arXiv subjects

Haithem E. Taha

Publications and source records attributed to Haithem E. Taha.

4 recordsLinked to original sources

arXiv2026

Is No-Slip Necessary for Vorticity Generation and Shedding over a Circular Cylinder?

It is traditionally believed that the no-slip boundary condition is necessary for vorticity generation, as might be implied by the Lighthill vorticity generation mechanism. However, the investigations of Morton (1984) and Terrington et al. (2020) assert that the vorticity-generation mechanism is independent of the no-slip boundary condition. To investigate this hypothesis, we simulate viscous flow over a circular cylinder in the laminar periodic von Kármán vortex-shedding regime at Re = 170, without enforcing the no-slip condition at the wall. Instead, we close the wall tangential velocity and its normal derivative using one-sided finite-difference approximations. Accordingly, the wall tangential velocity is dynamically determined from the evolving interior solution rather than prescribed. The resulting flows exhibit qualitatively similar patterns of periodic vortex shedding across all three wall treatments (no-slip, second- and third-order one-sided approximations), although the mean drag coefficient, r.m.s. lift coefficient, and Strouhal number differ from those of the standard no-slip simulation. More significantly, the velocity distributions just outside the boundary layer closely match those of the standard no-slip simulation, regardless of the approximation order. In particular, the circulation evaluated along a contour at the edge of the boundary layer, which corresponds to the total vorticity contained within the layer in the no-slip case, is found to be remarkably insensitive to the wall treatment. These results suggest that the no-slip condition is not necessary for vorticity generation or periodic shedding. However, it may still be required for accurate quantitative prediction of the integral flow quantities and shedding dynamics.

physics.flu-dyn↗

arXiv2023

Vortex Dynamics: A Variational Approach Using the Principle of Least Action

The study of vortex dynamics using a variational formulation has an extensive history and a rich literature. The standard Hamiltonian function that describes the dynamics of interacting point vortices of constant strength is the Kirchhoff-Routh (KR) function. This function was not obtained from basic definitions of classical mechanics (i.e., in terms of kinetic and potential energies), but it was rather devised to match the already known differential equations of motion for constant-strength point vortices given by the Bio-Savart law. Instead, we develop a new variational formulation for vortex dynamics based on the principle of least action. As an application, we consider a system of non-deforming, free vortex patches of constant-strength. Interestingly, the obtained equations of motion are second-order differential equations defining vortex accelerations, not velocities. In the special case of constant-strength point vortices, the new formulation reduces to the motion determined from the KR function. However, for finite-core vortices, the resulting dynamics are more complex than those obtained from the KR formulation. For example, a pair of equal-strength, counter-rotating vortices could be initialized with different velocities, resulting in interesting patterns which cannot be handled by the KR approach. Also, the developed model easily admits external body forces (e.g., electromagnetic). The interaction between the electrodynamic force and the hydrodynamic vortex force leads to a rich, counter-intuitive behavior that could not be handled by the KR formulation. Finally, this new variational formulation, which is derived from first principles in mechanics, can be easily extended to deforming and/or arbitrary time-varying vortices.

physics.flu-dyn↗

arXiv2022

What Does Nature Minimize In Every Incompressible Flow?

In this paper, we discover the fundamental quantity that Nature minimizes in almost all flows encountered in everyday life: river, rain, flow in a pipe, blood flow, airflow over an airplane, etc. We show that the norm of the pressure gradient over the field is minimum at every instant of time! We call it the principle of minimum pressure gradient (PMPG). The principle is deeply rooted in classical mechanics via Gauss' principle of least constraint. Therefore, while we prove mathematically that Navier-Stokes' equation represents the necessary condition for minimization of the pressure gradient, the PMPG stands on its own philosophy independent of Navier-Stokes'. It turns any fluid mechanics problem into a minimization one. We demonstrate this intriguing property by solving three of the classical problems in fluid mechanics using the PMPG without resorting to Navier-Stokes' equation. In fact, the inviscid version of the PMPG allowed solving the long-standing problem of the aerohydrodynamic lift over smooth cylindrical shapes where Euler's equation fails to provide a unique answer. Moreover, the result challenges the accepted wisdom about lift generation on an airfoil, which has prevailed over a century. The PMPG is expected to be transformative for theoretical modeling of fluid mechanics as it encodes a complicated nonlinear partial differential equation into a simple minimization problem. The principle even transcends Navier-Stokes' equations in its applicability to non-Newtonian fluids with arbitrary constitutive relations and fluids subject to arbitrary forcing (e.g. electric or magnetic).

physics.flu-dyn↗

arXiv2021

A Variational Theory of Lift

In this paper, we revive a special, less-common, variational principle in analytical mechanics (Hertz' principle of least curvature) to develop a novel variational analogue of Euler's equations for the dynamics of an ideal fluid. The new variational formulation is fundamentally different from those formulations based on Hamilton's principle of least action. Using this new variational formulation, we generalize the century-old problem of the flow over a two-dimensional body, to find that lift is a direct consequence of curvature. The developed variational principle reduces to the classical Kutta-Zhukovsky condition in the special case of a sharp-edged airfoil, which challenges the accepted wisdom about the Kutta condition being a manifestation of viscous effects. Rather, we found that it represents conservation of momentum. Moreover, the developed variational principle provides, for the first time, a theoretical model for lift over smooth shapes without sharp edges where the Kutta condition is not applicable. We discuss how this fundamental divergence from current theory can explain discrepancies in computational studies and experiments with superfluids.

physics.flu-dyn↗