arXiv subjects

Rama Govindarajan

Publications and source records attributed to Rama Govindarajan.

At least 55 records · Page 3Linked to original sources

arXiv2018

Spatio-temporal Patterns of Indian Monsoon Rainfall

The primary objective of this paper is to analyze a set of canonical spatial patterns that approximate the daily rainfall across the Indian region, as identified in the companion paper where we developed a discrete representation of the Indian summer monsoon rainfall using state variables with spatio-temporal coherence maintained using a Markov Random Field prior. In particular, we use these spatio-temporal patterns to study the variation of rainfall during the monsoon season. Firstly, the ten patterns are divided into three families of patterns distinguished by their total rainfall amount and geographic spread. These families are then used to establish `active' and `break' spells of the Indian monsoon at the all-India level. Subsequently, we characterize the behavior of these patterns in time by estimating probabilities of transition from one pattern to another across days in a season. Patterns tend to be `sticky': the self-transition is the most common. We also identify most commonly occurring sequences of patterns. This leads to a simple seasonal evolution model for the summer monsoon rainfall. The discrete representation introduced in the companion paper also identifies typical temporal rainfall patterns for individual locations. This enables us to determine wet and dry spells at local and regional scales. Lastly, we specify sets of locations that tend to have such spells simultaneously, and thus come up with a new regionalization of the landmass.

stat.AP↗

arXiv2018

Is there solid-on-solid contact in a sphere-wall collision in a viscous fluid?

We study experimentally the collision between a sphere falling through a viscous fluid, and a solid plate below. It is known that there is a well-defined threshold Stokes number above which the sphere rebounds from such a collision. Our experiment tests for direct contact between the colliding bodies, and contrary to prior theoretical predictions, shows that solid-on-solid contact occurs even for Stokes numbers just above the threshold for rebounding. The dissipation is fluid-dominated, though details of the contact mechanics depend on the surface and bulk properties of the solids. Our experiments and a model calculation indicate that mechanical contact between the two colliding objects is generic and will occur for any realistic surface roughness.

physics.flu-dyn↗

arXiv2016

Relaxation of a highly deformed elastic filament at a fluid interface

We perform experiments to investigate the relaxation of a highly deformed elastic filament at a liquid-air interface. The dynamics for filaments of differing length, diameter and elastic modulus collapse to a single curve when the time-dependence is scaled by a time scale $τ= 8 πμL_o^4/B$. The relaxation, however, is completed in a very small fraction of the time $τ$. Even though the time scale $τ$ can be obtained by balancing the linear bending and viscous forces, it appears to control the highly nonlinear regime of our experiments. Nonlinear numerical simulations show that the force due to tension along the filament is comparable to the bending force, producing a net elastic restoring force that is much smaller than either term. We perform particle image velocimetry at the liquid-air interface to support the results of the numerics. Finally, we find that when the filament is initialized in asymmetric shapes, it rapidly goes to a shape with symmetric stresses. This symmetrisation process is entirely non-linear; we show that the symmetric curvature state minimizes energy at arbitrarily large deformation.

physics.flu-dyn↗

arXiv2016

Algebraic disturbances and their consequences in rotating channel flow transition

It is now established that subcritical mechanisms play a crucial role in the transition to turbulence of non-rotating plane shear flows. The role of these mechanisms in rotating channel flow is examined here in the linear and nonlinear stages. Distinct patterns of behaviour are found: the transient growth leading to nonlinearity at low rotation rates $Ro$, a highly chaotic intermediate $Ro$ regime, a localised weak chaos at higher $Ro$, and complete stabilization of transient disturbances at very high $Ro$. At very low $Ro$, the transient growth amplitudes are close to those for non-rotating flow, but Coriolis forces already assert themselves by producing distinct asymmetry about the channel centreline. Nonlinear processes are then triggered, in a streak-breakdown mode of transition. The high $Ro$ regimes do not show these signatures, here the leading eigenmode emerges as dominant in the early stages. Elongated structures plastered close to one wall are seen at higher rotation rates. Rotation is shown to reduce non-normality in the linear operator, in an indirect manifestation of Taylor--Proudman effects. Although the critical Reynolds for exponential growth of instabilities is known to vary a lot with rotation rate, we show that the energy critical Reynolds number is insensitive to rotation rate. It is hoped that these findings will motivate experimental verification, and examination of other rotating flows in this light.

physics.flu-dyn↗

arXiv2016

Linear stability analysis and direct numerical simulation of two layer channel flow

We study the stability of two-fluid flow through a plane channel at Reynolds numbers of a hundred to a thousand in the linear and nonlinear regimes. The two fluids have the same density but different viscosities. The fluids, when miscible, are separated from each other by a mixed layer of small but finite thickness, across which viscosity changes from that of one fluid to that of the other. When immiscible, the interface is sharp. Our study spans a range of Schmidt numbers, viscosity ratios and location and thickness of the mixed layer. A region of instability distinct from that of the Tollmien-Schlichting mode is obtained at moderate Reynolds numbers. We show that the overlap of the layer of viscosity-stratification with the critical layer of the dominant disturbance provides a mechanism for this instability. At very low values of diffusivity, the miscible flow behaves exactly like the immiscible in terms of stability characteristics. High levels of miscibility make the flow more stable. At intermediate levels of diffusivity however, in both linear and non-linear regimes, miscible flow can be more unstable than the corresponding immiscible flow without surface tension.

physics.flu-dyn↗

arXiv2016

Dynamics of circular arrangements of vorticity in two dimensions

The merger of two like-signed vortices is a well-studied problem, but in a turbulent flow, we may often have more than two like-signed vortices interacting. We study the merger of three or more identical co-rotating vortices initially arranged on the vertices of a regular polygon. At low to moderate Reynolds numbers, we find an additional stage in the merger process, absent in the merger of two vortices, where an annular vortical structure is formed and is long-lived. Vortex merger is slowed down significantly due to this. Such annular vortices are known at far higher Reynolds numbers in studies of tropical cyclones, which have been noticed to a break down into individual vortices. In the pre-annular stage, vortical structures in a viscous flow are found here to tilt and realign in a manner similar to the inviscid case, but the pronounced filaments visible in the latter are practically absent in the former. Interestingly at higher Reynolds numbers, the merger of an odd number of vortices is found to proceed very differently from that of an even number. The former process is rapid and chaotic whereas the latter proceeds more slowly via pairing events. The annular vortex takes the form of a generalised Lamb-Oseen vortex (GLO), and diffuses inwards until it forms a standard Lamb-Oseen vortex. For lower Reynolds number, the numerical (fully nonlinear) evolution of the GLO vortex follows exactly the analytical evolution until merger. At higher Reynolds numbers, the annulus goes through instabilities whose nonlinear stages show a pronounced difference between even and odd mode disturbances. It is hoped that the present findings, that multiple vortex merger is qualitatively different from the merger of two vortices, will motivate studies on how multiple vortex interactions affect the inverse cascade in two-dimensional turbulence.

physics.flu-dyn↗

arXiv2016

Attraction-induced jamming in the flow of foam through a channel

We study the flow of a pressure-driven foam through a straight channel using numerical simulations, and examine the effects of a tuneable attractive potential between bubbles. This potential, which accounts for the effects of disjoining pressure in the liquid films between separating bubbles, is shown here to introduce jamming and stick-slip flow in a straight channel. We report on the behaviour of these new regimes by varying the strength of the attractive potential. It is seen that there is a force threshold below which the flow jams, and on increasing the driving force, a cross over from intermittent (stick-slip) to smooth flow is observed. This threshold force below which the foam jams increases linearly with the strength of the attractive potential. By examining the spectra of energy fluctuations, we show that stick-slip flow is characterized by low frequency rearrangements and strongly local behaviour, whereas steady flow shows a broad spectrum of energy drop events and collective behaviour. Our work suggests that the stick-slip and the jamming regimes occur due to the increased stabilization of contact networks by the attractive potential - as the strength of attraction is increased, bubbles are increasingly trapped within networks, and there is a decrease in the number of contact changes.

cond-mat.soft↗

arXiv2015

Caustics and clustering in the vicinity of a vortex

We study the formation of caustics in vortex-dominated \flows. We \find that only particles starting within a critical distance of a vortex which scales as the square roots of the particle inertia and the circulation can form sling caustics. We show that particles starting in an annular region around this critical radius contribute the densest clusters in the \flow. The large density spikes occurring for such particles, even at small inertia, are indicative that these particles will experience large collision rates.

physics.flu-dyn↗

arXiv2014

Do liquid drops roll or slide on inclined surfaces?

We study the motion of a two-dimensional droplet on an inclined surface, under the action of gravity, using a diffuse interface model which allows for arbitrary equilibrium contact angles. The kinematics of motion is analysed by decomposing the gradient of the velocity inside the droplet into a shear and a residual flow. This decomposition helps in distinguishing sliding versus rolling motion of the drop. Our detailed study confirms intuition, in that rolling motion dominates as the droplet shape approaches a circle, and the viscosity contrast between the droplet and the ambient fluid becomes large. As a consequence of kinematics, the amount of rotation in a general droplet shape follows a universal curve characterised by geometry, and independent of Bond number, surface inclination and equilibrium contact angle, but determined by the slip length and viscosity contrast. Our results open the way towards a rational design of droplet-surface properties, both when rolling motion is desirable (as in self-cleaning hydrophobic droplets) or when it must be prevented (as in insecticide sprays on leaves).

cond-mat.soft↗

arXiv2013

Attracting fixed points for heavy particles in the vicinity of a vortex pair

We study the behaviour of heavy inertial particles in the flow field of two like-signed vortices. In a frame co-rotating with the two vortices, we find that stable fixed points exist for these heavy inertial particles; these stable frame-fixed points exist only for particle Stokes number $St<St_{cr}$. We estimate $St_{cr}$ and compare this with direct numerical simulations, and find that the addition of viscosity increases the $St_{cr}$ slightly. We also find that the fixed points become more stable with increasing $St$ until they abruptly disappear at $St=St_{cr}$. These frame-fixed points are between fixed points and limit cycles in character.

physics.flu-dyn↗

arXiv2012

Oscillatory settling in wormlike-micelle solutions: bursts and a long time scale

We study the dynamics of a spherical steel ball falling freely through a solution of entangled wormlike-micelles. If the sphere diameter is larger than a threshold value, the settling velocity shows repeated short oscillatory bursts separated by long periods of relative quiescence. We propose a model incorporating the interplay of settling-induced flow, viscoelastic stress and, as in M. E. Cates, D. A. Head and A. Ajdari, Phys. Rev. E, 2002, 66, 025202(R) and A. Aradian and M. E. Cates, Phys. Rev. E, 2006, 73, 041508, a slow structural variable for which our experiments offer independent evidence.

cond-mat.soft↗

arXiv2010

Vortex shedding patterns, their competition, and chaos in flow past inline oscillating rectangular cylinders

The flow past inline oscillating rectangular cylinders is studied numerically at a Reynolds number representative of two-dimensional flow. A symmetric mode, known as S-II, consisting of a pair of oppositely-signed vortices on each side, observed recently in experiments, is obtained computationally. A new symmetric mode, named here as S-III, is also found. At low oscillation amplitudes, the vortex shedding pattern transitions from antisymmetric to symmetric smoothly via a regime of intermediate phase. At higher amplitudes, this intermediate regime is chaotic. The finding of chaos extends and complements the recent work of Perdikaris et al. [1]. Moreover it shows that the chaos results from a competition between antisymmetric and symmetric shedding modes. Rectangular cylinders rather than square are seen to facilitate these observations. A global, and very reliable, measure is used to establish the existence of chaos.

physics.flu-dyn↗

arXiv2008

Linear and Secondary Instabilities in Incompressible Axisymmetric Boundary Layers: Effect of Transverse Curvature

The incompressible boundary layer in the axial flow past a cylinder has been shown Tutty et. al.(\cite{tutty}) to be stabler than a two-dimensional boundary layer, with the helical mode being the least stable. In this paper the secondary instability of this flow is studied. The laminar flow is shown here to be always stable at high transverse curvatures to secondary disturbances, which, together with a similar observation for the linear modes implies that the flow past a thin cylinder is likely to remain laminar. The azimuthal wavenumber of the pair of least stable secondary modes ($m_+$ and $m_-$) are related to that of the primary ($n$) by $m_+=2n$ and $m_-=-n$. The base flow is shown to be inviscidly stable at any curvature.

physics.flu-dyn↗

arXiv2008

Random Vortex-Street Model for a Self-Similar Plane Turbulent Jet

We ask what determines the (small) angle of turbulent jets. To answer this question we first construct a deterministic vortex-street model representing the large scale structure in a self-similar plane turbulent jet. Without adjustable parameters the model reproduces the mean velocity profiles and the transverse positions of the large scale structures, including their mean sweeping velocities, in a quantitative agreement with experiments. Nevertheless the exact self similar arrangement of the vortices (or any other deterministic model) necessarily leads to a collapse of the jet angle. The observed (small) angle results from a competition between vortex sweeping tending to strongly collapse the jet and randomness in the vortex structure, with the latter resulting in a weak spreading of the jet.

nlin.CD↗

arXiv2006

Gravity-free hydraulic jumps and metal femtocups

Hydraulic jumps created by gravity are seen every day in the kitchen sink. We show that at small scales a circular hydraulic jump can be created in the absence of gravity, by surface tension. The theory is motivated by our experimental finding of a height discontinuity in spreading submicron molten metal droplets created by pulsed-laser ablation. By careful control of initial conditions, we show that this leads to solid femtolitre cups of gold, silver, copper, niobium and tin.

physics.flu-dyn↗

arXiv2006

The critical Reynolds number of a laminar mixing layer

It has hitherto been widely considered that a mixing layer is unstable at all Reynolds numbers. However this is untenable from energy considerations, which demand that there must exist a non-zero Reynolds number below which disturbances cannot extract energy from the mean flow. It is shown here that a linear stability analysis of similarity solutions of the plane mixing layer, including the effects of flow non-parallelism, using the minimal composite theory and the properties of adjoints following Govindarajan & Narasimha (2005), resolves the issue by yielding non-zero critical Reynolds numbers for coflowing streams of any velocity ratio. The critical Reynolds number so found, based on the vorticity thickness and the velocity differential as scales, varies in the narrow range of 59 to 55 as the velocity ratio goes from zero to unity.

physics.flu-dyn↗

arXiv2006

The effect of wall heating on instability of channel flow

A comprehensive study of the effect of wall heating or cooling on the linear, transient and secondary growth of instability in channel flow is conducted. The effect of viscosity stratification, heat diffusivity and of buoyancy are estimated separately, with some unexpected results. From linear stability results, it has been accepted that heat diffusivity does not affect stability. However, we show that realistic Prandtl numbers cause a transient growth of disturbances that is an order of magnitude higher than at zero Prandtl number. Buoyancy, even at fairly low levels, gives rise to high levels of subcritical energy growth. Unusually for transient growth, both of these are spanwise-independent and not in the form of streamwise vortices. At moderate Grashof numbers, exponential growth dominates, with distinct Rayleigh-Benard and Poiseuille modes for Grashof numbers upto $\sim 25000$, which merge thereafter. Wall heating has a converse effect on the secondary instability compared to the primary, destabilising significantly when viscosity decreases towards the wall. It is hoped that the work will motivate experimental and numerical efforts to understand the role of wall heating in the control of channel and pipe flows.

physics.flu-dyn↗

arXiv2006

The signature of laminar instabilities in the zone of transition to turbulence

We demonstrate that the space-time statistics of the birth of turbulent spots in boundary layers can be reconstructed qualitatively from the average behavior of macroscopic measures in the transition zone. The conclusion in \cite{vg04} that there exists a connection between the patterns in laminar instability and the birth of turbulent spots is strengthened. We examine why the relationship between instability and transition to turbulence is manifest in some cases and appears to be totally absent in others. Novel cellular automaton type simulations of the transition zone are conducted, and the pattern of spot birth is obtained from secondary instability analysis. The validity of the hypothesis of concentrated breakdown, according to which most turbulent spots originate at a particular streamwise location, is assessed. The predictions made lend themselves to straightforward experimental verification.

physics.flu-dyn↗