An Analytical Solution for the Stochastic Model of a Turbulent Cascade

Masoudi, A. A.; Anaraki, P. Azimi

doi:10.1142/s0217984906011323

Mod. Phys. Lett. B

2006

DOI: 10.1142/s0217984906011323

|View full text |Cite

An Analytical Solution for the Stochastic Model of a Turbulent Cascade

A. A. Masoudi

P. Azimi Anaraki

Abstract: In this paper we are going to derive the Fokker-Planck equation (FPE) which is based on the Langevin equation for the stochastic model of a turbulent cascade and then we exactly solve the FPE for a certain case and find an explicit form of the probability distribution function (PDF) by the operator method. Finally, by using this PDF, we calculate the velocity moments for this system.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2009

2020

Publication Types

Select...

Article3

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Quantitative study on energy dissipation mechanism of metal rubber by an enhanced turbulence model

Zhou

Liang

et al. 2019

Mod. Phys. Lett. B

View full text Add to dashboard Cite

This paper studies the energy dissipation of metal rubber with an enhanced turbulence model. Based on the catastrophe theory which is a highly generalized mathematical tool, a new method for studying turbulence is proposed, which can quantitatively analyze the energy dissipation of the whole turbulence developed to process and strictly deduce the expression of the energy spectrum density in different turbulence development stages. Then, a theoretical model of sound absorption performance in full-frequency is established by this enhanced turbulence model. Furthermore, the sound absorption property and energy dissipation of metal rubber are studied under different structural parameters. This paper not only demonstrates −10/9 and −5/3 power laws of the energy spectrum but also finds −3 power laws at high frequencies. Finally, the accuracy of the enhanced turbulence model and the feasibility of the metal rubber research method based on the enhanced turbulence model are verified by wind tunnel test and standing wave tube test, respectively. This study not only has a theoretical guidance for the preparation of metal rubber but also has a new perspective for the study of turbulent phase transition and even other complex phase transitions.

show abstract

Quantitative study on energy dissipation mechanism of metal rubber by an enhanced turbulence model

Zhou

Liang

et al. 2019

Mod. Phys. Lett. B

View full text Add to dashboard Cite

show abstract

Multi-dimensional complex phase transition model by catastrophe theory developing Kolmogorov turbulence theory

Zhou

Liang

et al. 2020

Mod. Phys. Lett. B

View full text Add to dashboard Cite

In this paper, a novel multi-dimensional complex non-equilibrium phase transition model is put forward to describe quantitatively the physical development process of turbulence and develop the Kolmogorov turbulence theory from the catastrophe theory, in which the well-known −5/3 power law is only a special case in this paper proving the accuracy of our methods. Catastrophe theory is a highly generalized mathematical tool that summarizes the laws of non-equilibrium phase transition. Every control variable in catastrophe theory could be skillfully expanded into multi-parameter multiplication with different indices and the relationship among these characteristic indices can be determined by dimensionless analysis. Thus, the state variables can be expressed quantitatively with multiple parameters, and the multi-dimensional non-equilibrium phase transition theory is established. As an example, by adopting the folding catastrophe model, we strictly derive out the quantitative relationship between energy and wave number with respect to a new scale index [Formula: see text] to quantitative study the whole process of the laminar flow to turbulence, in which [Formula: see text] varies from [Formula: see text] to [Formula: see text] corresponding to energy containing range and [Formula: see text] to energy containing scale where [Formula: see text] power law is deduced, and at [Formula: see text] the [Formula: see text] law of Kolmogorov turbulence theory is obtained, and fully developed turbulence phase starts at [Formula: see text] giving [Formula: see text] law. Furthermore, this theory presented is verified by our wind tunnel experiments. This novel non-equilibrium phase transition methods cannot only provide a new insight into the turbulence model, but also be applied to other non-equilibrium phase transitions.

show abstract

An Analytical Solution for the Typical Energy Cascade in Turbulence

Azimi¹,

Masoudi²

2009

J. of Applied Sciences

View full text Add to dashboard Cite

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

An Analytical Solution for the Stochastic Model of a Turbulent Cascade

Cited by 3 publications

References 4 publications

Quantitative study on energy dissipation mechanism of metal rubber by an enhanced turbulence model

Quantitative study on energy dissipation mechanism of metal rubber by an enhanced turbulence model

Multi-dimensional complex phase transition model by catastrophe theory developing Kolmogorov turbulence theory

An Analytical Solution for the Typical Energy Cascade in Turbulence

Contact Info

Product

Resources

About