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Influence of the vorticity-scalar correlation on mixing
Phys. Rev. Fluids 9, 104502 – Published 18 October, 2024
DOI: https://doi.org/10.1103/PhysRevFluids.9.104502
Abstract
We investigate the role of the correlation between a scalar quantity and the vorticity in two-dimensional mixing at infinite Péclet number. We assess, using a diffusivity-independent mixing norm, the dynamics of both Galerkin-truncated ensembles and freely evolving two-dimensional scalar mixing. Both statistical mechanics and numerical experiments show how the mixing rate is attenuated when vorticity and scalar are initially correlated. Since the vorticity is shown to be a poorly mixing scalar, the results suggest that, in general, mixing can be enhanced by minimizing the correlation between vorticity and passive scalar.
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References (35)
- F. Raynal and J.-N. Gence, Energy saving in chaotic laminar mixing, Int. J. Heat Mass Transf. 40, 3267 (1997).
- E. Gouillart, N. Kuncio, O. Dauchot, B. Dubrulle, S. Roux, and J.-L. Thiffeault, Walls inhibit chaotic mixing, Phys. Rev. Lett. 99, 114501 (2007).
- E. Gouillart, O. Dauchot, B. Dubrulle, S. Roux, and J. L. Thiffeault, Slow decay of concentration variance due to no-slip walls in chaotic mixing, Phys. Rev. E 78, 026211 (2008).
- B. Kadoch, W. J. T. Bos, and K. Schneider, Efficiency of laminar and turbulent mixing in wall-bounded flows, Phys. Rev. E 101, 043104 (2020).
- D. P. G. Foures, C. P. Caulfield, and P. J. Schmid, Optimal mixing in two-dimensional plane Poiseuille flow at finite Péclet number, J. Fluid Mech. 748, 241 (2014).
- M. F. Eggl and P. J. Schmid, Mixing enhancement in binary fluids using optimised stirring strategies, J. Fluid Mech. 899, A24 (2020).
- M. Farazmand, Optimal initial condition of passive tracers for their maximal mixing in finite time, Phys. Rev. Fluids 2, 054601 (2017).
- M. Singh, E. Germaine, L. Mydlarski, and L. Cortelezzi, Dependence of scalar mixing on initial conditions in turbulent channel flow, Phys. Rev. Fluids 8, 124605 (2023).
- A. A. Schekochihin, P. H. Haynes, and S. C. Cowley, Diffusion of passive scalar in a finite-scale random flow, Phys. Rev. E 70, 046304 (2004).
- P. H. Haynes and J. Vanneste, What controls the decay of passive scalars in smooth flows? Phys. Fluids 17, 097103 (2005).
- W. Liu and G. Haller, Strange eigenmodes and decay of variance in the mixing of diffusive tracers, Physica D 188, 1 (2004).
- J. Sukhatme and R. T. Pierrehumbert, Decay of passive scalars under the action of single scale smooth velocity fields in bounded two-dimensional domains: From non-self-similar probability distribution functions to self-similar eigenmodes, Phys. Rev. E 66, 056302 (2002).
- G. Holloway and S. S. Kristmannsson, Stirring and transport of tracer fields by geostrophic turbulence, J. Fluid Mech. 141, 27 (1984).
- M. Lesieur and J. R. Herring, Diffusion of a passive scalar in two-dimensional turbulence, J. Fluid Mech. 161, 77 (1985).
- M. Linkmann, M. Buzzicotti, and L. Biferale, Nonuniversal behaviour of helical two-dimensional three-component turbulence, Eur. Phys. J. E 41, 4 (2018).
- G. Falkovich, K. Gawedzki, and M. Vergassola, Particles and fields in fluid turbulence, Rev. Mod. Phys. 73, 913 (2001).
- A. Celani, M. Cencini, A. Mazzino, and M. Vergassola, Active versus passive scalar turbulence, Phys. Rev. Lett. 89, 234502 (2002).
- A. Celani, M. Cencini, A. Mazzino, and M. Vergassola, Active and passive fields face to face, New J. Phys. 6, 72 (2004).
- O. Mercier, X.-Y. Yin, and J.-C. Nave, The characteristic mapping method for the linear advection of arbitrary sets, SIAM J. Sci. Comput. 42, A1663 (2020).
- X.-Y. Yin, O. Mercier, B. Yadav, K. Schneider, and J.-C. Nave, A characteristic mapping method for the two-dimensional incompressible Euler equations, J. Comput. Phys. 424, 109781 (2021).
- D. Fyfe, D. Montgomery, and G. Joyce, Dissipative, forced turbulence in two-dimensional magnetohydrodynamics, J. Plasma Phys. 17, 369 (1977).
- R. H. Kraichnan and D. Montgomery, Two-dimensional turbulence, Rep. Prog. Phys. 43, 547 (1980).
- G. Mathew, I. Mezić, and L. Petzold, A multiscale measure for mixing, Physica D 211, 23 (2005).
- J.-L. Thiffeault, Using multiscale norms to quantify mixing and transport, Nonlinearity 25, R1 (2012).
- Z. Lin, J.-L. Thiffeault, and C. R. Doering, Optimal stirring strategies for passive scalar mixing, J. Fluid Mech. 675, 465 (2011).
- C. Heffernan and Colm-cille P. Caulfield, Robust and efficient identification of optimal mixing perturbations using proxy multiscale measures, Philos. Trans. R. Soc. A 380, 20210026 (2022).
- M. C. Zelati, G. Crippa, G. Iyer, and A. L. Mazzucato, Mixing in incompressible flows: Transport, dissipation, and their interplay, Notices Amer. Math. Soc. 2024, 593 (2024).
- C. E. Leith, Diffusion approximation for turbulent scalar fields, Phys. Fluids 11, 1612 (1968).
- S. A. Orszag, Numerical methods for the simulation of turbulence, Phys. Fluids 12, II-250 (1969).
- P. D. Mininni, D. Rosenberg, R. Reddy, and A. Pouquet, A hybrid MPI-OpenMP scheme for scalable parallel pseudospectral computations for fluid turbulence, Parallel Computing 37, 316 (2011).
- E. Lunasin, Z. Lin, A. Novikov, A. Mazzucato, and C. R. Doering, Optimal mixing and optimal stirring for fixed energy, fixed power, or fixed palenstrophy flows, J. Math. Phys. 53, 115611 (2012).
- G. Joyce and D. Montgomery, Negative temperature states for the two-dimensional guiding-centre plasma, J. Plasma Phys. 10, 107 (1973).
- D. Montgomery and G. Joyce, Statistical mechanics of “negative temperature” states, Phys. Fluids 17, 1139 (1974).
- J. Miller, Statistical mechanics of Euler equations in two dimensions, Phys. Rev. Lett. 65, 2137 (1990).
- R. Robert and J. Sommeria, Statistical equilibrium states for two-dimensional flows, J. Fluid Mech. 229, 291 (1991).
