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Batchelor (1967)Batchelor, G. K. , An Introduction to Fluid Dynamics (Cambridge University Press, 1967).
Bilson and Bremhorst (2007)Bilson, M. and Bremhorst, K. , “Direct numerical simulation of turbulent Taylor–Couette flow,” J. Fluid Mech. 579, 227270 (2007).
Borcia et al. (2014)Borcia, I. D. , Ghasemi, A. , and Harlander, U. , “Inertial wave mode excitation in a rotating annulus with partially librating boundaries,” Fluid Dyn. Res. 46, 041423 (2014).
Bretherton and Turner (1968)Bretherton, F. P. and Turner, J. S. , “On the mixing of angular momentum in a stirred rotating fluid,” J. Fluid Mech. 32, 449464 (1968).
Busse (2010)Busse, F. H. , “Zonal flow induced by longitudinal librations of a rotating cylindrical cavity,” Physica D 240, 208 (2010).
Calkins et al. (2010)Calkins, M. A. , Noir, J. , Eldredge, J. , and Aurnou, J. M. , “Axisymmetric simulations of libration-driven fluid dynamics in a spherical shell geometry,” Phys. Fluids 22, 086602 (2010).
Celik et al. (2008)Celik, I. B. , Ghia, U. , and Roache, P. J. , “Procedure for estimation and reporting of uncertainty due to discretization in CFD applications,” J. Fluids Eng. 130(7), 078001 (2008).
Chen and Lin (2002)Chen, C. T. and Lin, M. H. , “Effect of rotation on Goertler vortices in the boundary layer flow on a curved surface,” Int. J. Numer. Methods Fluids 40, 1327 (2002).
Choi et al. (1993)Choi, H. , Moin, P. , and Kim, J. , “Direct numerical simulations of turbulent-flow over riblets,” J. Fluid Mech. 255, 503 (1993).
Czarny et al. (2003)Czarny, O. , Serre, E. , Bontoux, P. , and Lueptow, R. M. , “Interaction between Ekman pumping and the centrifugal instability in Taylor–Couette flow,” Phys. Fluids 15, 467477 (2003).
Davidson (2013)Davidson, P. A. , Turbulence in Rotating, Stratified and Electrically Conducting Fluids (Cambridge University Press, 2013).
Drazin and Reid (1981)Drazin, P. and Reid, W. , Hydrodynamic Stability (Cambridge University Press, 1981).
Floryan (1986)Floryan, L. M. , “Görtler instability of boundary layers over concave and convex walls,” Phys. Fluids 29, 2380 (1986).
Görtler (1955)Görtler, H. , “Dreidimensionales zur Stabilitätstheorie laminarer Grenzschichten,” J. Appl. Math. Mech. 35(9-10), 362363 (1955).
Greenspan and Howard (1963)Greenspan, H. P. and Howard, L. N. , “On a time-dependent motion of a rotating fluid,” J. Fluid Mech. 17, 385 (1963).
Griffiths (2003)Griffiths, S. , “The nonlinear evolution of zonally symmetric equatorial inertial instability,” J. Fluid Mech. 474, 245 (2003).
Kim and Moin (1985)Kim, J. and Moin, P. , “Application of a fractional step-method to incompressible Navier-Stokes equations,” J. Comput. Phys. 59, 308 (1985).
Klein et al. (2014)Klein, M. , Seelig, T. , Kurgansky, M. V. , Borcia, I. D. , Ghasemi, A. , Will, A. , Schaller, E. , Egbers, C. , and Harlander, U. , “Wave attractors and wave excitation in a liquid bounded by a frustum and a cylinder: Experiment, simulation and theory,” J. Fluid Mech. 751, 255 (2014).
Kloosterziel et al. (2007)Kloosterziel, R. C. , Carnevale, G. F. , and Orlandi, P. , “Inertial instability in rotating and stratified fluids: Barotropic vortices,” J. Fluid Mech. 583, 379 (2007).
Kloosterziel and van Heijst (1991)Kloosterziel, R. C. and van Heijst, G. J. F. , “An experimental study of unstable barotropic vortices in a rotating fluid,” J. Fluid Mech. 223, 124 (1991).
Le (1994)Le, H. , “Direct numerical simulation of turbulent flow over a backward-facing step,” Ph.D. thesis, Department of Mechanical Engineering Stanford University, 1994.
Lopez and Marques (2011)Lopez, J. M. and Marques, F. , “Instabilities and inertial waves generated in a librating cylinder,” J. Fluid Mech. 687, 171 (2011).
Maas (2001)Maas, L. R. M. , “Wave focusing and ensuing mean flow due to symmetry breaking in rotating fluids,” J. Fluid Mech. 437, 13 (2001).
Manton (1973)Manton, M. J. , “A note on the mixing of angular momentum in a neutrally buoyant fluid,” Aust. J. Phys. 26, 607 (1973).
Marcus (1984)Marcus, P. S. , “Simulation of Taylor–Couette flow. Part 1. Numerical methods and comparison with experiment,” J. Fluid Mech. 146, 45 (1984).
Moin (1995)Moin, P. , “Large eddy simulation of backward-facing stop flow with application to coaxial jet combustors,” Air Force Office of Scientific Research 2-DJA-420, 1995.
Morinishi et al. (1998)Morinishi, Y. , Lund, T. S. , Vasilyev, V. O. , and Moin, P. , “Fully conservative higher order finite difference schemes for incompressible flow,” J. Comput. Phys. 143, 90 (1998).
Moser and Moin (1984)Moser, R. D. and Moin, P. , “Direct numerical simulation of curved turbulent channel flow,” NASA TM-85974, 1984.
Neitzel and Davis (1981)Neitzel, G. P. and Davis, S. H. , “Centrifugal instabilities during spin-down to rest in finite cylinders. Numerical experiments,” J. Fluid Mech. 102, 329 (1981).
Noir et al. (2010)Noir, J. , Calkins, M. A. , Cantwell, J. , and Aurnou, J. M. , “Experimental study of libration-driven zonal flows in a straight cylinder,” Phys. Earth Planet. Inter. 182, 98106 (2010).
Noir et al. (2009)Noir, J. , Hemmerlin, F. , Wicht, J. , Baca, S. , and Aurnou, J. , “An experimental and numerical study of librationally driven flow in planetary cores and subsurface oceans,” Phys. Earth Planet. Inter. 173, 141152 (2009).
Orlandi (2000)Orlandi, P. , Fluid Flow Phenomena—A Numerical Toolkit (Kluwer, 2000).
Rayleigh (1916)Lord Rayleigh , “On the dynamics of revolving fluids,” Proc. R. Soc. A 93, 148 (1916).
Saric (1994)Saric, W. S. , “Görtler vortices,” Annu. Rev. Fluid Mech. 26, 379 (1994).
Sauret et al. (2013)Sauret, A. , Cébron, D. , and Le Bars, M. , “Spontaneous generation of inertial waves from boundary turbulence in a librating sphere,” J. Fluid Mech. 728, R5 (2013).
Sauret et al. (2012)Sauret, A. , Cébron, D. , Le Bars, M. , and Le Dizès, S. , “Fluid flows in librating cylinder,” Phys. Fluids 24, 122 (2012).
Scorer (1965)Scorer, R. S. , Report Entitled: Vorticity in Nature, Department of Mathematics, Imperial College, London, 1965.
Scorer (1966)Scorer, R. S. , “Origin of cyclones,” Sci. J. 2, 46 (1966).
Thompson (1979)Thompson, R. O. R. Y. , “A mechanism for angular momentum mixing,” Geophys. Astrophys. Fluid Dyn. 12, 221 (1979).
Thompson et al. (1985)Thompson, J. E. , Warsi, Z. U. A. , and Mastin, C. W. , Numerical Grid Generation: Foundations and Applications (North-Holland, New York, US, 1985).
Wang (1970)Wang, C. Y. , “Cylindrical tank of fluid oscillating about a steady rotation,” J. Fluid Mech. 41, 581 (1970).
Zebib and Bottaro (1993)Zebib, A. and Bottaro, A. , “Goertler vortices with system rotation: Linear theory,” Phys. Fluids A 5, 1206 (1993).
Zhang et al. (1997)Zhang, X. , Boyer, D. L. , and Fernando, H. J. S. , “Turbulence-induced rectified flows in rotating fluids,” J. Fluid Mech. 350, 97 (1997).

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Time periodic variation of the rotation rate of an annulus induces in supercritical regime an unstable Stokes boundary layer over the cylinder side walls, generating Görtler vortices in a portion of a libration cycle as a discrete event. Numerical results show that these vortices propagate into the fluid bulk and generate an azimuthal mean flow. Direct numerical simulations of the fluid flow in an annular container with librating outer (inner) cylinder side wall and Reynolds-averaged Navier–Stokes (RANS) equations as diagnostic equations are used to investigate generation mechanism of the retrograde (prograde) azimuthal mean flow in the bulk. First, we explain, phenomenologically, how absolute angular momentum of the bulk flow is mixed and changed due to the propagation of the Görtler vortices, causing a new vortex of basin size. Then we investigate the RANS equations for intermediate time scale of the development of the Görtler vortices and for long time scale of the order of several libration periods. The former exhibits sign selection of the azimuthal mean flow. Investigating the latter, we predict that the azimuthal mean flow is proportional to the libration amplitude squared and to the inverse square root of the Ekman number and libration frequency and then confirms this using the numerical data. Additionally, presence of an upscale cascade of energy is shown, using the kinetic energy budget of fluctuating flow.


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