Open problems in fluid mechanics

[coolguy]

hi
i m planning to write a paper in classical mechanics.Anybody know of any open issues in fluid mechanics?

 

[leptonsoliton]

From http://math.ucr.edu/home/baez/physics/General/open_questions.html#condensed

How can turbulence be understood and its effects calculated? One of the oldest problems of them all. A vast amount is known about turbulence, and we can simulate it on a computer, but much about it remains mysterious.

The Navier-Stokes equations are the basic equations describing fluid flow. Do these equations have solutions that last for all time, given arbitrary sufficiently nice initial data? Or do singularities develop in the fluid flow, which prevent the solution from continuing. This is more of a question of mathematical physics than physics per se--but it's related to the previous question, since (one might argue) how can we deeply understand turbulence if we don't even know that the equations for fluid motion have solutions? At the turn of the millennium, the Clay Mathematics Institute offered a $1,000,000 prize for solving this problem.


From http://www.geocities.com/ednitou/

Climate prediction
Turbulence


From https://www.amazon.com/dp/3764365935/?tag=pfamazon01-20

Mathematical Fluid Mechanics: Recent Results and Open Questions (Advances in Mathematical Fluid Mechanics) (Hardcover)
by Jiri Neustupa (Editor), Patrick Penel (Editor)
Mathematical modeling and numerical simulation in fluid mechanics are topics of great importance both in theory and technical applications. The present book attempts to describe the current status in various areas of research. The 10 chapters, mostly survey articles, are written by internationally renowned specialists and offer a range of approaches to and views of the essential questions and problems. In particular, the theories of incompressible and compressible Navier-Stokes equations are considered, as well as stability theory and numerical methods in fluid mechanics. Although the book is primarily written for researchers in the field, it will also serve as a valuable source of information to graduate students.

 

[momentum_waves]

From http://math.ucr.edu/home/baez/physic...html#condensed

How can turbulence be understood and its effects calculated? One of the oldest problems of them all. A vast amount is known about turbulence, and we can simulate it on a computer, but much about it remains mysterious.

The Navier-Stokes equations are the basic equations describing fluid flow. Do these equations have solutions that last for all time, given arbitrary sufficiently nice initial data? Or do singularities develop in the fluid flow, which prevent the solution from continuing. This is more of a question of mathematical physics than physics per se--but it's related to the previous question, since (one might argue) how can we deeply understand turbulence if we don't even know that the equations for fluid motion have solutions? At the turn of the millennium, the Clay Mathematics Institute offered a $1,000,000 prize for solving this problem.

The N-S equations offer a very fertile ground for further research.

Wave solution research is beginning to show that turbulence is essentially a wave phenomenon - wave motion, breaking, & interaction. Take a look at <www.adthermtech.com/wordpress3> for a few papers introducing early research in this area. The research has been fascinating & is ongoing.

Local singularities in the velocity, pressure & thermal flow fields do appear to exist, but do not necessarily cause a blow-up over time - rather traveling with the flow. Characteristic surfaces exist, standing & traveling.

Have fun - I have.

mw...