flows. The development of FSM was initiated in close collaboration with C. Speziale (then at Boston University). The objective of FSM is to provide the proper amount of turbulence modeling for the unresolved scales while directly computing the largest scales. The strategy is implemented by using state-of-theart turbulence models (as developed for Reynolds averaged Navier-Stokes (RANS)) and scaling of the model terms with a "contribution function." The contribution function is dependent on the local and instantaneous "physical" resolution in the computation. This physical resolution is determined during the actual simulation by comparing the size of the smallest relevant scales to the local grid size used in the computation. The contribution function is designed such that it provides no modeling if the computation is locally well resolved so that it approaches direct numerical simulations (DNS) in the fine-grid limit and such that it provides modeling of all scales in the coarse-grid limit and thus approaches a RANS calculation. In between these resolution limits, the contribution function adjusts the necessary modeling for the unresolved scales while the larger (resolved) scales are computed as in large eddy simulation (LES). However, FSM is distinctly different from LES in that it allows for a consistent transition between RANS, LES, and DNS within the same simulation depending on the local flow behavior and "physical" resolution. As a consequence, FSM should require considerably fewer grid points for a given calculation than would be necessary for a LES. This conjecture is substantiated by employing FSM to calculate the flow over a backward-facing step and a plane wake behind a bluff body, both at low Mach number, and supersonic axisymmetric wakes. These examples were chosen such that they expose, on the one hand, the inherent difficulties of simulating (physically) complex flows, and, on the other hand, demonstrate the potential of the FSM approach for simulations of turbulent compressible flows for complex geometries.

Supersonic axisymmetric base flows are prototypical for flows behind projectiles and missiles, For these flows, drag reduction can be achieved by means of passive control of the near wake. Thereby, large (turbulent) coherent structures play a dominant role. The objective of the present investigation is to elucidate if and how successful passive flow control techniques modify these structures. To this end, first Direct Numerical Simulations (DNS) for a Reynolds number of Re_D = 100,000 and Mach number of Ma =2.46 were performed using a high-order accurate and highly parallelized research code which was developed at the University of Arizona. Thereby, roughly 52 million grid points were employed. The DNS data serve to visualize typical structures of the unsteady flow field and to verify that the use of less computational costly RANS/LES methods is applicable for this flow. Two of these methods, the Flow Simulation Methodology (FSM) and Detached Eddy Simulations (DES), were then employed to investigate the supersonic base flow at Re_D =3.3 × 10⁶ and Ma = 2.46 using between 460,000 and seven million grid points. For the DES, the commercial CFD-code Cobalt was employed. This unstructured grid solver allowed then to perform simulations with boat-tailing. The obtained mean flow data are compared to available experimental results.