ICTS

1. A. P. Baburaj

On separating plumes from boundary layers in turbulent convection

We present a simple criterion to separate plumes from boundary layers using only the velocity field in turbulent convection, which is very advantageous to use in PIV studies of the near-plate dynamics of turbulent convection. We first show qualitatively that the criteria for detecting coherent structures from wall shear turbulence are inadequate for this task. Based on the physical picture of the distinction between a plume and a boundary layer, we propose that the negative values of the horizontal divergence of the horizontal velocity field close to the hot surface separates plumes from the boundary layers. The criterion is then verified by comparing the length and the area ratio of the plumes obtained by the criteria with the expected value from theoretcal understanding as well as from other criteria that uses temperature fields. The consequences of using such a criteria on understanding the velocity field close to the hot surface is then discussed.

 

2. A. Sameen

Mixing in lid rotating Rayleigh-Benard convection

TBA

 

3. Abhishek Kumar

Energy spectra and fluxes of buoyancy-driven flows

Buoyancy-induced flows come in two categories: stably stratified flows and Rayleigh-Bénard convection (RBC). Turbulent aspects of these flows are an active field of research. An important unsolved problem in this field is how to quantify the small-scale quantities, e.g., spectra and fluxes of kinetic energy (KE) and potential energy (PE) of these flows. Using direct numerical simulations performed at high resolution, we demonstrate that the stably stratified turbulence at moderate stratification exhibits Bolgiano-Obukhov scaling, due to the conversion of kinetic energy to potential energy via buoyancy. We show that the KE flux decreases with the wavenumber (k) which yield k^{-11/5} and k^{-7/5} scaling for KE and PE spectra respectively. For RBC, we performed simulation at grid resolution 4096^3 on a cubical box and have shown a delicate balance of dissipation and energy supply rate by buoyancy. This balance leads to a constant KE flux and rules out the Bolgiano-Obukhov scaling, and we observe Kolmogorov’s spectrum ^[1-3].

References:

1. Kumar, Chatterjee, and Verma, Phys. Rev. E, 90, 023016 (2014).
2. Kumar and Verma, Phys. Rev. E, 91, 043014 (2015).
3. Verma, Kumar, and Pandey, New J. Phys., 19, 025012 (2017).

 

4. Ambrish Pandey

Turbulent superstructures in Rayleigh-Benard convection

In thermal convection, the large-scale patterns of the temperature and velocity field in horizontally extended cells are termed as the turbulent superstructures^[1]. We study the formation of turbulent superstructures in Rayleigh-Bénard convection^[2] by performing direct numerical simulations in a rectangular box of dimensions 25:25:1 for Prandtl numbers Pr = 0.021, 0.7, 7, and for Rayleigh number Ra ≥ 10^5 using a spectral element solver Nek5000^{[3, 4]}. The simulation domain is divided into a finite number of elements and the turbulent fields are spectrally expanded using Lagrangian interpolation polynomials on the basis of Legendre functions. We conduct the statistical analysis of the spatial correlation scales and fluctuations. The temperature field is diffused for small Prandtl number, whereas thermal structures become sharper with increasing Prandtl number. We detect defects in the mean patterns of temperature and velocity field, and observe that their dynamics evolve on a time scale of the order of a vertical diffusive time for all the Prandtl numbers. We also study the variation of turbulent transport of heat and momentum with varying Prandtl and Rayleigh numbers.

1. M. S. Emran and J. Schumacher, J. Fluid Mech., 776, 96–108, 2015.
2. F. Chillà and J. Schumacher, Eur. Phys. J. E, 35, 58, 2012.
3. P. F. Fischer, J. Comp. Phys., 133 (1), 84–101, 1997.
4. J. D. Scheel, M. S. Emran, and J. Schumacher, New J. Phys., 15, 113063, 2013.

 

5. Anirban Guha

Canonical Hamiltonian understanding of stratified flows

We show that the equations of interacting waves in stratified shear flows become the canonical Hamilton equations, where the pseudo-energy serves as the Hamiltonian of the system. The contributions of each wave to the pseudo-momentum are the generalized momenta, and the the waves' phases, scaled by the wavenumber, are the generalized coordinates. The conservation of pseudo-momentum and pseudo-energy in the linearized system reflects the growth mechanism of counter-propagating waves via action-at-a-distance. The subset of the linearized dynamical system, consisting of only these counter-propagating waves, reduces the complexity of the dynamics by factor $2$ while preserving the canonical Hamiltonian form.

 

6. Avishek Ranjan

Inernally-driven inertial waves in geodynamo simulations

A. Ranjan^[1], P. A. Davidson^[1], U. R. Christensen^[2], J. Wicht^{[2] [1]}Department of Engineering, University of Cambridge, UK ^[2]Max Planck Institute for Solar system research, Gottingen, Germany

Inertial waves are oscillations in a rotating fluid, such as the Earth's core, which result from the restoring action of the Coriolis force and the conservation of angular momentum. Low-frequency inertial waves, with group velocity nearly aligned to the rotation axis, are known to create columnar flow structures from localized blobs of buoyancy (an initial value problem with no imposed time-scale). Columnar vortices vertically spanning much of the core are a robust feature of many geodynamo simulations with rapid rotation. These are often interpreted in terms of columnar eigen-modes of convection, steady solutions of a boundary-value problem(BVP) in a sphere. However, the turbulent convection dynamics in the core is likely to be unsteady and the assumptions in the BVP are hardly justified for the core. Could it be that the mechanism of structure formation that is applicable in the case of localized buoyant blobs is alsoimportant in the core, given that a preferential concentration of buoyancy near the equator is predicted to exist? We identify internally-driven inertial waves in a geodynamo simulation at high Rayleigh number (42 times supercritical) and low Ekman number E=3x10^-5. We use the MagIC pseudo-spectral DNS code which solves the Navier-Stokes equations, coupled with the magnetic-induction and temperature equations, in the Boussinesq approximation for a rotating, electrically-conducting fluid in a spherical shell representative of core's geometry. Using cylindrical co-ordinates, we study the time-series of (a) azimuthal temperature gradient and (b) a time-derivative of vertical velocity (dw/dt). In these results, we find internally-driven inertial waves triggered by buoyant anomalies near the equator. These are low-frequency inertial waves which propagate vertically upwards (downwards) north (south) of the equator on a fast time-scale. We find that the slopes observed in the time-series of dw/dt match closely with those expected from the group speed of low-frequency inertial waves. Moreover, the spectrum of dw/dt lies in the inertial wave frequency range. Our results suggest that the columnar flow in the rotation-dominated core, an important ingredient for the maintenance of the dipolar magnetic field, is driven and maintained on a fast-time scale by low-frequency, internally-driven inertial waves.

 

7. Binod Sreenivasan

Confinement of rotating convection by a laterally varying magnetic field: Implications for the Earth's tangent cylinder

We examine the onset of convection in a rapidly rotating fluid layer subject to a laterally varying axial magnetic field. The inhomogeneity of the field gives rise to a unique mode of instability where convection is entirely confined to the peak-field region. The localization of the flow by the magnetic field occurs when the field strength (measured by the Elsasser number) is small and viscosity controls the smallest length scale of convection. The localized excitation of viscous-mode convection by a laterally varying magnetic field provides a mechanism for the formation of isolated off-axis plumes within Earth's tangent cylinder. The polar vortices in the Earth's core may therefore be non-axisymmetric. 

 

8. Bipin Kumar

Droplet dynamics in cloud turbulence: A numerical investigation

A 3D direct numerical simulation (DNS) of cloud droplet has been carried out to study variation of droplet size distribution (DSD) of monsoon convective clouds during their developmental stage. DNS is performed for Eulerian description of velocity, temperature and vapour fields in combination with Lagrangian ensembles of cloud droplets in a decaying turbulence. Initial conditions are taken from airborne observation during Cloud Aerosol Interaction and Precipitation Enhancement EXperiment (CAIPEEX). 

Evaporation at the cloud-edges initiates mixing at small scale and gradually introduces larger-scale fluctuations of the temperature, moisture, and vertical velocity due to droplet evaporation. Our focus is on early evolution of simulated fields that show intriguing similarities to the CAIPEEX cloud observations. A strong dilution at the cloud edge, accompanied by significant spatial variations of the droplet concentration, mean radius, and spectral width, are found in both the DNS and in observations.

DSDs in the cloud edges and the cloud core from both the simulation and CAIPEEX showed considerable similarities in their microphysical nature and the mixing characteristics despite a large variation in spatial range. For high resolution observations, distribution of mean radii (rm) matches with that obtained from DNS. Furthermore, at cloud edges, a bimodal DSD is obtained from both DNS and observation. This bi-modality is due to partial evaporation of droplets as they are subjected to mixing.

 

9. Jayant Bhattacharjee

Scales and scaling in turbulence is stably stratified fluids

TBA

 

10. Jaywant Arakeri

​Rayleigh-Benard convection and axially homogeneous convection: comparison

TBA

 

11. K. R. Sreenivas

Convection in the Nocturnal Surface Layer: Stability and Impact on Micro-meteorology

TBA

 

12. Kamal Kant Chandrakar

Experimental investigation of cloud formation and growth in turbulent moist convection: turbulence induced droplet activation and growth

Clouds are an important element of the Earth system; they play a significant role in the earth’s radiation budget, and in the hydrological cycle. They are a large-scale moist convection system with flow properties in the turbulent regime. Interestingly, turbulent fluctuations affect the cloud droplet growth in both phases: I) Condensation growth, II) Collisional growth. However, in the recent past, most attention has been on droplet inertial effects on the collision process in a turbulent environment. Effects of turbulent scalar fluctuations, like water vapor concentration and temperature field on the droplet activation and condensation growth process also require attention. We have investigated these processes experimentally in the Michigan Tech turbulent-cloud chamber (π-chamber) [1].

Cloud formation and growth in a turbulent environment is studied by creating turbulent moist Rayleigh- Bénard convection in the π-chamber [2]. Subsequently, cloud formation is achieved by injecting aerosols into the water-supersaturated environment created by the isobaric mixing of saturated air at different temperatures. In steady state, the injection and activation of aerosol particles to form cloud droplets is balanced by cloud droplet growth through condensation and subsequent loss by gravitational settling. A long steady cloud environment provides perfect condition for the droplet-turbulent interaction study. A range of steady-state droplet number concentrations is achieved by supplying aerosols at different rates. As steady-state droplet number concentration is decreased the mean droplet size increases as expected, but also the width of the size distribution increases. This increase in the width is associated with larger supersaturation fluctuations due to the slow droplet microphysical response (sink) compared to the fast turbulent mixing (source) [1]. Observed standard deviation of squared droplet radius follows a linear function of the combined time scale of the system (a combination of the phase relaxation time and the turbulence correlation time). A stochastic differential equation approach for turbulent supersaturation field also predicts the same linear response and agrees with the experimental observation. Similarly, from comparison between activated and injected aerosol size distribution, it was found that the droplet activation depends on both mean and fluctuations of the supersaturation [3]. As a result, influence of the turbulent fluctuations on these cloud microphysical processes affect precipitation and reflectivity of incoming solar radiation.

References:

1. Chandrakar, K.K., Cantrell, W., Chang, K., Ciochetto, D., Niedermeier, D., Ovchinnikov, M., Shaw, R.A. and Yang, F., 2016. Aerosol indirect effect from turbulence-induced broadening of cloud-droplet size distributions. Proceedings of the National Academy of Sciences, 113(50), pp.14243-14248.
2. Chang, K., Bench, J., Brege, M., Cantrell, W., Chandrakar, K., Ciochetto, D., Mazzoleni, C., Mazzoleni, L.R., Niedermeier, D. and Shaw, R.A., 2016. A laboratory facility to study gas-aerosol-cloud interactions in a turbulent environment: The Π Chamber. Bulletin of the American Meteorological Society, (2016), 97, 2343–2358.
3. Chandrakar, K. K., Cantrell, W., Ciochetto, D., Karki, S., Kinney, G., & Shaw, R. A. (2017). Aerosol removal and cloud collapse accelerated by supersaturation fluctuations in turbulence. Geophysical Research Letters, doi: :10.1002/2017GL072762.

 

13. Kirti Chandra Sahu

The dynamics of rising bubbles and falling drops

The dynamics of a rising air bubble and a falling drop in another medium is investigated numerically and experimentally. A phase plot in the Gallilei (Ga) and Eotvos (Eo) numbers plane, which separates four distinct regions in terms of bubble behaviour, namely axisymmetric, skirted, spiralling and break-up regions is presented. The experimental results are compared with those of numerical simulations to show the similarities and differences. The behaviour of a rising bubble is also contrasted with that of a falling drop in terms of vortex shedding, shape and path instabilities. The effect of initial shape of a falling drop is also studied.

 

14. Mahendra Verma

Quantification of small-scales and large-scale turbulence in thermal convection

Thermal convection plays a major role in turbulence processes in the interiors and atmospheres of planets and stars. In this talk we present the current status of the turbulence phenomenology of turbulent thermal convection. Using pseudospectral simulations of turbulent thermal convection at very high resolution (4096^3) and high Rayleigh number(1.1 × 10^11) with unit Prandtl number, we conclude that convective turbulence exhibits behaviour similar to hydrodynamic turbulence, that is, Kolmogorov’s k^(−5/3) energy spectrum with nearly constant energy flux. The shell-to-shell energy transfer is forward and local, along with a nearly isotropic energy distribution in Fourier space. This result rules out Bolgiano-Obukhov spectrum for thermal convection. We also compute the rms values of various terms of the momentum equation of turbulent convection. We show that the acceleration of a fluid parcel is provided primarily by the pressure gradient; the buoyancy and viscous term are quite close to each other. Thus, in convective turbulence, the effect of buoyancy is annulled by viscous force, leading to behaviour similar to hydrodynamic turbulence (Kolmogorov’s theory).

References: M. K. Verma, A. Kumar, and A. Pandey, New J. Phys. 19, 025012 (2017).

 

15. Mani Mathur

Modelling internal gravity waves for oceanic applications

TBA

 

16. Pankaj Kumar Mishra

Dynamics of the density of the quantized vortex lines in superfluid turbulence

Quantum turbulence is associated with the turbulence behaviour shown by the superfluid helium (⁴He) at low temperature due to the presence of quantized vortices. ⁴He exhibits a superfluid behaviour below a critical temperature called as the lambda transition point. At a low but finite temperature, the flow of this fluid can be described as an intimate mixture of two fluids, which are mutually coupled to each other. One of the fluid component is a superfluid having a zero viscosity while the other component is a normal viscous fluid. In the experiment it is observed that as the superfluid is subject under a constant temperature gradient along the horizontal direction of a channel the normal component flows along the gradient direction while the superfluid component flows in the opposite direction to conserve the mass of the flow. The turbulence behaviour shown by this configuration of the flow is termed as “counterflow turbulence”. As the counter flow velocity, which is the difference in the velocity of the normal and superfluid component, is increased the flow undergoes through different states. For low counter flow velocity (known as T-I state) the normal component remains laminar, while superfluid component becomes turbulent. However, for large counter flow velocity (also known as T-II state) both normal and superfluid component becomes turbulent. The detailed structure of the velocity components in these states and their coupling with the quantized vortices are not clear.

In this talk we will present our recent numerical results on the dynamics of the density of the quantized vortex tangles for the two cases of the normal component of the superfluid helium flow in a channel. In the first case we consider the time frozen parabolic profile of the normal component and study its effect on the steady state behaviour of the quantized tangle. Based upon our numerical observation we propose a phenomenological model for the production and decay of the density of the quantized vortex tangle that show a significant deviation from the Vinen’s model [1]. In the second case we consider the coupled dynamics of normal and superfluid component in which the normal component can evolve with time. We calculate the profiles of the normal velocity, the mutual friction, the vortex line density and other flow properties and compared them to the case where the dynamic of the normal component is “frozen”. We have found that the coupling between the normal and superfluid components leads to flattening of the normal velocity profile, increasingly more pronounced with temperature, as the mutual friction, and therefore, coupling becomes stronger [2].

1. D. Khomenko, L. Kondaurova, V. S. L’vov, P. Mishra, A. Pomyalov, I. Procaccia, Phys. Rev. B 91 180504 (R) (2015).
2. D. khomenko, P. Mishra, A. Pomyalov, J. Low Temp Phys 187, 405 (2017).

 

17. Prateek Sharma

TBA

 

18. R Lakkaraju

In-line moving bubbles in a column

Briefly: Our investigations on moving in-line pair of unequal size bubbles shows hairpin-like and toroidal-like vortex structures in the liquid wake. Bubbles undergo vigorous shape oscillations and sway in lateral directions while rising in the quiscent liquid columns. The trailing bubble always speeds-up in the leading bubble's wake and the observed speed-up depends on the gravity level.

The rise and deformation of a pair of unequal sized bubbles released in-line with a finite vertical separation in a column of quiescent liquid under varying gravity levels are numerically studied using one-fluid model coupled with volume-of-fluid technique. The bubble and liquid medium are considered incompressible and immiscible. The leading and trailing bubbles have showed non-spherical shape during their ascent, though initially released as sphere. Simulations are performed for the bubble Archimedes numbers 320 < Ar < 5200, the Eotvos numbers 0.4 < Eo < 64, and the Morton numbers M o < 10 −9 . The trailing bubble always accelerates in the leading bubble’s wake and finally coalesces. Vigorous shape oscillations are observed during the bubble merging stage and the resultant bubble rises with lateral sways. The rise velocity ratio of the trailing bubble to the leading bubble increases with the gravity level and the ratio shows a power-law scaling with time, i.e., v v L s ∝ t α , with α > 0. The scaling exponent α ≈ 2 at higher gravity levels. The trailing bubble acceleration is connected with hair-pin like vortex structures generated on the leading bubble’s rear side which create upward moving jets. The leading bubble (which is big in size) always has a strong-short wake, compared to the trailing bubble with a weak-long wake. The initially quiescent liquid gets churned due to bubbles rise and the volume averaged liquid kinetic energy shows interesting power-law scaling behavior with time and the exponent saturates to a value 0.6 with increase in the gravity level.

 

19. R. Narasimha

The cumulus cloud as a transient diabatic plume

TBA

 

20. Rama Govindrarajan

Vortices driving droplets driving buoyancy driving vortices

In the flow of a fluid containing a dilute suspension of small particulate matter, the fluid flow dictates the dynamics of the particles in a one-way coupling. For example such particles would be slowly centrifuged out of the vicinity of a vortex, and preferentially cluster outside. If the particles are water droplets however, and are suspended in air supersaturated in water vapour, such clustering results in non-uniform condensation, and therefore an inhomogeneous temperature distribution. In a model system we show that the dynamics of vortices is changed significantly due to the buoyancy. We also show that the determining parameter is the product of the time scales of particle inertia and condensation.

 

21. Richard Stevens

Superstructures in Rayleigh-Benard convection

In this talk I will present a study of the heat transfer and the flow structures that are formed in Rayleigh-Benard convection in very large aspect ratio cells. We consider three-dimensional direct numerical simulations (DNS) in a laterally periodic geometry with aspect ratios up to \Gamma=128 in the Rayleigh number range Ra=10^7-10^9. We find, similarly as in other wall bounded flows such as pipe and channel flow, that the large scale flow structures change significantly with increasing aspect ratio due to the formation of superstructures in the large aspect ratio regime. Up to an aspect ratio of about 8 we find the formation of one large scale flow structure. For larger boxes we find the formation of multiple of these extremely large convection rolls. The results will be illustrated by movies of horizontal cross-section of the bulk and the boundary layer and analyze them by using spectra in the boundary layer and the bulk. In addition, we study the effect of the large scale flow structures on the mean and higher order temperature and velocity statistics in the boundary layer and the bulk by comparing the simulation results obtained in different aspect ratio boxes.

 

22. S. F. Anwer

LES of stably stratified turbulent channel flow

TBA

 

23. Sudhakar Subudhi

Rayleigh-Benard convection in Nanofluids

The nanosized solid particles (nanoparticles) having a particle size in the range of 1-100 nm, blended with the base fluid by different techniques is called nanofluids. An important feature to use nanofluids is an ability to adjust the thermal (thermal conductivity) and physical properties (size, shape, wettability) by changing parameters of nanofluid synthesis for innumerable applications. Some of the key areas of nanofluid applications are nuclear systems, cooling, electronics cooling, microfluidic, nanofluidic, drug delivery, solar water application and so on. The main objective of this topic is to investigate the Rayleigh – Bénard convection in an alumina-water (Al₂O₃/Water) nanofluid filled cavity. The dependency of the Nusselt number on the particle size, particle concentration, aspect ratio and Rayleigh number for Al₂O₃/Water nanofluids is investigated. Also, the empirical correlations to predict the variation of natural convection heat transfer in Al₂O₃/DW nanofluids with respect to particle concentration, particle size and Rayleigh number are developed. Finally, the mechanisms responsible for the enhancement or deterioration of heat transfer in Al₂O₃/DW nanofluids is studied by applying the statistical analysis.

 

24. Thara Prabhakaran

Mini-convective layer during fog

TBA

 

25. Vishal Vasan

Analysis of an instability in density stratified flows

In this talk I will highlight some recent developments in the analysis of partial differential equations and instability theory. As a motivating example, I will consider a typical shear flow instability in viscous density stratified fluids. The main thrust of the talk is three key points: i) a non-traditional formulation of the fluid instability problem, (ii) the translation of the instability problem to a related one, (iii) the analysis of the related instability problem. The final point will motivate a discussion and review of a body of literature developed in the last three decades in the field of partial differential equations. Time permitting, I will briefly present some other fluid instability problems that are also of interest and amenable to the techniques presented in this talk.