A new flow simulation methodology (FSM) for computing turbulent shear flows is presented. The development of FSM was initiated in close collaboration with C. Speziale (then at Boston University). The centerpiece of FSM is a strategy to provide the proper amount of modeling of the subgrid scales. The strategy is implemented by use of a “contribution function” which is dependent on the local and instantaneous “physical” resolution in the computation. This physical resolution is obtained 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 the computation approaches a direct numerical simulation in the fine grid limit, or provides modeling of all scales in the coarse grid limit and thus approaches an unsteady 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 traditional large-eddy simulations (LES). However, a LES that is based on the present strategy is distinctly different from traditional LES in that the required amount of modeling is determined by physical considerations, and that state-of-the-art turbulence models (as developed for Reynolds-averaged Navier-Stokes) can be employed for modeling of the unresolved scales. Thus, in contrast to traditional LES based on the Smagorinsky model, with FSM a consistent approach (in the local sense) to the coarse grid and fine grid limits is possible. As a consequence of this, FSM should require much fewer grid points for a given calculation than traditional LES or, for a given grid size, should allow computations for larger Reynolds numbers. In the present paper, the fundamental aspects of FSM are presented and discussed. Several examples are provided. The examples were chosen such that they expose, on the one hand, the inherent difficulties of simulating complex wall bounded flows, and on the other hand demonstrate the potential of the FSM approach.

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Direct numerical simulations (DNS) based on the complete Navier-Stokes equations are employed to investigate transitional wall jets. To allow for realistic comparison with laboratory experiments, the spatial model is used for the simulations. Our simulations have shown that when the wall jet is forced with large amplitude disturbances, nonlinear mechanisms can cause the ejection of vortex pairs from the wall layer that then can repeatedly interact with the wall jet layer and thus strongly influence the breakdown process. The vortex ejection is preceded by apparent 'mergings' of disturbance vortices in a subharmonic cascade. From our results it can be conjectured that this merging process is due to a 2D secondary instability mechanism. (Author) Abstract Direct numerical simulations (DNS) based on the complete Navier-Stokes equations are employed to investigate transitional wall jets. To allow for realistic comparison with laboratory experiments, the spatial model is used for the simulations. Our simulations have shown that when the wall jet is forced with large amplitude disturbances, nonlinear mechanisms can cause the ejection of vortex pairs from the wall layer that then can repeatedly interact with the wall jet layer and thus strongly influence the breakdown process. The vortex ejection is preceeded by apparent "mergings" of disturbance vortices in a subharmonic cascade. From our results it can be conjectured that this merging process is due to a two-dimensional secondary instability mechanism.

The transition process in a supersonic flat-plate boundary layer at Mach 2 is investigated numerically using linear stability theory (LST) and direct numerical simulations (DNS). The experimental investigations by Kosinov and his co-workers serve as a reference and provide the physical conditions for the numerical set-up. In these experiments, the weakly nonlinear regime of transition was studied. This led to the discovery of asymmetric subharmonic resonance triads, which appear to be relevant for transition in a Mach 2 boundary layer. These triads were composed of one primary oblique wave of frequency 20kHz and two oblique subharmonic waves of frequency 10kHz. While the experimentalists have focused on this new breakdown mechanism, we have found that the experimental data also indicate the presence of another mechanism related to oblique breakdown. This might be the first experimental evidence of the oblique breakdown mechanism in a supersonic boundary layer. With the simulations presented here, the possible presence of oblique breakdown mechanisms in the experiments is explored by deliberately suppressing subharmonic resonances in the DNS and by comparing the numerical results with the experimental data. The DNS results show excellent agreement with the experimental measurements for both linear and nonlinear transition stages. Most importantly, the results clearly show the characteristic features of oblique breakdown. In addition, we also investigated the subharmonic transition route using LST and DNS. When forcing both the subharmonic and the fundamental frequencies in the DNS, a subharmonic resonance mechanism similar to that in the experiments can be observed.

Direct numerical simulations (DNS) based on the incompressible Navier-Stokes equations are employed to investigate secondary instability mechanisms in a forced transitional wall jet. Our simulations indicate that in addition to a commonly known two-dimensional subharmonic resonance associated with the outer free shear layer region of the wall jet, three-dimensional fundamental and subharmonic resonances associated with the nearwall boundary layer region may play a role in the transition process as well. For example, twodimensional vortical structures in the near-wall region can be weakened enough through moderate three-dimensional forcing that ejection of vortex pairs from the wall into the ambient fluid is prevented. Similar observations have been made in large-eddy simulations (LES) of a bypass transition process where (random in time) large amplitude three-dimensional forcing is applied. Vortical structures with a strong spanwise coherence are observed in the outer region of the wall jet, but the near-wall region remains predominantly three-dimensional.