A new research adds to the work of Prandtl, father of modern aerodynamics

In 1942, Ludwig Prandtl – considered the father of modern aerodynamics – published "Führer durch die Strömungslehre", the first book of his time on fluid mechanics and was translated into English from German. in 1952 under the title "Essentials of Fluid Mechanics". The book was particularly successful, so that Prandtl students continued to maintain and develop it with new discoveries after his death. Today, the work is available under the revised title "Prandtl – The Basics of Fluid Mechanics", as an augmented and revised version of the original book with contributions from leading researchers in the field of mechanics. fluids.

Over the years, the last three pages of Prandtl's original book on mountain and valley winds have captured the attention of the meteorological research community, but these pages have been largely neglected to the point that the content and the exact mathematical solutions have disappeared from the current expanded version of the book. But today, in the era of supercomputers, Inanc Senocak, an associate professor in mechanical engineering and materials science at the Swanson School of Engineering at the University of Pittsburgh, is discovering new perspectives in the field. Prandtl's original work, with important implications for nocturnal weather forecasting in mountainous terrain.

Drs. Senocak and Cheng-Nian Xiao, a postdoctoral researcher in Dr. Senocak's lab, recently published an article entitled "Stability of the Prandtl Model for Katabatic Slope Flow", published in the Journal of Fluid Mechanics. The researchers used both linear stability theory and direct numerical simulations to discover, for the first time, fluid instabilities in the Prandtl model for katabatic slope flows.

The katabatic slope flows are gravity-driven winds, running over large layers of ice or, at night, on mountain slopes, where fresh air comes down. Understanding these winds is essential for reliable weather forecasts, important for air quality, aviation and agriculture. But the complexity of the terrain, the stratification of the atmosphere and the fluid turbulence make it difficult to model the winds around the mountains. As Prandtl's model does not define the conditions under which a slope flow would become turbulent, it is difficult, for example, to predict the weather that it will do in the Salt Lake City area, in Utah. , where prolonged inversions create a difficult environment for the air. quality.

"Now that we have more powerful supercomputers, we can improve the complexity of the terrain with better spatial resolution in the mathematical model," says Dr. Senocak. "However, the numerical models of weather forecasting still use simplified models, appeared at a time when computing power was insufficient."

The researchers discovered that, although the Prandtl model is subject to unique fluid instabilities, which appear as a function of slope angle and a new dimensionless number, they named the parameter Disturbance of stratification The measurement of the disturbance of stratification of the atmosphere by the background. cooling on the surface. The concept of dimensionless number, for example the Reynolds number, plays an important role in the thermal sciences and fluids in general because it captures the essence of competing processes in a problem.

An important implication of their conclusion is that for a given fluid such as air, the dynamic stability of katabatic slope flows can not simply be determined by a single dimensionless parameter, such as the Richardson number, as is currently practiced in fluid dynamics and community meteorology. The Richardson number expresses a relationship between buoyancy and wind shear and is commonly used for weather forecasting, investigation of currents in the oceans, lakes and reservoirs, and measurement of atmospheric turbulence expected in the aviation.

"There was a lack of an overall concept and Richardson's number was the alternative," Senocak said. "We are not saying that Richardson's number is unimportant, but when a mountain or valley is protected from larger-scale meteorological movements, it does not enter the image. way to explain the theory of these descents and flows into the valley. "

This discovery will not only be important for agriculture, aviation and weather forecasts, according to Dr. Senocak, but it will also be essential for research on climate change and the associated elevation of the level of the sea, as well as for the accurate prediction of surface katabatic wind profiles over large ice sheets and glaciers are essential in the energy balance of ice melt. He notes that even in the fluid dynamics community, the discovery of this surprising new type of instability should be of great interest to research.

Next, Mr. Senocak advises and sponsors a team of experienced designers to determine if researchers can actually observe these fluid instabilities in the lab on a much smaller scale than a mountain.