Dynamics

Chaos Theory.

Chaos is the science of surprises, of the nonlinear and the unpredictable. It teaches us to expect the unexpected. While most traditional science deals with supposedly predictable phenomena like gravity, electricity, or chemical reactions, Chaos Theory deals with nonlinear things that are effectively impossible to predict or control, like turbulence, weather, the stock market, our brain states, and so on. These phenomena are often described by Fractal Mathematics, which captures the Infinite Complexity of Nature. Many natural objects exhibit Fractal Properties, including landscapes, clouds, trees, organs, rivers etc, and many of the systems in which we live exhibit Complex, Chaotic behavior. Recognizing the Chaotic, Fractal Nature of our world can give us new insight, power, and wisdom. 

Principles of Chaos

The Butterfly Effect: This effect grants the power to cause a hurricane in China to a butterfly flapping its wings in New Mexico. It may take a very long time, but the connection is real. If the butterfly had not flapped its wings at just the right point in space/time, the hurricane would not have happened. A more rigorous way to express this is that small changes in the initial conditions lead to drastic changes in the results. Our lives are an ongoing demonstration of this principle. 

Unpredictability: Because we can never know all the initial conditions of a complex system in sufficient (i.e. perfect) detail, we cannot hope to predict the ultimate fate of a complex system. Even slight errors in measuring the state of a system will be amplified dramatically, rendering any prediction useless. Since it is impossible to measure the effects of all the butterflies (etc) in the world, accurate long-range weather prediction will always remain impossible.

Order / Disorder: Chaos is not simply disorder. Chaos explores the transitions between order and disorder, which often occur in surprising ways.

Mixing: Turbulence ensures that two adjacent points in a complex system will eventually end up in very different positions after some time has elapsed. 

Fractals: A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos. Geometrically, they exist in between our familiar dimensions. Fractal patterns are extremely familiar, since nature is full of fractals. For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc.

2

21/1/2016 - skipped school today because i wasn’t feeling so well. but hey look on the bright side!!!, at least i get to finish my physic flashcards at home!! ლ(╹◡╹ლ)

3

Spinflo

An interactive science toy that visualizes fluid dynamics when you apply force - video embedded below:

Spinflo is an interactive gadget that allows you to see patterns created by fluid in motion. By using the touch of your hand, you can create turbulent or smooth flows, spinning it in different directions with different speeds. The patterns are dynamic and intricate, and just plain fun to see!

You can find out more at the project website here, Kickstarter page here, and the Spinflo Tumblr here

The above image is the Kármán vortex street caused by wind flowing around the Juan Fernández Islands off the Chilean coast. It is a delight for the eyes, portraying the turbulent side of nature.


Vortex shedding

In fluid dynamics, vortex shedding is an oscillating flow that takes place when a fluid such as air or water flows past a bluff (as opposed to streamlined) body at certain velocities, depending on the size and shape of the body.

In this flow, vortices are created at the back of the body and detach periodically from either side of the body. These linear chain of spiral eddies are called von Karman vortice

                                                        Source

The fluid flow past the object creates alternating low-pressure vortices on the downstream side of the object. Ergo, the object will tend to move toward the low-pressure zone.

Airplanes and  Lift

The main thing to know is that a difference in pressure across the wing–low pressure over the top and higher pressure below–creates the net upward force we call lift.

Upon reaching a certain velocity, the aircraft’s lift is more than its weight and as a result, the aircraft takes off .


Vortex Induced Vibrations

When the vortices are not formed symmetrically around the body (with respect to its midplane), different lift forces develop on each side of the body, thus leading to motion transverse to the flow.

These are know in fluid dynamics as vortex-induced vibrations (VIV). They are important factor to be taken into consideration because constant vibration of any object leads to fatigue and eventually failure.

                                                          Source


Chimneys and their spiraled heads

Tall chimneys constructed of thin-walled steel tube can be sufficiently flexible that, in air flow with a speed in the critical range, vortex shedding can drive the chimney into violent oscillations that can damage or destroy the chimney.

They are  protected from this phenomenon by installing a series of fences (sometimes called strakes or spoilers) at the top and running down the exterior of the chimney for approximately 20% of its length. The fences are usually located in a helical pattern.

The fences prevent strong vortex shedding with low separation frequencies.

Final Thoughts

In this post i wanted to introduce you this amazing phenomenon that occurs in nature known as vortex shedding. We will look at the technical side of this phenomenon in another post. 

Have a great day!

EDIT: If this fascinated you,do check out this NASA article