We are interested in viscous effects on linear and nonlinear wave-phenomena. Such waves can occur at the interface of two im-miscible fluids e.g. an air-water interface. The oscillations may either occur on a base state of rest or one with flow and the resultant interface motion can be very complex due to the combined effect of viscosity and non-linearity. A lot of early theoretical work on capillary and gravity surface waves have used inviscid, irrotational equations (Laplace equation with nonlinear boundary conditions) combined with perturbation techniques to achieve significant progress in our theoretical understanding of waves and their stability. In the last two decades or so, algorithms (like VOF and level-set methods) for simulating these flows have enormously matured accompanied by numerical progress in accurate computation of surface curvatures (for solving surface tension dominated flows). It is now possible to simulate complex wave phenomena involving two phase flows with high density ratios like that of air-water involving high surface tension to good accuracy. This allows us to numerically investigate complex phenomena like droplet pinch-off, atomization, bubble entrainment, wave-breaking etc. through Direct Numerical Simulation of two phase flows. We develop in house computational tools and are actively involved in studying some of the above phenomena.  

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It is known that the interface between two viscous fluids can act as a source of vorticity. An oscillating interface (under the restoring forces of gravity and/or surface tension) produces a boundary layer around itself and the motion of the interface is coupled to this boundary layer. In two dimensions and for small wave amplitudes, this layer grows by diffusion. Our current research tries to understand the effect of vorticity on these oscillations especially in the large amplitude non linear regime [2]. We have an in house developed Volume Of Fluid based Navier Stokes solver using which we are  investigating such and related free and forced oscillation problems.

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In another study, we have numerically discovered stationary wave patterns downstream of standing hydraulic jumps in 2D Cartesian geometries. These hydraulic jumps occur on films which are so thin that the boundary layer is as thick as the film itself. Thus there is vorticity in the entire fluid layer. Interestingly we find vortices underneath each crest for the first few oscillations. Despite the strong effect of vorticity, we find that Benjamin & Lighthill's Q, R and S framework (coefficients of the KdV equation) for describing inviscid, irrotational non-linear waves remains relevant to these stationary wave patterns as well [1].

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Publications: 

3. Axisymmetric viscous interfacial oscillations - Theory and simulations, Palas Kumar Farsoiya, Y. S. Mayya and Ratul Dasgupta,
   J. Fluid Mech. (In press) , 2017.

2. Numerical simulation of laminar, standing hydraulic jumps in a planar geometry, Ratul Dasgupta, Gaurav Tomar and Rama Govindarajan,    Eur. Phys. J. E , 2015, 38 (5).

1. Viscous standing capillary waves - Linear and nonlinear regime, Palas Kumar Farsoiya and Ratul Dasgupta, Presented at the 6th      International and 43rd National Conference on Fluid Mechanics and Fluid Power, MNIT Allahabad, Dec. 2016.