Taylor-Couette flow is a canonical flow to study Taylor-Görtler (TG) instability or centrifugal instability and the associated vortices. TG instability has been traditionally associated with flow over curved surfaces or geometries. In the computational study, we confirm the presence of TG-like near-wall vortical structures in two lid-driven flow systems, the Vogel-Escudier (VE) and the lid-driven cavity (LDC) flows. The VE flow is generated inside a circular cylinder by a rotating lid (top lid in the present study), while the LDC flow is generated inside a square or rectangular cavity by the linear movement of the lid. We look at the emergence of these vortical structures through reconstructed phase space diagrams and find that the TG-like vortices are seen in the chaotic regimes in both flows. In the VE flow, these vortices are seen when the side-wall boundary layer instability sets in at large Re. The VE flow is observed to go to a chaotic state in a sequence of events from a steady state at low Re. In contrast to VE flows, in the LDC flow with no curved boundaries, TG-like vortices are seen at the emergence of unsteadiness when the flow exhibits a limit cycle. The LDC flow is observed to have transitioned to chaos from the steady state through a periodic oscillatory state. Various aspect ratio cavities are examined in both flows for the presence of TG-like vortices. This article is part of the theme issue 'Taylor-Couette and related flows on the centennial of Taylor's seminal Philosophical transactions paper (Part 2)'.

Oceanic flows are energetically dominated by low vertical modes. However, disturbances in the form of atmospheric storms, eddy interactions with various forms of boundaries, or spontaneous emission by coherent structures can generate weak high-baroclinic modes. The feedback of the low-energy high-baroclinic modes on large-scale energetically dominant low modes may be weak or strong depending on the flow Rossby number. In this paper we study this interaction using an idealized setup by constraining the flow dynamics to a high-energy barotropic mode and a single low-energy high-baroclinic mode. Our investigation points out that at low Rossby numbers the barotropic flow organizes into large-scale coherent vortices via an inverse energy flux while the baroclinic flow accumulates predominantly in anticyclonic barotropic vortices. In contrast, with increasing Rossby number, the baroclinic flow catalyzes a forward flux of barotropic energy. The barotropic coherent vortices decrease in size and number, with a strong preference for cyclonic coherent vortices at higher Rossby numbers. On partitioning the flow domain into strain-dominant and vorticity-dominant regions based on the baro-tropic flow, we find that at higher Rossby numbers baroclinic flow accumulates in strain-dominant regions, away from vortex cores. Additionally, a major fraction of the forward energy flux of the flow takes place in strain-dominant regions. Overall, one of the key outcomes of this study is the finding that even a low-energy high-baroclinic flow can deplete and dissipate large-scale coherent structures at O(1) Rossby numbers.

We present a simple, novel kinematic criterion - that uses only the horizontal velocity fields and is free of arbitrary thresholds - to separate line plumes from local boundary layers in a plane close to the hot plate in turbulent convection. We first show that the horizontal divergence of the horizontal velocity field has negative and positive values in two-dimensional (2D), laminar similarity solutions of plumes and boundary layers, respectively. Following this observation, based on the understanding that fluid elements predominantly undergo horizontal shear in the boundary layers and vertical shear in the plumes, we propose that the dominant eigenvalue of the 2D strain rate tensor is negative inside the plumes and positive inside the boundary layers. Using velocity fields from our experiments, we then show that plumes can indeed be extracted as regions of negative, which are identical to the regions with negative. Exploring the connection of these plume structures to Lagrangian coherent structures (LCS) in the instantaneous limit, we show that the centrelines of such plume regions are captured by attracting LCS that do not have dominant repelling LCS in their vicinity. Classifying the flow near the hot plate based on the distribution of eigenvalues of the 2D strain rate tensor, we then show that the effect of shear due to the large-scale flow is felt more in regions close to where the local boundary layers turn into plumes. The lengths and areas of the plume regions, detected by the criterion applied to our experimental and computational velocity fields, are then shown to agree with our theoretical estimates from scaling arguments. Using velocity fields from numerical simulations, we then show that the criterion detects all the upwellings, while the available criteria based on temperature and flux thresholds miss some of these upwellings. The plumes detected by the criterion are also shown to be thicker at Prandtl numbers greater than one, expectedly so, due to the thicker velocity boundary layers of the plumes at 1$]]>.

This paper examines the effect of unstable thermal stratification on vortex breakdown in Vogel-Escudier flow. A three-dimensional direct numerical simulation of Navier-Stokes and energy equations are used to simulate a flow inside a cylindrical container generated by rotating the top lid. The top and bottom are kept at two constant temperatures such that unstable stratification is maintained. The rotation speed is related to the Reynolds number (Re), and buoyancy is linked to the Rayleigh number (Ra). The streamline and vertical velocity contour plots indicate different regimes of the flow depending on the Re and Ra. The convection dominated (CD) regime has a characteristic large-scale circulation similar to the Rayleigh-Bénard convection, and the rotation dominated (RD) regime has a central axial vortex and breakdowns. A transitional regime between RD and CD regimes is also identified from energy consideration. The influence of Ra on a vortex breakdown bubble and its relation to azimuthal vorticity is investigated in detail. Consistent with the literature on Vogel-Escudier flow, the azimuthal vorticity is shown to be essential for the breakdown in the presence of buoyancy as well. In the low Re limits, the energy of flow tends to be associated with the r-z plane velocity field, while at large Re, the energy is associated with the out-of-the-plane velocity field. Thermal plumes align along the axis for large rotations and are affected by the vortex breakdown bubble. The velocity perturbation structures and plumes show a remarkable distinction between rotation and convection-dominated regimes in the topology.

Heat transport in natural convection commonly encountered in natural and engineering flows is affected by buoyancy forces and shear. The effect of rotational shear on heat transport is examined here. Direct numerical simulation of Rayleigh-Bénard convection (RBC) with a rotating lid is performed at various rotation Reynolds numbers (Re) and Rayleigh numbers (Ra). The simulations are done for a range Ra∈[2×103,2×107] and Re∈[300,3000]. The rotating lid induces a shear into the flow resulting in two prominent flow regimes: a rotation-dominated (RD) regime and a convection-dominated (CD) regime. The RD and CD regimes are identified based on the heat transport scaling exponent of Ra. The flow topology in these two regimes is distinct, with the CD flow showing more RBC-like flow structures while the RD regime shows a central axial vortex flow. The variations of boundary layer thickness with Ra and Re also demonstrate the regimes. A parameter χ(Ra,Re) is developed to demarcate the two regimes.

We perform a direct numerical simulation of three-dimensional Navier-Stokes equations for a Rayleigh-Bénard convection system in a stationary cylinder with the top cold lid rotating. This convection system with an imposed swirl flow is a canonical problem for investigating axial vortices under unstable thermal gradients. The base flow is established by rotating the top lid and the fluid moves azimuthally along the side vertical wall into a meridional flow in the r-z plane. This forms an axial vortex core at the axis of the cylinder. This axial core, under a certain rotational Reynolds number (Re), breaks down to a vortex breakdown bubble whose dynamics are modified under thermal convection. We study the effect of rotation on varying Re for a Rayleigh number Ra = 2 × 105. The equations are formulated in such a way that the rotating-lid cylinder and Rayleigh-Bénard convection are extreme cases of the same numerical set up. From the present study, we find that as the rotational rate is increased, the system dynamics shift from a convection-dominated flow regime to a rotation-dominated regime. This shift in dynamics is quantified using the volume-averaged and time-averaged temperature, the heat flux, the thickness of the Bödewadt boundary layer and the relative Nusselt number. These quantities are shown to demarcate the convection- A nd rotation-dominated regimes, as compared to the qualitative description of flow patterns from velocity and temperature contours.

In the present study, we investigate the phenomenon of transition of a thermoacoustic system involving two-phase flow, from aperiodic oscillations to limit cycle oscillations. Experiments were performed in a laboratory scale model of a spray combustor. A needle spray injector is used to generate a droplet spray having one-dimensional velocity field. This simplified design of the injector helps in keeping away the geometric complexities involved in the real spray atomizers. We investigate the stability of the spray combustor in response to the variation of the flame location inside the combustor. Equivalence ratio is maintained constant throughout the experiment. The dynamics of the system is captured by measuring the unsteady pressure fluctuations present in the system. As the flame location is gradually varied, self-excited high-amplitude acoustic oscillations are observed in the combustor. We observe the transition of the system behavior from low-amplitude aperiodic oscillations to large amplitude limit cycle oscillations occurring through intermittency. This intermittent state mainly consists of a sequence of high-amplitude bursts of periodic oscillations separated by low-amplitude aperiodic regions. Moreover, the experimental results highlight that during intermittency, the maximum amplitude of bursts, near to the onset of intermittency, is as much as three times higher than the maximum amplitude of the limit cycle oscillations. These high-amplitude intermittent loads can have stronger adverse effects on the structural properties of the engine than the low-amplitude cyclic loading caused by the sustained limit cycle oscillations. Evolution of the three different dynamical states of the spray combustion system (viz., stable, intermittency, and limit cycle) is studied in three-dimensional phase space by using a phase space reconstruction tool from the dynamical system theory. We report the first experimental observation of type-II intermittency in a spray combustion system. The statistical distributions of the length of aperiodic (turbulent) phase with respect to the control parameter, first return map and recurrence plot (RP) techniques are employed to confirm the type of intermittency.

Combustion instability is a nonlinear process with interaction between combustion and acoustics. The nonlinearity in the combustion process is observed in the flame dynamics. In our study of a ducted laminar premixed V-flame, we varied the distance between the flame anchor and the duct exit. We observed that the thermoacoustic system bifurcates from a stable state to a frequency locked state, followed by quasi-periodicity, period 3 oscillations, and finally chaotic oscillations. During the occurrence of these dynamical states, the role of flame dynamics is investigated using high speed imaging. We observed wrinkle formation, its propagation and growth along flame front, rollup of the flame, separation, and annihilation of flame elements during instability. From the present study it is found that each dynamical state is characterized by a particular sequence of flame behavior, highlighting the role of nonlinear flame dynamics in establishing the observed dynamical state.

In the present study, we investigate the phenomenon of transition of a thermoacoustic system involving two-phase flow, from aperiodic oscillations to limit cycle oscillations. Experiments were performed in a laboratory scale model of a spray combustor. A needle spray injector is used to generate a droplet spray having one dimensional velocity field. This simplified design of the injector helps in keeping away the geometric complexities involved in the real spray atomizers. We investigate the stability of the spray combustor in response to the variation of the flame location inside the combustor. Equivalence ratio is maintained constant throughout the experiment. The dynamics of the system is captured by measuring the unsteady pressure fluctuations present in the system. As the flame location is gradually varied, self-excited high amplitude acoustic oscillations are observed in the combustor. We observe the transition of the system behaviour from low amplitude aperiodic oscillations to large amplitude limit cycle oscillations occurring through intermittency. This intermittent state mainly consists of a sequence of highamplitude periodic bursts separated by low amplitude aperiodic regions. Moreover, the experimental results highlight that during intermittency, the maximum amplitude of bursts oscillations, near to the onset of intermittency, is as much as three times higher than the maximum amplitude of the limit cycle oscillations. These high amplitude intermittent loads can have stronger adverse effects on the structural properties of the engine than the low amplitude cyclic loading caused by the sustained limit cycle oscillations. Evolution of the three different dynamical states of the spray combustion system (viz. stable, intermittency and limit cycle) are studied in three dimensional phase space by using a phase space reconstruction tool from the dynamical system theory. We report the first experimental observation of type-II intermittency in a spray combustion system. The statistical distributions of the length of aperiodic (turbulent) phase with respect to the control parameter, first return map and recurrence plot techniques are employed to confirm the type of intermittency.

This study investigates a laboratory-scale combustor consisting of a tube (a quarter-wavelength resonator with an open end at the top, and a closed end at the bottom) with a laminar V-flame inside it. The parameter of interest is the axial position of the flame relative to the tube. This position was varied in a step-by-step manner by moving the flame in small steps from the top end towards the bottom end of the tube. In each step, the pressure-time history was recorded and its frequency content was analysed. Nonlinear time series analysis was performed on the recorded pressure-time history to identify the dynamic states. As the flame got lowered, a range of dynamic states were observed. These include limit cycles at low and high amplitudes, but also highly irregular oscillations. The instability frequencies showed a continuously decreasing trend, as well. A set of thermal imaging with a large wavelength infra-red camera, was performed to understand the reason of this behaviour. Finally, the flame was filmed with a high-speed camera, and the images were used to explain the oscillation pattern during the limit cycle.

Propulsion systems such as gas turbines are susceptible to combustion instability, when operated at lean equivalence ratio [1]. During combustion instability, there is a nonlinear interaction between combustion and acoustics leading to large amplitude acoustic oscillations. These large amplitude oscillations are detrimental to the stability of the combustor and can cause damages to the structural integrity of the combustor, flame flash back or blow off. The main source of nonlinearity is in the heat release rate caused due to the velocity perturbations at the flame holder [2]. The heat release rate fluctuations are due to the variation in the flame surface area. Hence there is a need to understand the flame dynamics that contributes to the heat release rate fluctuations. The present study aims in understanding the stability of a V - flame combustor by varying the flame location inside an acoustic resonator. By varying the flame location the instability regimes of the combustor are identified. At the flame locations where the system exhibits combustion instability, acoustic pressure oscillations are acquired simultaneously with high speed images of the flame front fluctuations so that a correlation can be made between them. Tools from dynamical systems theory are applied to the pressure signal to quantify different dynamical states of the system during combustion instability. Moreover the flame dynamics at each dynamical state are investigated. It is observed that combustion instability is characterized by interesting dynamical states such as frequency locked state, quasi-periodic oscillations, period 3 oscillations and chaotic oscillations. High speed imaging of the flame reveals different interesting patterns of flame behavior during combustion instability. Flame wrinkling, roll up of flame elements, separation as islands of the flame elements and mutual annihilation of flame elements were some of the interesting flame behavior observed. This study helps in understanding the role of nonlinear heat release rate mechanism in establishing different dynamical states during combustion instability.