The similarity theory of free turbulent shear flows of viscoelastic fluids

Prandtl, 1925, 7. Bericht über Untersuchungen zur ausgebildeten Turbulenz, ZAMM, 5, 136, 10.1002/zamm.19250050212 Tollmien, 1926, Berechnung turbulenter Ausbreitungsvorgänge, ZAMM, 6, 468, 10.1002/zamm.19260060604 Schlichting, 1930, Über das ebene Windschattenproblem, Ing.-Arch., 1, 533, 10.1007/BF02079870 von Görtler, 1942, Berechnung von Aufgaben der freien Turbulenz auf Grund eines neuen Näherungsansatzes, ZAMM, 22, 244, 10.1002/zamm.19420220503 Hinze, 1959 Townsend, 1976 Tennekes, 1972 Pope, 2000 Guimarães, 2020, Direct numerical simulations of turbulent viscoelastic jets, J. Fluid Mech., 899, A11, 10.1017/jfm.2020.402 Guimarães, 2022, Turbulent planar wakes of viscoelastic fluids analysed by direct numerical simulations, J. Fluid Mech., 946, A26, 10.1017/jfm.2022.559 Rallison, 1995, Instability of a high-speed submerged elastic jet, J. Fluid Mech., 288, 311, 10.1017/S0022112095001157 Ray, 2015, Absolute/convective instability of planar viscoelastic jets, Phys. Fluids, 27, 10.1063/1.4906441 Yamani, 2021, Spectral universality of elastoinertial turbulence, Phys. Rev. Lett., 127, 10.1103/PhysRevLett.127.074501 Yamani, 2023, Spatiotemporal signatures of elastoinertial turbulence in viscoelastic planar jets, Phys. Rev. Fluids, 8, 10.1103/PhysRevFluids.8.064610 Guimarães, 2023, Viscoelastic jet instabilities studied by direct numerical simulations, Phys. Rev. Fluids, 8, 10.1103/PhysRevFluids.8.103301 M.C. Guimarães, F.T. Pinho, C.B. da Silva, Mixing of passive scalar and polymer concentration in turbulent viscoelastic planar jets and wakes analysed by direct numerical simulations, in: Bulletin of the American Physical Society: 75th Annual Meeting of the Division of Fluid Dynamics, Indianapolis, USA, 2022. Hameduddin, 2018, Geometric decomposition of the conformation tensor in viscoelastic turbulence, J. Fluid Mech., 842, 395, 10.1017/jfm.2018.118 Hameduddin, 2019, The mean conformation tensor in viscoelastic turbulence, J. Fluid Mech., 865, 363, 10.1017/jfm.2019.46 Bird, 1980, Polymer solution rheology based on a finitely extensible bead-spring chain model, J. Non-Newton. Fluid Mech., 7, 213, 10.1016/0377-0257(80)85007-5 Sureshkumar, 1997, Direct numerical simulation of the turbulent channel flow of a polymer solution, Phys. Fluids, 9, 743, 10.1063/1.869229 Canuto, 1987 Lele, 1992, Compact finite difference schemes with spectral-like resolution, J. Comput. Phys., 103, 16, 10.1016/0021-9991(92)90324-R Williamson, 1980, Low-storage Runge-Kutta schemes, J. Comput. Phys., 35, 48, 10.1016/0021-9991(80)90033-9 Kim, 1985, Application of a fractional-step method to incompressible Navier-Stokes equations, J. Comput. Phys., 59, 308, 10.1016/0021-9991(85)90148-2 Vaithianathan, 2006, An improved algorithm for simulating three-dimensional, viscoelastic turbulence, J. Non-Newton. Fluid Mech., 140, 3, 10.1016/j.jnnfm.2006.03.018 Kurganov, 2000, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations, J. Comput. Phys., 160, 241, 10.1006/jcph.2000.6459 Pinho, 2008, A low Reynolds number turbulence closure for viscoelastic fluids, J. Non-Newton. Fluid Mech., 154, 89, 10.1016/j.jnnfm.2008.02.008 Valente, 2014, The effect of viscoelasticity on the turbulent kinetic energy cascade, J. Fluid Mech., 760, 39, 10.1017/jfm.2014.585 Valente, 2016, Energy spectra in elasto-inertial turbulence, Phys. Fluids, 28, 10.1063/1.4955102 Li, 2012, Influence of polymer additives on turbulent energy cascading in forced homogeneous isotropic turbulence studied by direct numerical simulations, Chin. Phys. B, 21, 10.1088/1674-1056/21/11/114701 Nguyen, 2016, Small scale dynamics of isotropic viscoelastic turbulence, Phys. Rev. Fluids, 1, 10.1103/PhysRevFluids.1.083301 Armstrong, 1974, Kinetic theory and rheology of dilute solutions of flexible macromolecules. I. Steady state behavior, J. Chem. Phys., 60, 724, 10.1063/1.1681141 Sarnecki, 1959 Krug, 2017, Revisiting the law of the wake in wall turbulence, J. Fluid Mech., 811, 421, 10.1017/jfm.2016.788 Guimarães, 2019, Similarity laws for transpired turbulent flows subjected to pressure gradients, separation and wall heat transfer, Int. J. Heat Fluid Flow, 78, 10.1016/j.ijheatfluidflow.2019.108436 Bray, 1985, Unified modelling approach for premixed turbulent combustion Part 1: General formulation, Combust. Flame, 61, 87, 10.1016/0010-2180(85)90075-6 Prandtl, 1945 Wilcox, 2006 Corrsin, 1955 Klebanoff, 1955