I wanted to know what a point vortex would do near a corner with an arbitrary angle. Time to dust off the complex analysis! A really useful summary of using complex analysis to model potential flow is here. I will use the method of images to ensure that there is no flow through the wall, […]

# Category: fluids

I want to have the ink on a photo clump together, leading to a black and white image. This is a sort of flow, so my first thought isr to take a look at the advection-diffusion equation. Let’s say that the ink distribution across an image is , the diffusion factor is , and the […]

## Line Integral Convolution

Line integral convolution, or LIC, is a nice way to get a sense of the directions of a flow field. By averaging a noisy image along sections of streamlines, you get some nice streaks. Look at this example, applied to the flow around a spinning cylinder: There are a couple main parameters to tweak: the […]

## Evenly Spaced Streamlines

There’s a whole body of literature out there for illustrating vector fields. One topic is ‘evenly spaced streamlines’: lines that follow a direction field, and don’t get too close to each other. How do we do this? From a starting point, use the midpoint method to figure out the position of the next point. If […]

## Ph.D. Research: Problem Solving

A PhD is an exercise in learning to define and solve problems. This post will describe some of those problems and how I addressed them. I would have liked to see this sort of post back then, and hopefully this will give some idea of the process. This is, of course, very focused on experimental […]

## Proper Orthogonal Decomposition

Time for some competing acronyms. Fluids people like to call this technique Proper Orthogonal Decomposition (POD), statisticians call it Principal Component Analysis (PCA), and so on and so on. Whatever you want to call it, it’s basically an eigenvector decomposition of the data you toss into it. That means that it optimally splits the data […]

## Processing Vector Fields

In my PhD research, I had to deal with a lot of data. Particularly with movies of particles moving around in water. These movies were processed, via Particle Image Velocimetry, to give vector fields of the velocity in the flow. For an example, here’s some rough data that I took of a cylinder in flow, […]

## My PhD: Vortex Generation and Modeling

My PhD focused on the “Experimental Generation and Modeling of Vortical Gusts and Their Interactions with an Airfoil.” You can see my thesis here. I was interested in seeing the effect of a vortex interacting with a parallel wing. Most research on the topic has been based on helicopters or propellers, but those have periodically […]