Fluid Mechanics and Waves Seminar - Fall 2017

We present the development of an accurate and efficient multiscale, short-crested gravity wave model. A key component of the investigation involves an exploration into atmospheric turbulence along with the wind-driven water waves it generates. In particular, we examine the local distribution of turbulence along a space-time path rather than that of traditional spatial distributions. These temporal distributions are functions of a set of so-called characteristic variables, which represent the large scale dynamics of the space-time region under consideration. Through the use of a self-affine coherent structure, we “pave” large scale averages of atmospheric velocity and pressure to construct a wind curve whose fractal dimension is consistent with theory and observation. The kernel provides exact perturbation relations for the characteristic frequency and variance of the wind-sea. This immediately gives rise to an expression for the local pressure in terms of the kinetic energy of the atmosphere, which serves as an initiator of the transfer of energy across the air-sea interface. We cement this energy transfer mechanism in terms of the dispersion relation and group velocity of the inchoate water-waves, providing unambiguous local source terms for a system of frequency-integrated balance equations—equations that preserve discrete spectral moments of the short-crested gravity waves—in which the solution is more tractable than that of traditional, frequency-resolving spectral methods. We discretize the high-frequency wave model with the use of unstructured Runge-Kutta discontinuous Galerkin (RKDG) finite element methods, where all the primary variables including the integrated direction of the moment field use discontinuous polynomial spaces of arbitrary order. Hindcasts over Lake Erie evaluate the wind-sea assumptions inherent to the model and preliminary results indicate that this frequency-integrated approach runs almost 40 times as fast as a discrete spectral model while producing similar error measures.

With the introduction of high-performance and nano-scale CMOS technologies, silicon has made its foray into very high speed and millimeter wave applications. Wireless data links including chip-to-chip and base-station to base-station have standards in the 60GHz band. Si-based receivers and transmitters are being developed for automotive radar, atmosphere monitoring and medical applications in the 60GHz to 100GHz range.

It is well known that Maxwell’s equations can fully describe the physics of these problems. The difficulty lies in adapting the current generation of Electro Magnetic (EM) tools to accurately and efficiently solve the problems. Quasi-static approximations simply do not suffice. Meshing of structures being simulated needs to be fine enough to capture the very small skin depth at these frequencies. The challenge lies in the implementation of the 3D full-wave Electro Magnetic (EM) solvers which can correctly model the effects accurately and efficiently. We describe the use of the EMX 3D simulator to model these high frequency effects. We describe how the fast multipole method (FMM) algorithm can be very efficient for even solving the problems arising from the large problems and dense meshing that arise from the solution at high frequencies. We describe some novel features of the formulation and advances in numeric techniques that allow the simulator to be accurate and fast enough to be used extensively in industry. The solver is two orders of magnitude faster than the finite-element based solvers that were previously widely used. Several designs, fabricated on a variety of process technologies will be presented with comparisons to measurement.

Starting as a new post doctor at NJIT I will give a talk about the research I performed during my PhD thesis at the University of Oslo in Norway. The PhD thesis focused on the propagation of surface gravity waves on deep water.

Dispersion is a fundamental property of surface gravity waves on deep water. The simplest and most widely used theory is linear wave theory which assumes that the linear dispersion relation is satisfied. In the talk I will start with presenting experiments from a long and narrow wavetank at the University of Oslo showing that the linear dispersion relation is not satisfied when a random unidirectional wave field of weakly nonlinear waves has high steepness and narrow bandwidth. For broad bandwidths, however, the experiments are in better agreement with linear theory. Unidirectional simulations of the Zakharov equation were also performed and compared well with the experiments. Next I will present numerical simulations of directional waves using the nonlinear Schrödinger equation and the modified nonlinear Schrödinger equation. These simulations also show deviation from the linear dispersion relation when the bandwith is narrow. Data from the wave basin at the Marine Research Institute of Netherlands were also analyzed and agreed with the numerical simulations.

At last I will revisit the experiments. By computing the coherence and phase of the experimental data I will show that the coherence and phase of the experimental waves deviates from linear wave theory when the bandwidth is narrow while for broad bandwidths the experiments are in better agreement with linear theory. Simulations of the modified nonlinear Schrödinger equation were also performed and agreed with the experiments.

Development of This is an industrial fluid mechanics flow problem. In this talk it will be shown how nonlinear evolution equation for film thickness can be obtained from Navier-Stokes equation and its nonlinear boundary conditions (due to deformation of the free surface). Finally, the entire system of equations will be solved analytically by using the singular perturbation technique and the method of characteristics. The results will show an initially non-uniform distributed film will produce a planar film at large time while initial planar film remains planar. Bingham plastic liquid will produce faster thin film in compare to Newtonian fluid.odified Bingham Plastic Liquid Film Over an Unsteady Stretching Sheet

It is an interesting and often open problem to prove shape theorems for the range of self-interacting random walks. Internal Diffusion Limited Aggregation (IDLA) on the lattice can be viewed as the growing range of a random walk each time after exiting the current range gets transported to the origin. In the variant called Uniform IDLA, the walker instead gets transported to a uniform point inside the current range, after each exit. In both models the limiting shape of the range is proven to be a Euclidean ball. Kozma conjectured that for the model where the walker is excited towards the origin (no matter how this is interpreted) every time it exits the current range, a shape theorem should also exist.

Motivated by this, we constructed a lattice free model of random growth in the Euclidean space and allowed for other probability distributions driving the particle's exit from domain and relocation after the exit. For this model we prove a hydrodynamic limit which allows us to obtain a shape theorem. When the exit distribution is given by harmonic measure (from inside), which corresponds to the original problem, the conjecture is still unsolved.

We will discuss advances and difficulties on this problem.

Understanding the breakup of a liquid film is complicated by the fact that there is no obvious instability driving breakup: surface tension favors a film of uniform thickness over a deformed one. Here, we identify two mechanisms driving a film toward (infinite time) pinch-off. In the first problem, we show how the rise of a bubble is arrested in a narrow tube, on account of the lubricating film pinching off. In the second problem, breakup of a free liquid film is driven by a strong temperature gradient across the pinch region.

In this talk, I will present new central and central DG schemes for solving ideal magnetohydrodynamic (MHD) equations while preserving globally divergence-free magnetic field on triangular grids. These schemes incorporate the constrained transport (CT) scheme of Evans and Hawley with central schemes and central DG methods on overlapping cells which have no need for solving Riemann problems across cell edges where there are discontinuities of the numerical solution. The schemes are formally second-order accurate with major development on the reconstruction of globally divergence-free magnetic field on polygonal dual mesh. Moreover, the computational cost is reduced by solving the complete set of governing equations on the primal grid while only solving the magnetic induction equation on the polygonal dual mesh.