Time-Dependent 2-D Vector Field Topology: An Approach Inspired by Lagrangian Coherent Structures

This paper presents an approach to a time-dependent variant of the concept of vector field topology for 2-D vector fields. Vector field topology is defined for steady vector fields and aims at discriminating the domain of a vector field into regions of qualitatively different behaviour. The presented approach represents a generalization for saddle-type critical points and their separatrices to unsteady vector fields based on generalized streak lines, with the classical vector field topology as its special case for steady vector fields. The concept is closely related to that of Lagrangian coherent structures obtained as ridges in the finite-time Lyapunov exponent field. The proposed approach is evaluated on both 2-D time-dependent synthetic and vector fields from computational fluid dynamics

Numerical simulation of roughness effects on the flow past a circular cylinder

In the present work large eddy simulations of the flow past a rough cylinder are performed at a Reynolds number of Re = 4.2 × 105 and an equivalent sand-grain surface roughness height ks = 0.02D. In order to determine the effects of the surface roughness on the boundary layer transition and as a consequence on the wake topology, results are compared to those of the smooth cylinder. It is shown that surface roughness triggers the transition to turbulence in the boundary layer, thus leading to an early separation caused by the increased drag and momentum deficit. Thus, the drag coefficient increases up to CD 1.122 (if compared to the smooth cylinder it should be about CD 0.3 - 0.5). The wake topology also changes and resembles more the subcritical wake observed for the smooth cylinder at lower Reynolds numbers than the expected critical wake at this Reynolds number.Peer ReviewedPostprint (author's final draft

Solving the incompressible surface Navier-Stokes equation by surface finite elements

We consider a numerical approach for the incompressible surface Navier-Stokes equation on surfaces with arbitrary genus $g(\mathcal{S})$. The approach is based on a reformulation of the equation in Cartesian coordinates of the embedding $\mathbb{R}^3$, penalization of the normal component, a Chorin projection method and discretization in space by surface finite elements for each component. The approach thus requires only standard ingredients which most finite element implementations can offer. We compare computational results with discrete exterior calculus (DEC) simulations on a torus and demonstrate the interplay of the flow field with the topology by showing realizations of the Poincar\'e-Hopf theorem on $n$-tori

Discrete exterior calculus (DEC) for the surface Navier-Stokes equation

We consider a numerical approach for the incompressible surface Navier-Stokes equation. The approach is based on the covariant form and uses discrete exterior calculus (DEC) in space and a semi-implicit discretization in time. The discretization is described in detail and related to finite difference schemes on staggered grids in flat space for which we demonstrate second order convergence. We compare computational results with a vorticity-stream function approach for surfaces with genus 0 and demonstrate the interplay between topology, geometry and flow properties. Our discretization also allows to handle harmonic vector fields, which we demonstrate on a torus.Comment: 21 pages, 9 figure

Scientific Visualization Using the Flow Analysis Software Toolkit (FAST)

Over the past few years the Flow Analysis Software Toolkit (FAST) has matured into a useful tool for visualizing and analyzing scientific data on high-performance graphics workstations. Originally designed for visualizing the results of fluid dynamics research, FAST has demonstrated its flexibility by being used in several other areas of scientific research. These research areas include earth and space sciences, acid rain and ozone modelling, and automotive design, just to name a few. This paper describes the current status of FAST, including the basic concepts, architecture, existing functionality and features, and some of the known applications for which FAST is being used. A few of the applications, by both NASA and non-NASA agencies, are outlined in more detail. Described in the Outlines are the goals of each visualization project, the techniques or 'tricks' used lo produce the desired results, and custom modifications to FAST, if any, done to further enhance the analysis. Some of the future directions for FAST are also described

HydroSHEDS

HydroSHEDS (Hydrological data and maps based on SHuttle Elevation Derivatives at multiple Scales) is a mapping product that provides hydrographic information for regional and global-scale applications in a consistent format. Derived from elevation data of the Shuttle Radar Topography Mission (SRTM), the application offers users a suite of geo-referenced data sets (vector and raster), including stream networks, watershed boundaries, drainage directions, and ancillary data layers such as flow accumulations, distances, and river topology information. Educational levels: Middle school, High school, Undergraduate lower division, Undergraduate upper division, Graduate or professional