Pavan Pranjivan Mehta- PhD Student at International School for Advanced Studies
Pavan Pranjivan Mehta
- PhD Student at International School for Advanced Studies
Development of Turbulence models addressing Non-locality using Fractional Calculus.
About
6
Publications
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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.
Current institution
Additional affiliations
September 2015 - October 2016
University of Manchester
Position
- Master Student (MSc Thermal and Fluids Engineering)
August 2020 - December 2021
July 2019 - August 2020
Education
October 2022 - September 2025
Field of study
- Mathematical Analysis, Modelling and Applications
September 2020 - December 2021
September 2015 - October 2016
Publications
Publications (6)
Turbulence is a non-local phenomenon and has multiple-scales. Non-locality can be addressed either implicitly or explicitly. Implicitly, by subsequent resolution of all spatio-temporal scales. However, if directly solved for the temporal or spatially averaged fields, a closure problem arises on account of missing information between two points. To...
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...
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...
Recently, general fractional calculus was introduced by Kochubei (2011) and Luchko (2021) as a further generalisation of fractional calculus, where the derivative and integral operator admits arbitrary kernel. Such a formalism will have many applications in physics and engineering, since the kernel is no longer restricted. We first extend the work...
Turbulence is a non-local phenomenon and has multiple-scales. Non-locality can be addressed either implicitly or explicitly. Implicitly, by subsequent resolution of all spatio-temporal scales. However, if directly solved for the temporal or spatially averaged fields, a closure problem arises on account of missing information between two points. To...
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...
