Sources of complexity in fluid flow

In the first part of this thesis, one-point and two-point statistics of the Navier–Stokes-alpha-beta (NS-alpha-beta) regularization model in homogeneous isotropic turbulence are explored. The results are compared to the limit cases of the Navier–Stokes-alpha (NS-alpha) model and the NS-alpha-beta model without subgrid-scale (SGS) stress, as well as with high-resolution direct numerical simulation (DNS). After reviewing spectra of different energy norms, probability density functions (PDFs) of the filtered and unfiltered velocity increments along with longitudinal velocity structure functions of the regularization models and DNS results are presented. Differences in the statistical properties of the unfiltered and filtered velocity fields entering the governing equations of the NS-alpha and NS-alpha-beta models are highlighted and the usability of both velocity fields for realistic flow predictions is discussed. The influence of the modified viscous term in the NS-alpha-beta model is studied through comparison to the case where the underlying SGS stress tensor is neglected. Whereas the filtered velocity field is found to have physically more viable PDFs and structure functions for the approximation of DNS results, the unfiltered velocity field is found to have flatness factors close to DNS results. In the second part of this thesis, the a priori testing strategy is adopted to study three different alpha regularization models, namely the NS-alpha model, the Leray-alpha model, and the Clark-alpha model. Specifically, high-resolution DNS data of homogeneous isotropic turbulence is used to compute the mean SGS dissipation, the spatial distribution of the SGS dissipation, and the spatial distribution of elements of the SGS stress tensor. Predictions of the three regularization models are compared to the exact values of the SGS stress tensor, as defined in the filtered Navier–Stokes equations. The potential of the three regularization models to provide good approximations is quantified using spatial correlation coefficients. Whereas the Clark-alpha model exhibits the highest spatial correlation coefficients for the SGS dissipation and the SGS stress tensor elements, the Leray-alpha model provides lower correlation coefficients, and the NS-alpha model exhibits the lowest correlation coefficients of the three models. Our results indicate the presence of an optimal choice of the filter parameter alpha depending on the large-eddy simulation grid resolution. In the third part of this thesis, a simple model for simulating flows of active suspensions is investigated. The approach is based on dissipative particle dynamics (DPD). While the model is potentially applicable to a wide range of self-propelled particle systems, the specific class of self-motile bacterial suspensions is considered as a modeling scenario. To mimic the rod-like geometry of a bacterium, two DPD particles are connected by a stiff harmonic spring to form an aggregate DPD molecule. Bacterial motility is modeled through a constant self-propulsion force applied along the axis of each such aggregate molecule. The model accounts for hydrodynamic interactions between self-propelled agents through the pairwise dissipative interactions conventional to DPD. Detailed studies of the influence of agent concentration, pairwise dissipative interactions, and Stokes friction on the statistics of the system are provided. The simulations are used to explore the influence of hydrodynamic interactions in active suspensions. For high agent concentrations in combination with dominating pairwise dissipative forces, strongly correlated motion patterns and a fluid-like spectral distributions of kinetic energy are found. In contrast, systems dominated by Stokes friction exhibit weaker spatial correlations of the velocity field. These results indicate that hydrodynamic interactions may play an important role in the formation of spatially extended structures in active suspensions.

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