Considering the physical context of the question, the formation and dynamics of turbulent flow are influenced by various factors, including flow velocity, fluid viscosity, geometric characteristics of the system, boundary conditions, and the presence of external forces such as pressure gradients or magnetic fields.

To understand and attempt to propose alternatives for predicting the behavior of turbulence is a complex challenge due to its chaotic and nonlinear nature. In general, researchers have developed mathematical models and computational methods to describe and simulate turbulent flow, such as the Navier-Stokes equation and computational fluid dynamics (CFD) simulations. However, the results are still preliminary, and many variables need to be considered and improved in this field.

A promising approach is the use of advanced data analysis techniques and machine learning, which can help extract patterns and complex relationships from turbulent data and enhance predictive capabilities. However, in a concrete manner, conducting experiments in the laboratory and observing turbulent phenomena in nature are essential to answer your question.

Howdy Sanjibonny Buragohain,

What are you seeking to accomplish here? Your comments and the literature with which you must be familiar, given your skills and education, indicate that you have seen versions of an answer to your question. Your involvement in Renewable Energy implies wind power concerns and the problems of wind turbines in the atmospheric boundary layer are on your mind, but numerous journal articles are available. The literature is extensive and summaries are easy to find online, so I wonder how we can help here: could you be more specific?

The reply of Andre Francisco Pugas is excellent and recommended as being well stated from that perspective. However, each of you use the word "chaotic" and that is a report on human limitations because the turbulent fluid is acting deterministically everywhere and everywhen it exists: molecular unrest is that fast an hybrid analog-digital computer. Our models and equations are all approximations and much less capable than the fluid, but we try.

So, how can we help from here?

Happy Trails, Len

As suggested from its title, the book by Tennekes, H., & Lumley, J. L. (1972). A first course in turbulence. MIT Press. Available on: https://www.academia.edu/download/54563360/Henk_Tennekes__John_L._Lumley_A_First_Course_in_Turbulence.pdf (more than 12 000 citations) is essential for a fundamental understanding of the physical mechanisms of turbulence and for the acquisition of the methodological elements related to the phenomenological approach applied to the analysis basic turbulent flows.

Description by the authors "This is the first book specifically designed to offer the student a smooth transitionary course between elementary fluid dynamics (which gives only last-minute attention to turbulence) and the professional literature on turbulent flow, where an advanced viewpoint is assumed.

The subject of turbulence, the most forbidding in fluid dynamics, has usually proved treacherous to the beginner, caught in the whirls and eddies of its nonlinearities and statistical imponderables. This is the first book specifically designed to offer the student a smooth transitionary course between elementary fluid dynamics (which gives only last-minute attention to turbulence) and the professional literature on turbulent flow, where an advanced viewpoint is assumed. Moreover, the text has been developed for students, engineers, and scientists with different technical backgrounds and interests. Almost all flows, natural and man-made, are turbulent. Thus the subject is the concern of geophysical and environmental scientists (in dealing with atmospheric jet streams, ocean currents, and the flow of rivers, for example), of astrophysicists (in studying the photospheres of the sun and stars or mapping gaseous nebulae), and of engineers (in calculating pipe flows, jets, or wakes). Many such examples are discussed in the book. The approach taken avoids the difficulties of advanced mathematical development on the one side and the morass of experimental detail and empirical data on the other. As a result of following its midstream course, the text gives the student a physical understanding of the subject and deepens his intuitive insight into those problems that cannot now be rigorously solved. In particular, dimensional analysis is used extensively in dealing with those problems whose exact solution is mathematically elusive. Dimensional reasoning, scale arguments, and similarity rules are introduced at the beginning and are applied throughout. A discussion of Reynolds stress and the kinetic theory of gases provides the contrast needed to put mixing-length theory into proper perspective: the authors present a thorough comparison between the mixing-length models and dimensional analysis of shear flows. This is followed by an extensive treatment of vorticity dynamics, including vortex stretching and vorticity budgets. Two chapters are devoted to boundary-free shear flows and well-bounded turbulent shear flows. The examples presented include wakes, jets, shear layers, thermal plumes, atmospheric boundary layers, pipe and channel flow, and boundary layers in pressure gradients. The spatial structure of turbulent flow has been the subject of analysis in the book up to this point, at which a compact but thorough introduction to statistical methods is given. This prepares the reader to understand the stochastic and spectral structure of turbulence. The remainder of the book consists of applications of the statistical approach to the study of turbulent transport (including diffusion and mixing) and turbulent spectra."

Howdy Sanjibonny Buragohain,

Allow me to temper my following remarks by noting that I am a maverick in this field, and while I have been involved in it extensively you should ignore me if you prefer the mainstream.

I believe Jamel Chahed has given very good advice for anyone choosing to work in the mainstream. The introduction to the book he quoted reads like a dream come true. The book contains the concepts one is supposed to affirm as an insider. However, the first few pages of my volume are coated with marginal notes of disagreement about boundaries set by the authors' truths and their excessive characterizations. Chapter 1, Section 1.1, The nature of turbulence, Irregularity claims "This makes a deterministic approach to turbulence problems impossible; instead one relies on statistical methods." "impossible," only "statistics" Pfffftt! and that was just the first page! I continued to read but I was regularly lost in their claims of what is illustrated by their equation terms and other mathematical devices, perhaps because I was so irritated by their excesses. I finally set the book aside. I already had an M.S. in Meteorology so I did have a basis for understanding their version of turbulence.

I affirm natural philosophy and understanding of the nature of Nature, instead of scraping off from our efforts anything that interferes with solvable equations and usable results, however approximate. As noted here and there, a young mountain stream has no problem negotiating a few stones in a rapids, so deterministic turbulent fluid dynamics must not be "impossible," it's just hard for humans.

Well it's an opinion that may provide comfort should you need a kindred spirit if you become frustrated when you read. It is a good book for what it is.

Happy Trails, Len

Leonard Hall Thank you for your remarks. Maverick Professors, as original as they are, have always struggled to progress their students normally. "In the Spiral Curriculum, a new topic is introduced to students in its most basic form without much detail or explanation. Then, as learning progresses, more details are introduced which build on these basics, adding depth and breadth to the content. This means that students revisit the same constructs as they progress through their education, with the process of adding more detail helping to re-enforce prior learning each time".

Excerpts from:

https://www.teachwire.net/news/ever-increasing-circles-what-the-spiral-curriculum-can-do-for-your-students/

Howdy Jamel Chahed

Thank you for your remarks. Of course, any theory of education has limits because students are a varied lot. The students who have liked my approach (few) responded to their being treated as inquiring persons.

In this case I find a bit of mystery because Sanjibonny Buragohain has shown awareness of the answer to her question, and her profile indicates even deeper understanding would be present. I would like to know what she seeks to know better and to help, by normal, spiral, personal, or whatever educational means she prefers.

Or, I may be completely off-track. It has happened before.

Happy Trails, Len