In this paper, we consider the evolution of decaying homogeneous anisotropic turbulence without mean velocity gradients, where only the slow pressure rate of strain is nonzero. A higher degree nonlinear return-to-isotropy model has been developed for the slow pressure–strain correlation, considering anisotropies in Reynolds stress, dissipation rate, and length scale tensor. Assumption of single length scale across the flow is not sufficient, from which stems the introduction of length scale anisotropy tensor, which has been assumed to be a linear function of Reynolds stress and dissipation tensor. The present model with anisotropy in length scale shows better agreement with well-accepted experimental results and an improvement over the Sarkar and Speziale (SS) quadratic model.

In the presence of mean strain or rotation, the anisotropy of turbulence increases due to the rapid pressure strain term. In this paper, we consider the modeling of the rapid pressure strain correlation of turbulence. The anisotropy of turbulence in the presence of mean strain is studied and a new model is formulated by calibrating the model constants at the rapid distortion limit. This model is tested for a range of plane strain and elliptic flows and compared to direct numerical simulation (DNS) results. The present model shows agreement with DNS and improvements over the earlier models like those by Launder et al. (1975, “Progress in the Development of a Reynolds-Stress Turbulence Closure,” J. Fluid Mech., 68(3), pp. 537–566.) and Speziale et al. (1991, “Modelling the Pressure–Strain Correlation of Turbulence: An Invariant Dynamical Systems Approach,” J. Fluid Mech., 227(1), pp. 245–272.) that have been reported to give satisfactory performance for hyperbolic flows but not satisfactory for elliptic flows.

In CFD modeling, the most widely used Reynolds stress models is the Speziale, Sarkar, Gatski (SSG) model. The present formulation, though similar in structure to the SSG model, is a mathematical variation assuming homogeneity of turbulence and is an improved model for the slow pressure strain of turbulence. The basic thrust is that anisotropy of dissipation tensor is not negligible when compared to the anisotropy of turbulent kinetic energy and affects the slow pressure strain rate. After an exhaustive survey of the available experimental results on return to isotropy, graphical plots reveal that the model performs as good as the SSG model.

This article presents numerical studies on the drag evolution of an axisymmetric body of revolution with microgrooves using Reynolds stress model-based computational fluid dynamics simulations. Experimental data of drag evolution along the non-grooved body were used to validate the numerical model predictions. After validation of the model predictions, a series of numerical simulations were performed to study the effect of toroidal grooving of the axisymmetric body on the drag evolution by varying the depth to the surface radius of the grooves at different Reynolds numbers. A maximum drag reduction of 43% was achieved with such effort. This was possible because of the drastic reduction of turbulent shear stress in the boundary layer, which has a direct relationship with the skin friction drag evolution along the body.

This research study delves into the realm of enhancing the Reynolds stress model through the remarkable capabilities of machine learning. Focusing on two key aspects, we investigate the modeling of fluctuating pressure-rate-of-strain tensor and uncertainty quantification in turbulent fluid flows. In the first part of our investigation, a neural network is employed to predict the pressure-strain correlation term for the frictional Reynolds number, even in cases where it was not trained. Through the use of high-fidelity datasets, we surpass the limitations of traditional numerical methods, achieving more accurate results with reduced computational costs. Going beyond conventional analysis, we explore the isotropic and anisotropic components of the pressure-strain correlation term. Intriguingly, our findings unveil the significant influence of production and redistribution terms on the anisotropic component by 50% and viscous dissipation impacts the isotropic part by 65% in wall-bounded turbulent flows. The second part introduces a novel approach for uncertainty quantification in the Reynolds stress model. Leveraging a binary classification model, we identify error-prone points within the simulation domain with an impressive accuracy of up to 95%. This critical step paves the way for a deeper understanding of uncertainties in turbulent flows for more reliable predictions. By harnessing the power of machine learning, our study provides two compelling ways to enhance the Reynolds stress model, contributing to a more efficient and dependable prediction of turbulent fluid dynamics.

Owing to the complexity of flow patterns, modelling of flow in coastal areas remains a challenge, even with the numerical techniques of today. In this paper, we have tried to address the problem of modelling the currents off the coast of Bay of Bengal. It is found that ocean modelling using coastal community models like Delft3D and MIKE21 could produce inherent errors if used to study depths of continental shelf greater than the 50 m isobaths (called Far-Shelf). This error can be partly overcome by adding a data processing tool like Artificial Neural Network (ANN) to improve velocity predictions. Predictions from such a proposed ANN model are seen to improve the correlation from as low as 0.28 for stand-alone model to more than 0.9 for ANN augmented results for Far-Shelf. This is because the ocean parameters in the Far-shelf are dependent not only on coastal processes but also on the interactions with the deep ocean. The advantage of better numerical accuracy strongly offsets the disadvantages of using such data-driven methods and will aid in getting a more accurate flow field.