Zhai, X. M.; Kurien, Susan Characteristic length scales of strongly rotating Boussinesq flow in variable-aspect-ratio domains. (English) Zbl 1415.76117 J. Fluid Mech. 856, 397-425 (2018). Summary: We quantify the variability of the characteristic length scales of isotropically forced Boussinesq flows with stratification and frame rotation, as functions of the ratio \(N/f\) of the Brunt-Väisälä frequency to the Coriolis frequency. The parameter ranges \(0<N<f\), domain aspect ratio \(1\leqslant \delta_d\leqslant 32\) and Burger number \(Bu=\delta_d N/f\leqslant 1\) are explored for two values of \(f\), one resulting in linear potential vorticity and the other in nonlinear potential vorticity. Characteristic length scales of the wave and vortical linear eigenmodes are separately quantified using \(n\)th-order spectral moments in both horizontal and vertical directions, for integer \(n\leqslant 3\). In flows with linear potential vorticity, the horizontal vortical length scale \(L_0\), characterizing a typical width of columnar structures, grows as \(\sim (N/f)^{1/2}\) at all orders of \(n\), regardless of domain aspect ratio. In unit-aspect-ratio domains, when intermediate scales are measured by filtering out the largest scales and using higher-order moments \(n>1\), the vortical-mode aspect ratio \(\delta_0\) asymptotes to a scaling of \(\sim(N/f)^{-1}\), in agreement with quasi-geostrophic estimates. In contrast, the \(\delta_0\) in tall-aspect-ratio domain flows yields a decay rate of at most \(\sim(N/f)^{-1/2}\) after large-scale filtering. Flows with nonlinear potential vorticity display consistently weaker dependence of the characteristic scales on \(N/f\) than the corresponding ones with linear potential vorticity. The wave-mode aspect ratios for all flows are essentially independent of \(N/f\). We highlight the differences of these flow structure scalings relative to those expected for quasi-geostrophic flows, and those observed in strongly stratified, non-quasi-geostrophic flows. MSC: 76B65 Rossby waves (MSC2010) 76U05 General theory of rotating fluids 76F45 Stratification effects in turbulence Keywords:quasi-geostrophic flows; rotating flows; stratified flows PDFBibTeX XMLCite \textit{X. M. Zhai} and \textit{S. Kurien}, J. Fluid Mech. 856, 397--425 (2018; Zbl 1415.76117) Full Text: DOI References: [1] Aluie, H.; Kurien, S., Joint downscale fluxes of energy and potential enstrophy in rotating and stratified Boussinesq flows, Europhys. Lett., 96, 44006, (2011) [2] Aubert, O.; Le Bars, M.; Le Gal, P.; Marcus, P. S., The universal aspect ratio of vortices in rotating stratified flows: experiments and observations, J. Fluid Mech., 706, 34-45, (2012) · Zbl 1275.76212 [3] Babin, A. V.; Mahalov, A.; Nicolaenko, B.; Kirchgässner, K.; Mielke, A., Long-time averaged Euler and Navier-Stokes equations for rotating fluids, Proceedings of the IUTAM/ISIMM Symposium on Structure and Dynamics of Nonlinear Waves in Fluids, Hanover, 1994, 7, 145-157, (1995), World Scientific · Zbl 0872.76097 [4] Babin, A.; Mahalov, A.; Nicolaenko, B.; Zhou, Y., On the asymptotic regimes and the strongly stratified limit of rotating Boussinesq equations, Theor. Comput. Fluid Dyn., 9, 3-4, 223-251, (1997) · Zbl 0912.76092 [5] Bartello, P., Geostrophic adjustment and inverse cascades in rotating stratified turbulence, J. Atmos. Sci., 52, 4410-4428, (1995) [6] Bartello, P.; Metais, O.; Lesieur, M., Coherent structures in rotating three-dimensional turbulence, J. Fluid Mech., 273, 1-29, (1994) [7] Billant, P.; Chomaz, J.-M., Self-similarity of strongly stratified inviscid flows, Phys. Fluids, 16, 6, 1645-1651, (2001) [8] Cambon, C.; Mansour, N. N.; Squires, K. D., Anisotropic structure of homogeneous turbulence subjected to uniform rotation, Center for Turbulence Research, (1994) [9] Charney, J. G., Geostrophic turbulence, J. Atmos. Sci., 28, 1087-1095, (1971) [10] Chasnov, J. R., Similarity states of passive scalar transport in isotropic turbulence, Phys. Fluids, 6, 2, 1036-1051, (1994) · Zbl 0827.76027 [11] Cushman-Roisin, B., Introduction to Geophysical Fluid Dynamics, (1994), Prentice-Hall [12] Embid, P.; Majda, A. J., Low Froude number limiting dynamics for stably stratified flow with small or finite Rossby numbers, Geophys. Astrophys. Fluid Dyn., 87, 1-50, (1998) [13] Ertel, H., Ein neuer hydrodynamischer wirbelsatz, Met. Z., 59, 271-281, (1942) · JFM 68.0588.01 [14] Frisch, U.; Kurien, S.; Pandit, R.; Pauls, W.; Ray, S. S.; Wirth, A.; Zhu, J.-Z., Hyperviscosity, galerkin-truncation and bottlenecks in turbulence, Phys. Rev. Lett., 101, (2008) [15] Godeferd, F. S.; Moisy, F., Structure and dynamics of rotating turbulence: a review of recent experimental and numerical results, Appl. Mech. Rev., 67, (2015) [16] Hassanzadeh, P.; Marcus, P. S.; Le Gal, P., The universal aspect ratio of vortices in rotating stratified flows: theory and simulation, J. Fluid Mech., 706, 46-57, (2012) · Zbl 1275.76216 [17] Hough, S. S., On the application of harmonic analysis to the dynamical theory of the tides. Part I. On Laplace’s ‘oscillations of the first species,’ and on the dynamics of ocean currents, Phil. Trans. R. Soc. Lond. A, 189, 201-257, (1897) · JFM 28.0862.01 [18] Ishihara, T.; Morishita, K.; Yokokawa, M.; Uno, A.; Kaneda, Y., Energy spectrum in high-resolution direct numerical simulations of turbulence, Phys. Rev. Fluids, 1, (2016) [19] Julien, K.; Knobloch, E.; Milliff, R.; Werne, J., Generalized quasi-geostrophy for spatially anisotropic rotationally constrained flows, J. Fluid Mech., 555, 233-274, (2006) · Zbl 1090.76077 [20] Kurien, S.; Smith, L. M., Asymptotics of unit Burger number rotating and stratified flows for small aspect-ratio, Physica D, 241, 3, 149-163, (2012) · Zbl 1426.76640 [21] Kurien, S.; Smith, L. M., Effect of rotation and domain aspect-ratio on layer formation in strongly stratified Boussinesq flows, J. Turbul., 15, 4, 241-271, (2014) [22] Kurien, S.; Smith, L.; Wingate, B., On the two-point correlation of potential vorticity in rotating and stratified turbulence, J. Fluid Mech., 555, 131-140, (2006) · Zbl 1090.76035 [23] Kurien, S.; Taylor, M. A., Direct numerical simulation of turbulence: data generation and statistical analysis, Los Alamos Sci., 29, 142-151, (2005) [24] Kurien, S.; Wingate, B.; Taylor, M. A., Anisotropic constraints on energy distribution in rotating and stratified flows, Europhys. Lett., 84, 24003, (2008) [25] Liechtenstein, L.; Godeferd, F.; Cambon, C., Nonlinear formation of structures in rotating, stratified turbulence, J. Turbul., 6, 1-18, (2005) [26] Lilly, D. K., Stratified turbulence and the mesoscale variability of the atmosphere, J. Atmos. Sci., 40, 749-761, (1983) [27] Majda, A. J., Introduction to PDEs and Waves for the Atmosphere and Ocean, 9, (2003), New York University Courant Institute of Mathematical Sciences · Zbl 1278.76004 [28] Marino, R.; Mininni, P. D.; Rosenberg, D.; Pouquet, A., Inverse cascades in rotating stratified turbulence: Fast growth of large scales, Europhys. Lett., 102, 44006, (2013) [29] Mcwilliams, J. C., A note on a uniformly valid model spanning the regimes of geostrophic and isotropic, stratified turbulence: balanced turbulence, J. Atmos. Sci., 42, 1773-1774, (1985) [30] Mcwilliams, J. C.; Molemaker, M. J.; Yavneh, I., Ageostrophic, anticyclonic instability of a geostrophic, barotropic boundary current, Phys. Fluids, 16, 3720-3725, (2004) · Zbl 1187.76340 [31] Mcwilliams, J. C.; Weiss, J. B.; Yavneh, I., The vortices of homogeneous geostrophic turbulence, J. Fluid Mech., 401, 1-26, (1999) · Zbl 0972.76042 [32] Nieves, D.; Grooms, I.; Julien, K.; Weiss, J. B., Investigations of non-hydrostatic, stably stratified and rapidly rotating flows, J. Fluid Mech., 801, 430-458, (2016) [33] Pedlosky, J., Geophysical Fluid Dynamics, (1986), Springer [34] Pope, S. B., Turbulent Flows, (2000), Cambridge University Press · Zbl 0966.76002 [35] Praud, O.; Fincham, A. M.; Sommeria, J., Decaying grid turbulence in a strongly stratified fluid, J. Fluid Mech., 522, 1-33, (2005) · Zbl 1060.76514 [36] Praud, O.; Sommeria, J.; Fincham, A. M., Decaying grid turbulence in a rotating stratified fluid, J. Fluid Mech., 547, 389-412, (2006) · Zbl 1138.76306 [37] Proudman, J., On the motion of solids in a liquid possessing vorticity, Proc. R. Soc. Lond. A, 92, 408-424, (1916) · JFM 46.1248.01 [38] Remmel, M.; Sukhatme, J.; Smith, L. M., Nonlinear inertia-gravity wave-mode interactions in three dimensional rotating stratified flows, Commun. Math. Sci., 8, 2, 357-376, (2010) · Zbl 1195.86011 [39] Rosenberg, D.; Pouquet, A.; Marino, R.; Minnini, P. D., Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high resolution direct numerical simulations, Phys. Fluids, 27, (2015) [40] Smith, L. M.; Chasnov, J.; Waleffe, F., Crossover from two- to three-dimensional turbulence, Phys. Rev. Lett., 77, 2467-2470, (1996) [41] Smith, L. M.; Waleffe, F., Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence, Phys. Fluids, 11, 1608-1622, (1999) · Zbl 1147.76500 [42] Smith, L. M.; Waleffe, F., Generation of slow, large scales in forced rotating, stratified turbulence, J. Fluid Mech., 451, 145-168, (2002) · Zbl 1009.76040 [43] Sukhatme, J.; Smith, L. M., Vortical and wave modes in 3d rotating stratified flows: Random large scale forcing, Geophys. Astrophys. Fluid Dyn., 102, 437-455, (2008) [44] Taylor, G. I., Motion of solids in fluids when the flow is not irrotational, Proc. R. Soc. Lond. A, 93, 92-113, (1917) · JFM 46.1248.02 [45] Vallis, G. K., Atmospheric and Oceanic Fluid Dynamics, (2006), Cambridge University Press [46] Waite, M. L., Potential enstrophy in stratified turbulence, J. Fluid Mech., 722, R4, (2013) · Zbl 1287.76145 [47] Waite, M. L.; Bartello, P., The transition from geostrophic to stratified turbulence, J. Fluid Mech., 568, 89-108, (2006) · Zbl 1177.76147 [48] Wang, H.; George, W. K., The integral scale in homogeneous isotropic turbulence, J. Fluid Mech., 459, 429-443, (2002) · Zbl 1016.76039 [49] Wingate, B.; Embid, P.; Holmes-Cerfon, M.; Taylor, M. A., Low Rossby limiting dynamics for stably stratified flow with finite Froude number, J. Fluid Mech., 676, 546-571, (2011) · Zbl 1241.76433 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.