arXiv subjects

Rama Govindarajan

Publications and source records attributed to Rama Govindarajan.

At least 37 records · Page 2Linked to original sources

arXiv2022

The waltz of tiny droplets and the flow they live in

This article describes the dynamics of small inertial particles centrifuging out of a single vortex. It shows the importance of caustics formation in the vicinity of a single vortex: both for particle collisions and void formation. From these single-vortex studies we provide estimates of the role of caustics in high Reynolds number turbulence, and in the case of clouds, estimate how they may help in rain initiation by bridging the droplet-growth bottleneck. We briefly describe how the Basset- Boussinesq history force may be calculated by a method which does not involve huge memory costs, and provide arguments for its possible importance for droplets in turbulence. We discuss how phase change could render cloud turbulence fundamentally different from turbulence in other situations.

physics.flu-dyn↗

arXiv2022

Effects of equatorially-confined shear flow on MRG and Rossby waves

Linear modal stability analysis of a mean zonal shear flow is carried out in the framework of rotating shallow water equations (RSWE), both under the $β$-plane approximation and in the full spherical coordinate system. Two base flows -- equatorial easterly (EE) and westerly (EW) -- with Gaussian profiles highly confined to small latitudes are analyzed. At low Froude number, mixed Rossby-gravity (MRG) and Rossby waves are found to be particularly affected by shear, with prominent changes at higher wavenumbers. These waves become practically non-dispersive at large wavenumbers in EE. The perturbations are found to be more confined equatorially in EE than in EW with the degree of confinement being more pronounced in the $β$-plane system compared to the full spherical system. At high Froude number, the phase speeds are significantly larger in the $β$-plane system for all families of waves. Under the $β$-plane approximation, exponentially unstable modes can be excited, having negative (positive) phase speed in EE (EW). Strikingly, this flow is always neutrally stable with the full spherical system. This speaks for the importance of studying the whole spherical system even for equatorially confined shear.

physics.flu-dyn↗

arXiv2022

Spirographic motion in a vortex

Studies of particle motion in vortical flows have mainly focused on point-like particles, either inertial or self-propelled. This approximation assumes that the velocity field that surrounds the particle is linear. We consider an inertialess rigid dumbbell in a two-dimensional steady vortex. While the system remains analytically tractable, the particle experiences the nonlinearity of the surrounding velocity field. By exploiting the rotational symmetry of the flow, we reduce the problem to that of a two-dimensional dynamical system, whose fixed points and periodic orbits can be used to explain the motion of the dumbbell. For all vortices in which the fluid angular velocity decreases with radial distance, the center of mass of the dumbbell follows a spirographic trajectory around the vortex center. This results from a periodic oscillation in the radial direction combined with revolution around the center. The shape of the trajectory depends strongly on the initial position and orientation of the dumbbell, but the dynamics is qualitatively the same irrespective of the form of the vortex. If the fluid angular velocity is not monotonic, the spirographic motion is altered by the existence of transport barriers, whose shape is now sensitive to the details of the vortex.

physics.flu-dyn↗

arXiv2021

Accurate solution method for the Maxey-Riley equation, and the effects of Basset history

The Maxey-Riley equation has been extensively used by the fluid dynamics community to study the dynamics of small inertial particles in fluid flow. However, most often, the Basset history force in this equation is neglected. Including the Basset force in numerical solutions of particulate flows involves storage requirements which rapidly increase in time. Thus the significance of the Basset history force in the dynamics has not been understood. In this paper, we show that the Maxey-Riley equation in its entirety can be exactly mapped as a forced, time-dependent Robin boundary condition of the one-dimensional heat equation, and solved using the Unified Transform Method. We obtain the exact solution for a general homogeneous time-dependent flow field, and apply it to a range of physically relevant situations. In a particle coming to a halt in a quiescent environment, the Basset history force speeds up the decay as stretched-exponential at short time while slowing it down to a power-law relaxation, $\sim t^{-3/2}$, at long time. A particle settling under gravity is shown to relax even more slowly to its terminal velocity ($\sim t^{-1/2}$), whereas this relaxation would be expected to take place exponentially fast if the history term were to be neglected. For a general flow, our approach makes possible a numerical scheme for arbitrary but smooth flows without increasing memory demands and with spectral accuracy. We use our numerical scheme to solve an example spatially varying flow of inertial particles in the vicinity of a point vortex. We show that the critical radius for caustics formation shrinks slightly due to history effects. Our scheme opens up a method for future studies to include the Basset history term in their calculations to spectral accuracy, without astronomical storage costs. Moreover our results indicate that the Basset history can affect dynamics significantly.

physics.flu-dyn↗

arXiv2021

Instability driven by settling and evaporation in a shear flow: a model for asperitas clouds

We study, by direct numerical simulations in two and three dimensions, the instability caused by the settling and evaporation of water droplets out of a cloudy layer saturated with vapour into a dry sub-cloud ambient, under conditions where mammatus clouds were shown to form by [1], but with the addition of background shear. We show that shear changes the type of cloud formation qualitatively, from mammatus-like to a newly identified cloud type called asperitas. Intermediate levels of shear are shown to be needed. Shear suppresses the growth of small-scale perturbations, giving rise to smooth, long-lasting structures, and smaller rates of mixing. Three-dimensionality is shown to make a qualitative difference, unlike in mammatus clouds. We also show that under non-cloud-like conditions, the instability can be very different.

physics.flu-dyn↗

arXiv2021

Transport of condensing droplets in Taylor-Green vortex flow in the presence of thermal noise

We study the role of phase change and thermal noise in particle transport in turbulent flows. We employ a toy model to extract the main physics: condensing droplets are modelled as heavy particles which grow in size, the ambient flow is modelled as a two-dimensional Taylor-Green (TG) flow consisting of an array of vortices delineated by separatrices, and thermal noise are modelled as uncorrelated Gaussian white noise. In general, heavy inertial particles are centrifuged out of regions of high vorticity and into regions of high strain. In cellular flows, we find, in agreement with earlier results, that droplets with Stokes numbers smaller than a critical value, $St < St_{\rm{cr}}$, remain trapped in the vortices in which they are initialised, while larger droplets move ballistically away from their initial positions by crossing separatrices. We independently vary the Péclet number $Pe$ characterising the amplitude of thermal noise and the condensation rate $Π$ to study their effects on the critical Stokes number for droplet trapping, as well as on the final states of motion of the droplets. We find that the imposition of thermal noise, or of a finite condensation rate, allows droplets of $St < St_{\rm{cr}}$ to leave their initial vortices. We find that the effects of thermal noise become negligible for growing droplets, and that growing droplets achieve ballistic motion when their Stokes numbers become $\mathcal{O}(1)$. We also find an intermediate regime prior to attaining the ballistic state, in which droplets move diffusively away from their initial vortices in the presence of thermal noise.

physics.flu-dyn↗

arXiv2021

Shapes of a filament on the surface of a bubble

The shape assumed by a slender elastic structure is a function both of the geometry of the space in which it exists and the forces it experiences. We explore by experiments and theoretical analysis, the morphological phase-space of a filament confined to the surface of a spherical bubble. The morphology is controlled by varying bending stiffness and weight of the filament, and its length relative to the bubble radius. When the dominant considerations are geometry of confinement and elastic energy, the filament lies along a geodesic and when gravitational energy becomes significant, a bifurcation occurs, with a part of the filament occupying a longitude and the rest along a curve approximated by a latitude. Far beyond the transition, when the filament is much longer than the diameter, it coils around the selected latitudinal region. A simple model with filament shape as a composite of two arcs captures the transition well and for better quantitative agreement with the subcritical nature of bifurcation, we study the morphology by numerical energy minimization. Our analysis of filament's morphological space spanned by a geometric parameter, and one that compares elastic energy with body forces, may provide guidance for packing slender structures on complex surfaces.

cond-mat.soft↗

arXiv2021

Virus transmission by aerosol transport during short conversations

Pathogens like the SARS-CoV-2 are transmitted not only through violent expiratory events like coughing, but also through routine activities like breathing/speaking/singing. We perform direct numerical simulations of the turbulent transport of potentially infectious aerosols in short conversations. It is shown that a two-way conversation significantly reduces the aerosol exposure compared to a relative monologue by one person and relative silence of the other. This is because the interaction of the jets ejected from the mouth of each speaker produce a "canceling" effect. Unequal conversation is shown to significantly increase the risk of infection to the person who talks less. Interestingly, a small height difference is worse for infection spread, due to reduced interference between the two speech jets, than two faces at the same level! For small axial separation, speech jets show large oscillations and reach the other person intermittently. We suggest a range of lateral separations between two people to minimize transmission risk. A realistic estimate of the infection probability is provided by including exposure through eyes and mouth, in addition to the more common method of using inhaled virions alone. We expect that our results will provide useful inputs to epidemiological models and to disease management.

physics.flu-dyn↗

arXiv2021

Surface tension as the destabiliser of a vortical interface

We study the dynamics of an initially flat interface between two immiscible fluids, with a vortex situated on it. We show how surface tension causes vorticity generation at a general curved interface. This creates a velocity jump across the interface which increases quadratically in time, and causes the Kelvin-Helmholtz instability. Surface tension thus acts as a destabiliser by vorticity creation, winning over its own tendency to stabilize by smoothing out interfacial perturbations to reduce surface energy. We further show that this instability is manifested within the vortex core at times larger than $\sim (k We)^{1/4}$ for a Weber number $We$ and perturbation wavenumber $k$, destroying the flow structure. The vorticity peels off into small-scale structures away from the interface. Using energy balance we provide the growth with time in total interface length. A density difference between the fluids produces additional instabilities outside the vortex core due to centrifugal effects. We demonstrate the importance of this mechanism in two-dimensional turbulence simulations with a prescribed initial interface. We show an increase in kinetic energy at large wave numbers due to the creation of small-scale vortices by the action of surface tension.

physics.flu-dyn↗

arXiv2021

Fluid dynamics in clouds: The sum of its parts

This entry is aimed at describing cloud physics with an emphasis on fluid dynamics. As is inevitable for a review of an enormously complicated problem, it is highly selective and reflects of the authors' focus. The range of scales involved, and the relevant physics at each scale is described. Particular attention is given to droplet dynamics and growth, and turbulence with and without thermodynamics.

physics.flu-dyn↗

arXiv2020

Wetting and wrapping of a floating droplet by a thin elastic filament

We study the wetting of a thin elastic filament floating on a fluid surface by a droplet of another, immiscible fluid. This quasi-2D experimental system is the lower-dimensional counterpart of the wetting and wrapping of a droplet by an elastic sheet. The simplicity of this system allows us to study the phenomenology of partial wetting and wrapping of the droplet by measuring angles of contact as a function of the elasticity of the filament, the applied tension and the curvature of the droplet. We find that a purely geometric theory gives a good description of the mechanical equilibria in the system. The estimates of applied tension and tension in the filament obey an elastic version of the Young-Laplace-Dupré relation. However, curvatures close to the contact line are not captured by the geometric theory, possibly because of 3D effects at the contact line. We also find that when a highly-bendable filament completely wraps the droplet, there is continuity of curvature at the droplet-filament interface, leading to seamless wrapping as observed in a 3D droplet.

cond-mat.soft↗

arXiv2020

Spatio-temporal relationships between rainfall and convective clouds during Indian Monsoon through a discrete lens

The Indian monsoon, a multi-variable process causing heavy rains during June-September every year, is very heterogeneous in space and time. We study the relationship between rainfall and Outgoing Longwave Radiation (OLR, convective cloud cover) for monsoon between 2004-2010. To identify, classify and visualize spatial patterns of rainfall and OLR we use a discrete and spatio-temporally coherent representation of the data, created using a statistical model based on Markov Random Field. Our approach clusters the days with similar spatial distributions of rainfall and OLR into a small number of spatial patterns. We find that eight daily spatial patterns each in rainfall and OLR, and seven joint patterns of rainfall and OLR, describe over 90\% of all days. Through these patterns, we find that OLR generally has a strong negative correlation with precipitation, but with significant spatial variations. In particular, peninsular India (except west coast) is under significant convective cloud cover over a majority of days but remains rainless. We also find that much of the monsoon rainfall co-occurs with low OLR, but some amount of rainfall in Eastern and North-western India in June occurs on OLR days, presumably from shallow clouds. To study day-to-day variations of both quantities, we identify spatial patterns in the temporal gradients computed from the observations. We find that changes in convective cloud activity across India most commonly occur due to the establishment of a north-south OLR gradient which persists for 1-2 days and shifts the convective cloud cover from light to deep or vice versa. Such changes are also accompanied by changes in the spatial distribution of precipitation. The present work thus provides a highly reduced description of the complex spatial patterns and their day-to-day variations, and could form a useful tool for future simplified descriptions of this process.

physics.ao-ph↗

arXiv2020

Early evolution of optimal perturbations in a viscosity-stratified channel

This work shows how the early stages of perturbation growth in a viscosity-stratified flow are different from those in a constant-viscosity flow, and how nonlinearity is a crucial ingredient. We derive the viscosity-varying adjoint Navier-Stokes equations, where gradients in viscosity force both the adjoint momentum and the adjoint scalar (here temperature). By the technique of direct-adjoint looping, we obtain the nonlinear optimal perturbation which maximises the perturbation kinetic energy of the nonlinear system. While we study three-dimensional plane Poiseuille (channel) flow with the walls at different temperatures, and a temperature-dependent viscosity, our findings are general for any flow with viscosity variations near walls. The Orr and modified lift-up mechanisms are in operation at low and high perturbation amplitudes respectively at our subcritical Reynolds number. The nonlinear optimal perturbation contains more energy on the hot (less-viscous) side, with a stronger initial lift-up. However, as the flow evolves, the important dynamics shifts to the cold (more-viscous) side, where wide high-speed streaks of low viscosity grow and persist, and strengthen the inflectional quality of the velocity profile. We provide a physical description of this process, and show that the evolution of the linear optimal perturbation misses most of the physics. The Prandtl number does not qualitatively affect the findings at these times. The study of nonlinear optimal perturbations is still in its infancy, and viscosity variations are ubiquitous. We hope that this first work on nonlinear optimal perturbation with viscosity variations will lead to wider studies on transition to turbulence in these flows.

physics.flu-dyn↗

arXiv2020

Waves, Algebraic Growth and Clumping in Sedimenting Disk Arrays

An array of spheres descending slowly through a viscous fluid always clumps [J.M. Crowley, J. Fluid Mech. {\bf 45}, 151 (1971)]. We show that anisotropic particle shape qualitatively transforms this iconic instability of collective sedimentation. In experiment and theory on disks, aligned facing their neighbours in a horizontal one-dimensional lattice and settling at Reynolds number $\sim 10^{-4}$ in a quasi-two-dimensional slab geometry, we find that for large enough lattice spacing the coupling of disk orientation and translation rescues the array from the clumping instability. Despite the absence of inertia the resulting dynamics displays the wavelike excitations of a mass-and-spring array, with a conserved "momentum" in the form of the collective tilt of the disks and an emergent spring stiffness from the viscous hydrodynamic interaction. However, the non-normal character of the dynamical matrix leads to algebraic growth of perturbations even in the linearly stable regime. Stability analysis demarcates a phase boundary in the plane of wavenumber and lattice spacing, separating the regimes of algebraically growing waves and clumping, in quantitative agreement with our experiments. Anisotropic shape thus suppresses the classic linear instability of sedimenting sphere arrays, introduces a new conserved variable, and opens a window to the physics of transient growth of linearly stable modes.

cond-mat.soft↗

arXiv2019

Statistics of Lagrangian Trajectories in a Rotating Turbulent Flow

We investigate the Lagrangian statistics of three-dimensional rotating turbulent flows through direct numerical simulations. We find that the emergence of coherent vortical structures because of the Coriolis force leads to a suppression of the "flight-crash" events reported by Xu, et al. [Proc. Natl. Acad. Sci. (U.S.A) 111, 7558 (2014)]. We perform systematic studies to trace the origins of this suppression in the emergent geometry of the flow and show why such a Lagrangian measure of irreversibility may fail in the presence of rotation.

physics.flu-dyn↗

arXiv2019

Understanding droplet collisions through a model flow: Insights from a Burgers vortex

We investigate the role of intense vortical structures, similar to those in a turbulent flow, in enhancing collisions (and coalescences) which lead to the formation of large aggregates in particle-laden flows. By using a Burgers vortex model, we show, in particular, that vortex stretching significantly enhances sharp inhomogeneities in spatial particle densities, related to the rapid ejection of particles from intense vortices. Furthermore our work shows how such spatial clustering leads to an enhancement of collision rates and extreme statistics of collisional velocities. We also study the role of poly-disperse suspensions in this enhancement. Our work uncovers an important principle which, {if valid for realistic turbulent flows, may be a factor in} how small nuclei water droplets in warm clouds can aggregate to sizes large enough to trigger rain.

physics.flu-dyn↗

arXiv2019

Flow structures govern particle collisions in turbulence

The role of the spatial structure of a turbulent flow in enhancing particle collision rates in suspensions is an open question. We show and quantify, as a function of particle inertia, the correlation between the multiscale structures of turbulence and particle collisions: Straining zones contribute predominantly to rapid head-on collisions compared to vortical regions. We also discover the importance of vortex-strain worm-rolls, which goes beyond ideas of preferential concentration and may explain the rapid growth of aggregates in natural processes, such as the initiation of rain in warm clouds.

physics.flu-dyn↗

arXiv2018

A Discrete View of the Indian Monsoon to Identify Spatial Patterns of Rainfall

We propose a representation of the Indian summer monsoon rainfall in terms of a probabilistic model based on a Markov Random Field, consisting of discrete state variables representing low and high rainfall at grid-scale and daily rainfall patterns across space and in time. These discrete states are conditioned on observed daily gridded rainfall data from the period 2000-2007. The model gives us a set of 10 spatial patterns of daily monsoon rainfall over India, which are robust over a range of user-chosen parameters as well as coherent in space and time. Each day in the monsoon season is assigned precisely one of the spatial patterns, that approximates the spatial distribution of rainfall on that day. Such approximations are quite accurate for nearly 95% of the days. Remarkably, these patterns are representative (with similar accuracy) of the monsoon seasons from 1901 to 2000 as well. Finally, we compare the proposed model with alternative approaches to extract spatial patterns of rainfall, using empirical orthogonal functions as well as clustering algorithms such as K-means and spectral clustering.

stat.AP↗