In this study, the behavior of pressure in the Rapid Distortion Limit, along with its concomitant modeling, are addressed. In the first part of the work, the role of pressure in the initiation, propagation and suppression of flow instabilities for quadratic flows is analyzed. The paradigm of analysis considers the Reynolds stress transport equations to govern the evolution of a dynamical system, in a state space composed of the Reynolds stress tensor components. This dynamical system is scrutinized via the identification of the invariant sets and the bifurcation analysis. The changing role of pressure in quadratic flows, viz. hyperbolic, shear and elliptic, is established mathematically and the underlying physics is explained. Along the maxim of "understanding before prediction", this allows for a deeper insight into the behavior of pressure, thus aiding in its modeling. The second part of this work deals with Rapid Pressure Strain Correlation modeling in earnest. Based on the comprehension developed in the preceding section, the classical pressure strain correlation modeling approaches are revisited. Their shortcomings, along with their successes, are articulated and explained, mathematically and from the viewpoint of the governing physics. Some of the salient issues addressed include, but are not limited to, the requisite nature of the model, viz. a linear or a nonlinear structure, the success of the extant models for hyperbolic flows, their inability to capture elliptic flows and the use of RDT simulations to validate models. Through this analysis, the schism between mathematical and physical guidelines and the engineering approach, at present, is substantiated. Subsequently, a model is developed that adheres to the classical modeling framework and shows excellent agreement with the RDT simulations. The performance of this model is compared to that of other nominations prevalent in engineering simulations. The work concludes with a summary, pertinent observations and recommendations for future research in the germane field.

This is the first volume in the series. It analyzes several fundamental methodology issues in numerical heat transfer and fluid flow and identifies certain areas of active application. The finite-volume approach is presented with the finite-element methods as well as with energy balance analysis. Applications include the latest development in turbulence modeling and current approaches to inverse problems.

Study of turbulence is of vital scientific, military and economic interest. Advances in several areas of external aerodynamics and internal combustor flows of interest to Air Force hinge on our ability to clearly understand and adequately predict the effects of turbulence. At the current time, however, there exists a substantial gap between our knowledge of the physics of turbulence phenomenon and the physics that is incorporated into turbulence models, especially subgrid closures. The disciplines of turbulence theory/analysis (e.g., rapid distortion theory, spectral closure models), high-order turbulence modeling (e.g., second-moment closures, structure-based models and realizability constraints) and turbulence simulation (DNS- direct numerical simulations, and LES- large eddy simulations) are evolving independently with very little cross fertilization of ideas. For example, the currently popular LES subgrid closures (e.g., Smagorinsky, dynamic Smagorinsky) are algebraic in nature; completely insensitive to extra rates of strain such as rotation, curvature, and buoyancy and, further, may not even be realizable. These major deficiencies in the LES-SGS modeling are tolerated despite the fact that, in higher order closures, these physical effects and mathematical constraints have long been represented adequately. Further, we would like to point out that the very premise of detached-eddy simulation (DES) approach - that is seen as the practical computational tool for turbulence - is erroneous. This is due to the fact that inhomogeneous spatial filtering is inevitable in this method, and yet the governing equations ignore the effects that necessarily arise with inhomogeneous filtering of the velocity field.

This work is devoted to the field of turbulence modeling. It is focused on the development of the complete second-order turbulence closure model. The alternative approach for obtaining the linear anisotropy invariant map based on the eigenvalues of the second-order tensors, which represent the important turbulent quantities like the Reynolds stress, turbulent dissipation tensor and pressure-strain correlation term, is proposed. The general modeling relationships between the corresponding tensors are derived using the kinematic constraints and validated for the particular classes of turbulent flows. The new modeling framework, based on application of the linear anisotropy invariant considerations, is placed in the context of the most recent Reynolds stress transport models, so that the innovation and advantages of the proposed methodology can be evaluated directly.

Based on a symposium held in June 1986 in Minneapolis, USA, this volume surveys current information on turbulence measurement and modelling, computational fluid mechanics, vortex flow and physical modelling, cavitation and two-phase flow, bluff body flow and fluid structure interaction.