Abstract
In this work we aim to understand the interplay between deformation and energy of a fluid particle in a turbulent flow, focusing on the role of the pressure Hessian. A new decomposition of the Hessian is proposed, defining a conservative Hessian which contains the stabilizing effects of the full Hessian on energy and deformation of fluid elements. This conservative Hessian is then used to construct models for the velocity gradient which allow controlling alignments and singularities.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
D. Buaria, A. Pumir, E. Bodenschatz, P.K. Yeung, Extreme velocity gradients in turbulent flows. New J Phys 21(4), 043004 (2019)
S.S. Girimaji, S.B. Pope, Material-element deformation in isotropic turbulence. J Fluid Mech 220, 427–458 (1990)
P.L. Johnson, C. Meneveau, Large-deviation joint statistics of the finite-time Lyapunov spectrum in isotropic turbulence. Phys Fluids 27(8), 085110 (2015)
P. Vieillefosse, Local interaction between vorticity and shear in a perfect incompressible fluid. J Phys France 43(6), 837–842 (1982)
P. Vieillefosse, Internal motion of a small element of fluid in an inviscid flow. Physica A 125(1), 150–162 (1984)
M. Chertkov, A. Pumir, B.I. Shraiman, Lagrangian tetrad dynamics and the phenomenology of turbulence. Phys Fluids 11(8), 2394–2410 (1999)
L. Chevillard, C. Meneveau, L. Biferale, F. Toschi, Modeling the pressure Hessian and viscous Laplacian in turbulence: Comparisons with direct numerical simulation and implications on velocity gradient dynamics. Phys Fluids 20(10), 101504 (2008)
J. Tom, M. Carbone, A.D. Bragg, Exploring the turbulent velocity gradients at different scales from the perspective of the strain-rate eigenframe. J Fluid Mech 910, A24 (2021)
M. Carbone, M. Iovieno, A.D. Bragg, Symmetry transformation and dimensionality reduction of the anisotropic pressure Hessian. J Fluid Mech 900, A38 (2020)
P.L. Johnson, C. Meneveau, A closure for Lagrangian velocity gradient evolution in turbulence using recent-deformation mapping of initially Gaussian fields. J Fluid Mech 804, 387–419 (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Carbone, M., Bragg, A., Tom, J., Wilczek, M., Iovieno, M. (2021). The Conservative Pressure Hessian and the Free Fluid Particle Model. In: Örlü, R., Talamelli, A., Peinke, J., Oberlack, M. (eds) Progress in Turbulence IX. iTi 2021. Springer Proceedings in Physics, vol 267. Springer, Cham. https://doi.org/10.1007/978-3-030-80716-0_29
Download citation
DOI: https://doi.org/10.1007/978-3-030-80716-0_29
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-80715-3
Online ISBN: 978-3-030-80716-0
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)