1. Jets in crossflow 

 Numerical simulation of jet in weak crossflow (jet Re = 800. Simulations performed using GERRIS)

2. Particle-laden flows in the dilute suspension limit

The approach that is commonly followed to model the motion of  the particle phase is the method of local volume averaging. We provide a brief introduction to the idea of volume averaging here. In the method of local volume averaging, the Lagrangian description of the particles is converted into an Eulerian formulation resulting in an Eulerian particle velocity field and a volume fraction field.  The basic idea behind volume averaging is that the governing equations defined only for the continuous phase can be spatially smoothed, resulting in a set of equations that are valid for the dispersed phase as well. Here, locally , the value of the quantity of interest is the value of the quantity averaged over a certain number of particles contained in an "averaging volume".  The size of the averaging volume is such that it is much larger than the particle diameter and interparticle distance (interparticle here refers to the distance between two particles of the dispersed phase) while it is much smaller than the length scale over which there is macroscopic changes observed in the flow.  This ensures that there is scale separation and the averaging would make sense. The restriction of particle diameter being much smaller compared to the interparticle distance brings in the dilute suspension limit. The resulting equations on the coarsened (volume averaged) scale is the volume averaged equation (sometimes referred to as two-fluid equations) .

Using the method of volume averaging, the two fluid equations accounting for the two-way coupling term (in this case the Stokes drag) are derived. We linearize the system of equations and look for exponentially growing mode (in time) .  Please refer to my following papers for more. 

1.  Warrier, S., Hemchandra, S., & Tomar, G. (2023). Stability of a particle-laden planar jet in the dilute suspension limit. Physics of Fluids, 35(8). 

   2. Warrier, S., & Tomar, G. (2025). Center mode instability of a dilute particle-laden swirling jet in a swirl flow combustor. Physics of Fluids, 37(1).

 3.  Cloud microphysics

The problem of global climate modelling is a multiscale phenomenon involving length scales ranging from few microns to 1000km. Clouds are mainly composed of water droplets and ice particles. At small length scales, there are physical as well as chemical processes like cloud condensation nuclei (CCN) activation, condensation, evaporation, collision and coalescence of droplets,  which collectively referred to as cloud microphysics. The physics occurring at these length scales dictates the droplet size distribution evolution which in turn influences the precipitation of rain forming clouds.  At the other end of the length scale spectrum  is the physics occurring over large distances where the bulk motion of the clouds over thousands of km are important. For accurate numerical weather prediction, the cloud microphysics has to be parameterized into the existing weather prediction models. This requires a dedicated study of the cloud microphysics . 

  Manuscript under preparation