Pavan Pranjivan MehtaScuola Internazionale Superiore di Studi Avanzati di Trieste | SISSA · Applied Mathematics Group
Pavan Pranjivan Mehta
Development of Turbulence models addressing Non-locality using Fractional Calculus.
About
3
Publications
2,344
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
28
Citations
Citations since 2017
Introduction
My current Research interest lies in developing a fundamental theory for Turbulence in the view of Fractional calculus and Stochastic Processes for solving the closure problem. For the numerical solutions, I am also developing Machine Learning methodologies to resolve turbulent dynamics and solve fractional closure models. In this avenue, I have discovered universality in Couette flow by formulating a fractional closure model.
Additional affiliations
August 2020 - December 2021
July 2019 - August 2020
March 2018 - December 2019
Education
October 2022 - September 2025
Field of study
- Mathematical Analysis, Modelling and Applications
September 2020 - December 2021
September 2015 - October 2016
Publications
Publications (3)
Its is a well known fact that Turbulence exhibits non-locality, however, modeling has largely received local treatment following the work of Prandl over mixing-length model. Thus, in this article we report our findings by formulating a non-local closure model for Reynolds-averaged Navier-Stokes (RANS) equation using Fractional Calculus. Two model f...
A fractional derivative is used to model non-local effects in turbulence. However, as the second moment does not exist, tempering the Levy distribution leads to finite moments, and thus, a new tempered fractional derivative free from all assumptions is formulated for non-local modelling of turbulent flows. The total shear stress is modelled here as...
The first fractional model for Reynolds stresses in wall-bounded turbulent flows was proposed by Wen Chen [2]. Here, we extend this formulation by allowing the fractional order α(y) of the model to vary with the distance from the wall (y) for turbulent Couette flow. Using available direct numerical simulation (DNS) data, we formulate an inverse pro...
Projects
Project (1)
Turbulence exhibits long range interactions and has multiple scales. Resolving all scales with fine grids implies non-locality is addressed by subsequent resolution of local dynamics. However, if only spatially or temporally averaged fields are solved for computational feasibility of real world applications, then addressing non-locality becomes important due to absence of information of interactions between two points. In this project, I demonstrate the use of variable order fractional gradients for wall bounded turbulent flows to address the duality of local and non-local characteristics.
