Featured Research

from universities, journals, and other organizations

Turbulent flows in 2-d can be calculated in new model

Date:
October 23, 2012
Source:
University of Copenhagen
Summary:
Turbulent flows have challenged researchers for centuries. It is impossible to predict chaotic weather more than a week in advance. Wind resistance on a plane cannot be calculated precisely, since it is determined by atmospheric turbulence. Now, however, researchers have succeeded in developing a statistical model that can replicate the chaotic flows and thereby provide a better understanding of the process.

Turbulent motion is chaotic, and even the largest computers can only reproduce this approximately. The motion of the atmosphere, the winds, is highly two-dimensional. The vertical motion of the air is about 1000 times smaller than the horizontal motion. Now scientists have developed a new statistical model of the behavior of turbulence in two-dimensions, which gives a better understanding of the process.
Credit: Peter Ditlevsen, Niels Bohr Institute

Turbulent flows have challenged researchers for centuries. It is impossible to predict chaotic weather more than a week in advance. Wind resistance on a plane or a car cannot be calculated precisely, since it is determined by atmospheric turbulence. Now, however, researchers from the Niels Bohr Institute have succeeded in developing a statistical model that can replicate the chaotic flows and thereby provide a better understanding of the process.

The research results are published in the scientific journal Physics of Fluids.

"Without knowing the movements in detail, we know that they happen in such a way that the kinetic energy is conserved," explains Peter Ditlevsen, a research associate professor at the Niels Bohr Institute at the University of Copenhagen. He explains that when a liquid or air is set in motion, for example, if you create large eddies in a bathtub by stirring the water, it will transpire, that when you stop stirring, smaller and smaller eddies will continue to be created, while the large ones slowly die out. Finally, the movement in the smallest eddies are converted into heat. The entire process is called an energy cascade from large scales to small scales and is absolutely fundamental for understanding chaotic turbulent flow.

If the motion is limited to only being able to take place on a single plane, that is, two dimensions (2D), instead of in a volume, that is, three dimensions (3D), it will happen quite differently. The reason is that the flow cannot release its energy as small eddies cannot easily be formed in two dimensions. In two dimensions, both the energy and eddy density (which is called enstrophy) is retained in the flow, unlike in three dimensions, where only the energy is preserved.

Complicated calculations in 3D

A complex motion equation that has been known for almost 200 years, the so-called Navier-Stokes equation, is used to calculate the air's turbulent 3D movements. But even the world's most powerful computers, which have been dedicated to just this purpose, can only provide an approximate solution to the equation.

In order to describe the turbulent cascade processes, the researchers have therefore developed simplified mathematical models that are much easier to fully investigate in with computer calculations. The models have the same behaviour as the Navier-Stokes equation, but the models have not been able to reproduce the so-called inverse cascade in 2D.

Until now, the models have been too limited to show both the eddy density cascades down to small scales and the energy cascades up to large scales. They have been able to simulate the one cascade or the other, but not both simultaneously.

Simpler calculations in 2D

However, Peter Ditlevsen has now succeeded in developing such a cascade model that can reproduce the double cascade process in 2D turbulence.

"Turbulence can occur as a somewhat exotic phenomena. Though not in this case: Motion in the atmosphere, the wind and the weather is largely two-dimensional. The movements on the vertical axis are 100 to 1000 times less than those on the horizontal axis. The air has a much more difficult time moving vertically, so the movement of the weather systems movement is two-dimensional turbulence. This means that it is possible to predict the weather a ways ahead of time. If the movement had been three-dimensional, it would be dominated by small eddies, which are completely unpredictable, like when you see autumn leaves randomly floating around in a courtyard," explains Peter Ditlevsen.

The turbulent flows occur over a vast span of scales, so when researchers want to understand the processes, they have to study simplified models.

"With the new model of the two-dimensional turbulence we are one step closer to understanding which factors in the motion equations govern how energy is distributed in the flow," explains Peter Ditlevsen.


Story Source:

The above story is based on materials provided by University of Copenhagen. Note: Materials may be edited for content and length.


Journal Reference:

  1. Peter D. Ditlevsen. A stochastic model of cascades in two-dimensional turbulence. Physics of Fluids, 2012; 24 (10): 105109 DOI: 10.1063/1.4761834

Cite This Page:

University of Copenhagen. "Turbulent flows in 2-d can be calculated in new model." ScienceDaily. ScienceDaily, 23 October 2012. <www.sciencedaily.com/releases/2012/10/121023112513.htm>.
University of Copenhagen. (2012, October 23). Turbulent flows in 2-d can be calculated in new model. ScienceDaily. Retrieved July 23, 2014 from www.sciencedaily.com/releases/2012/10/121023112513.htm
University of Copenhagen. "Turbulent flows in 2-d can be calculated in new model." ScienceDaily. www.sciencedaily.com/releases/2012/10/121023112513.htm (accessed July 23, 2014).

Share This




More Matter & Energy News

Wednesday, July 23, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

Government Approves East Coast Oil Exploration

Government Approves East Coast Oil Exploration

AP (July 18, 2014) The Obama administration approved the use of sonic cannons to discover deposits under the ocean floor by shooting sound waves 100 times louder than a jet engine through waters shared by endangered whales and turtles. (July 18) Video provided by AP
Powered by NewsLook.com
Sunken German U-Boat Clearly Visible For First Time

Sunken German U-Boat Clearly Visible For First Time

Newsy (July 18, 2014) The wreckage of the German submarine U-166 has become clearly visible for the first time since it was discovered in 2001. Video provided by Newsy
Powered by NewsLook.com
Obama: U.S. Must Have "smartest Airports, Best Power Grid"

Obama: U.S. Must Have "smartest Airports, Best Power Grid"

Reuters - US Online Video (July 17, 2014) President Barak Obama stopped by at a lunch counter in Delaware before making remarks about boosting the nation's infrastructure. Mana Rabiee reports. Video provided by Reuters
Powered by NewsLook.com
Crude Oil Prices Bounce Back After Falling Below $100 a Barrel

Crude Oil Prices Bounce Back After Falling Below $100 a Barrel

TheStreet (July 16, 2014) Oil Futures are bouncing back after tumbling below $100 a barrel for the first time since May yesterday. Jeff Grossman is the president of BRG Brokerage and trades at the NYMEX. Grossman tells TheStreet the Middle East is always a concern for oil traders. Oil prices were pushed down in recent weeks on Libya increasing its production. Supply disruptions in Iraq fading also contributed to prices falling. News from China's economic front showing a growth for the second quarter also calmed fears on its slowdown. Jeff Grossman talks to TheStreet's Susannah Lee on this and more on the Energy Department's Energy Information Administration (EIA) report. Video provided by TheStreet
Powered by NewsLook.com

Search ScienceDaily

Number of stories in archives: 140,361

Find with keyword(s):
Enter a keyword or phrase to search ScienceDaily for related topics and research stories.

Save/Print:
Share:

Breaking News:
from the past week

In Other News

... from NewsDaily.com

Science News

Health News

Environment News

Technology News



Save/Print:
Share:

Free Subscriptions


Get the latest science news with ScienceDaily's free email newsletters, updated daily and weekly. Or view hourly updated newsfeeds in your RSS reader:

Get Social & Mobile


Keep up to date with the latest news from ScienceDaily via social networks and mobile apps:

Have Feedback?


Tell us what you think of ScienceDaily -- we welcome both positive and negative comments. Have any problems using the site? Questions?
Mobile: iPhone Android Web
Follow: Facebook Twitter Google+
Subscribe: RSS Feeds Email Newsletters
Latest Headlines Health & Medicine Mind & Brain Space & Time Matter & Energy Computers & Math Plants & Animals Earth & Climate Fossils & Ruins