fuckyeahfluiddynamics

fuckyeahfluiddynamics:

Reader 3d-time asks:

Hi, there is a guy, at my college, who is doing a master’s degree thesis in turbulence. He says he uses fractals and computational methods. Can you explain how fractals can be used in fluid dynamics?

That’s a good question! Fractals are a relatively recent mathematical development, and they have several features that make them an attractive tool, especially in the field of turbulence. Firstly, fractals, especially the Mandelbrot set shown above, demonstrate that great complexity can be generated out of simple rules or equations. Secondly, fractals have a feature known as self-similarity, meaning that they appear essentially the same regardless of scale. If you zoom in on the Mandelbrot set, you keep finding copy after copy of the same pattern. Nature, of course, doesn’t have this perfect infinite self-similarity; at some point things break down into atoms if you keep zooming in. But it is possible to have self-similarity across a large range of scales. This is where turbulence comes in. Take a look at the turbulent plume of the volcanic eruption in the photo above. Physically, it contains scales ranging from hundreds of meters to millimeters, and these scales are connected to one another by their motion and the energy being passed from one scale to another. There have been theories suggested to describe the relationship between these scales, but no one has yet found a theory truly capable of explaining turbulence as we observe it. Both the self-similarity and the complex nature of fractals suggest they could be useful tools in finally unraveling turbulence. In fact, Mandelbrot himself wrote several papers connecting the two concepts. Perhaps your friend will help find the next hints!  (Image credit: U.S. Geological Survey, Wikimedia)

peace-love-buddhism
mainebornandraised:

“So many people live within unhappy circumstances and yet will not take the initiative to change their situation because they are conditioned to a life of security, conformity, and conservatism, all of which may appear to give one peace of mind, but in reality nothing is more damaging to the adventurous spirit within a man than a secure future. The very basic core of a man’s living spirit is his passion for adventure. The joy of life comes from our encounters with new experiences and hence there is no greater joy than to have an endlessly changing horizon, for each day to have a new and different sun.”

—  Christopher McCandless / Into The Wild

mainebornandraised:

So many people live within unhappy circumstances and yet will not take the initiative to change their situation because they are conditioned to a life of security, conformity, and conservatism, all of which may appear to give one peace of mind, but in reality nothing is more damaging to the adventurous spirit within a man than a secure future. The very basic core of a man’s living spirit is his passion for adventure. The joy of life comes from our encounters with new experiences and hence there is no greater joy than to have an endlessly changing horizon, for each day to have a new and different sun.
—  Christopher McCandless / Into The Wild