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Sanjeev Sanghi

Bio: Sanjeev Sanghi is an academic researcher from Indian Institute of Technology Delhi. The author has contributed to research in topics: Turbulence & Reynolds number. The author has an hindex of 12, co-authored 64 publications receiving 598 citations. Previous affiliations of Sanjeev Sanghi include Indian Institutes of Technology & City University of New York.


Papers
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TL;DR: In this article, the proper orthogonal decomposition (POD) has been applied to the analysis and low-dimensional modeling of turbulent flows, and the results show that the decomposition converges to within 5% deviation of the computational data for a maximum of 15 modes for different cases.
Abstract: The proper orthogonal decomposition (POD) has become a very useful tool in the analysis and low-dimensional modelling of flows. It provides an objective way of identifying the ‘coherent’ structures in a turbulent flow. The application of POD to the case of a thermally driven two-dimensional flow of air in a horizontal rotating cylinder is presented. The data for the POD analysis are obtained by numerical integrations of the governing equations of mass, momentum and energy. The decomposition based on POD modes or eigenfunctions is shown to converge to within 5% deviation of the computational data for a maximum of 15 modes for the different cases. The presence of degenerate eigenvalues is an indicator of travelling waves in the flow, and this is confirmed by symmetry in both space and time for the corresponding eigenfunctions. Wave speeds are also determined for these travelling waves. Furthermore, low-dimensional models are constructed employing a Galerkin procedure. The low-dimensional models yield accurate qualitative as well as quantitative behaviour of the system. Not more than 20 modes are required in the low-dimensional models to accurately model the system dynamics. The ability of low-dimensional models to accurately predict the system behaviour for the set of parameters different from the one they were constructed from is also examined. Copyright © 2010 Curtin University of Technology and John Wiley & Sons, Ltd.

84 citations

Journal ArticleDOI
TL;DR: Aubry et al. as discussed by the authors investigated the persistency of the intermittent behavior in higher -but still relatively low-dimensional dynamical systems, and showed that streaks, streamwise rolls, horseshoe vortical structures and shear layers, present in their models, are all connected to each other.
Abstract: Intermittent bursting events, similar to those characterizing the dynamics of near-wall turbulence, have been observed in a low-dimensional dynamical model (Aubry et al. 1988) built from eigenfunctions of the proper orthogonal decomposition (Lumley 1967). In the present work, we investigate the persistency of the intermittent behaviour in higher - but still of relatively low-dimensional dynamical systems. In particular, streamwise variations which were not accounted for in an explicit way in Aubry et al.'s model are now considered. Intermittent behaviour persists but can be of a different nature. Specifically, the non-zero streamwise modes become excited during the eruptive events so that rolls burst downstream into smaller scales. When structures have a finite length, they travel at a convection speed approximately equal to the mean velocity at the top of the layer (y+ ≈ 40). In all cases, intermittency seems to be due to homoclinic cycles connecting hyperbolic fixed points or more complex (apparently chaotic) limit sets. While these sets lie in the zero streamwise modes invariant subspace, the connecting orbits consist of nonzero streamwise modes travelling downstream. Chaotic limit sets connected by quasi-travelling waves have also been observed in a spatio-temporal chaotic regime of the Kuramoto–Sivashinsky equation (Aubry & Lian 1992a). When the limit sets lose their steadiness, the elongated rolls become randomly active, as they probably are in the real flow. A coherent structure study in our resulting flow fields is performed in order to relate our findings to experimental observations. It is shown that streaks, streamwise rolls, horseshoe vortical structures and shear layers, present in our models, are all connected to each other. Finally, criteria to determine a realistic value of the eddy viscosity parameter are developed.

71 citations

Journal ArticleDOI
TL;DR: A proper orthogonal decomposition analysis and low-dimensional modeling of thermally driven two-dimensional flow of air in a horizontal rotating cylinder, subject to the Boussinesq approximation, is considered in this article.
Abstract: A proper orthogonal decomposition (POD) analysis and low-dimensional modelling of thermally driven two-dimensional flow of air in a horizontal rotating cylinder, subject to the Boussinesq approximation, is considered. The problem is unsteady due to the harmonic nature of the gravitational buoyancy force with respect to the rotating observer and is characterized by four dimensionless numbers: gravitational Rayleigh number (Rag), the rotational Rayleigh number (RaΩ), the Taylor number (Ta) and Prandtl number (Pr). The data for the POD analysis are obtained by numerical integration of the governing equations of mass, momentum and energy. The POD is applied to the computational data for RaΩ varying in the range 102–106 while Rag and Pr are fixed at 105 and 0.71 respectively. The ratio of Ta to RaΩ is fixed at 100 so that the results apply to physically realistic situations. A new criterion, in the form of appropriately defined error norms, for assessing the truncation error of the POD expansion is proposed. It is shown that these error norms reflect the accuracy of the POD-based reconstructions of a given data ensemble better than the widely employed average energy criterion. The translational symmetry in both space and time of the pair of modes having degenerate (equal) eigenvalues confirms the presence of travelling waves in the flow for several different RaΩ values. The shifts in space and time of the structure of the degenerate modes are utilized to estimate the wave speeds in a given direction. The governing equations for the fluctuations are derived and low-dimensional models are constructed by employing a Galerkin procedure. For each of the five values of RaΩ, the low-dimensional models yield accurate qualitative as well as quantitative behaviour of the system. Sufficient modes are included in the low-dimensional models so that the modelling of the unresolved scales of motion is not needed to stabilize their solution. Not more than 20 modes are required in the low-dimensional models to accurately model the system dynamics. The ability of low-dimensional models to accurately predict the system behaviour for a set of parameters different from those from which they were constructed is also examined.

54 citations

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TL;DR: In this paper, a new procedure for extrapolating velocities at the outflow boundary in the computations of incompressible flows around rigid bodies is presented, based on the radial variation of the velocity field at large distances from the rigid body, which can be inferred from mass conservation and vorticity considerations.

43 citations

Journal ArticleDOI
TL;DR: In this paper, the influence of kinematic parameters such as the percentage overlap between translational and rotational phase ξ, the separation between two wings δ and Reynolds numbers Re on the evolvement of lift and drag has been investigated.
Abstract: The present study focuses on the analysis of the fluid dynamics associated with the flapping motion of finite-thickness wings. A two-dimensional numerical model for one and two-winged “clap and fling” stroke has been developed to probe the aerodynamics of insect flight. The influence of kinematic parameters such as the percentage overlap between translational and rotational phase ξ, the separation between two wings δ and Reynolds numbers Re on the evolvement of lift and drag has been investigated. In addition, the roles of the leading and trailing edge vortices on lift and drag in clap and fling type kinematics are highlighted. Based on a surrogate analysis, the overlap ratio ξ is identified as the most influential parameter in enhancing lift. On the other hand, with increase in separation δ, the reduction in drag is far more dominant than the decrease in lift. With an increase in Re (which ranges between 8 and 128), the mean drag coefficient decreases monotonously, whereas the mean lift coefficient decreases to a minimum and increases thereafter. This behavior of lift generation at higher Re was characterized by the “wing-wake interaction” mechanism which was absent at low Re.

42 citations


Cited by
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TL;DR: The Navier-Stokes equations are well-known to be a good model for turbulence as discussed by the authors, and the results of well over a century of increasingly sophisticated experiments are available at our disposal.
Abstract: It has often been remarked that turbulence is a subject of great scientific and technological importance, and yet one of the least understood (e.g. McComb 1990). To an outsider this may seem strange, since the basic physical laws of fluid mechanics are well established, an excellent mathematical model is available in the Navier-Stokes equations, and the results of well over a century of increasingly sophisticated experiments are at our disposal. One major difficulty, of course, is that the governing equations are nonlinear and little is known about their solutions at high Reynolds number, even in simple geometries. Even mathematical questions as basic as existence and uniqueness are unsettled in three spatial dimensions (cf Temam 1988). A second problem, more important from the physical viewpoint, is that experiments and the available mathematical evidence all indicate that turbulence involves the interaction of many degrees of freedom over broad ranges of spatial and temporal scales. One of the problems of turbulence is to derive this complex picture from the simple laws of mass and momentum balance enshrined in the NavierStokes equations. It was to this that Ruelle & Takens (1971) contributed with their suggestion that turbulence might be a manifestation in physical

3,721 citations

Journal ArticleDOI
TL;DR: In this article, a self-sustaining process for wall-bounded shear flows is investigated, which consists of streamwise rolls that redistribute the mean shear to create streaks that wiggle to maintain the rolls.
Abstract: A self-sustaining process conjectured to be generic for wall-bounded shear flows is investigated. The self-sustaining process consists of streamwise rolls that redistribute the mean shear to create streaks that wiggle to maintain the rolls. The process is analyzed and shown to be remarkably insensitive to whether there is no-slip or free-slip at the walls. A low-order model of the process is derived from the Navier–Stokes equations for a sinusoidal shear flow. The model has two unstable steady solutions above a critical Reynolds number, in addition to the stable laminar flow. For some parameter values, there is a second critical Reynolds number at which a homoclinic bifurcation gives rise to a stable periodic solution. This suggests a direct link between unstable steady solutions and almost periodic solutions that have been computed in plane Couette flow. It is argued that this self-sustaining process is responsible for the bifurcation of shear flows at low Reynolds numbers and perhaps also for controlling the near-wall region of turbulent shear flows at higher Reynolds numbers.

914 citations

Journal ArticleDOI
TL;DR: In this article, the spectral proper orthogonal decomposition (SPOD) has been studied in the context of the analysis of the Ginzburg-Landau equation and a turbulent jet.
Abstract: We consider the frequency domain form of proper orthogonal decomposition (POD), called spectral proper orthogonal decomposition (SPOD). Spectral POD is derived from a space–time POD problem for statistically stationary flows and leads to modes that each oscillate at a single frequency. This form of POD goes back to the original work of Lumley (Stochastic Tools in Turbulence, Academic Press, 1970), but has been overshadowed by a space-only form of POD since the 1990s. We clarify the relationship between these two forms of POD and show that SPOD modes represent structures that evolve coherently in space and time, while space-only POD modes in general do not. We also establish a relationship between SPOD and dynamic mode decomposition (DMD); we show that SPOD modes are in fact optimally averaged DMD modes obtained from an ensemble DMD problem for stationary flows. Accordingly, SPOD modes represent structures that are dynamic in the same sense as DMD modes but also optimally account for the statistical variability of turbulent flows. Finally, we establish a connection between SPOD and resolvent analysis. The key observation is that the resolvent-mode expansion coefficients must be regarded as statistical quantities to ensure convergent approximations of the flow statistics. When the expansion coefficients are uncorrelated, we show that SPOD and resolvent modes are identical. Our theoretical results and the overall utility of SPOD are demonstrated using two example problems: the complex Ginzburg–Landau equation and a turbulent jet.

756 citations

01 Jan 2016
TL;DR: The buoyancy effects in fluids is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can get it instantly.
Abstract: Thank you very much for reading buoyancy effects in fluids. Maybe you have knowledge that, people have look numerous times for their chosen books like this buoyancy effects in fluids, but end up in malicious downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they cope with some malicious bugs inside their computer. buoyancy effects in fluids is available in our book collection an online access to it is set as public so you can get it instantly. Our digital library saves in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the buoyancy effects in fluids is universally compatible with any devices to read.

285 citations