Steady fluid flows have very special topology. In this paper we describe necessary and sufficient conditions on the vorticity function of a 2D ideal flow on a surface with or without boundary, for which there exists a steady flow among isovorticed fields. For this we introduce the notion of an antiderivative (or circulation function) on a measured graph, the Reeb graph associated to the vortici...

The effects of an oscillatory zero-net-mass-flux jet (i.e. synthetic jet) acting on a separated flow over a hump are investigated in terms of two actuation parameters – actuator position and forcing frequency. By considering the vorticity flux balance and introducing a centroid of vorticity production over the hump surface, lift and drag acting on the hump can be expressed as a function of this...

The maximum principle is an important property of solutions to PDE. Correspondingly, it’s of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving(MPP) high order finite volume(FV) WENO s...

In this study, a composite system made of multiple porous block structure used for flow and heat transfer control will be analyzed. The primary objective of this study is to analyze the changes in the flow pattern and heat transfer characteristics due to the existence of the multiple porous block structure. A general flow model that accounts for the effects of the impermeable boundary and inert...

The long-time stability properties of a few multistep numerical schemes for the two-dimensional incompressible Navier–Stokes equations (formulated in vorticity-stream function) are investigated in this article. These semi-implicit numerical schemes use a combination of explicit Adams–Bashforth extrapolation for the nonlinear convection term and implicit Adams–Moulton interpolation for the visco...

A new approach to consider balance dynamics for modelling slow vortical motion is suggested within the rotating shallow water primitive equations. Instead of a traditional approach using divergence and ageostrophic vorticity as fast variables, the velocity is exactly expressed as a sum of the gradient part, described by a Bernoulli function, and the rest, an agradient part, proportional to the ...

A Green's function for a generalized two-dimensional (2D) fluid in an unbounded domain (the so-called α turbulence system) is discussed. The generalized 2D fluid is characterized by a relationship between an advected quantity q and the stream function ψ : namely, q=-(-Δ){α/2}ψ . Here, α is a real number and q is referred to as the vorticity. In this study, the Green's function refers to the str...

[1] The modification of near‐surface near‐inertial oscillations (NIOs) by the geostrophic vorticity is studied globally from an observational standpoint. Surface drifter are used to estimate NIO characteristics. Despite its spatial resolution limits, altimetry is used to estimate the geostrophic vorticity. Three characteristics of NIOs are considered: the relative frequency shift with respect t...

A numerical investigation has been performed to study the effect of eccentricity on unsteady state, laminar aiding mixed convection in a horizontal concentric and eccentric cylindrical annulus. The outer cylinder was kept at constant temperaturewhile inner heated with heat flux. involved solution transient momentum (Navier-Stokes) energy equation using finite difference method (FDM), where body...

We derive the vorticity equation for an incompressible fluid on a two-dimensional surface with arbitrary topology, embedded in three-dimensional Euclidean space and arising from first integral of flow, by using tailored Clebsch parameterization velocity field. In inviscid limit, we identify conserved energy enstrophy obtain corresponding noncanonical Hamiltonian structure. then discuss formulat...