Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-10T07:12:59.232Z Has data issue: false hasContentIssue false
  • English
  • Français

Spontaneous inertia–gravity wave emission in the differentially heated rotating annulus experiment

Published online by Cambridge University Press:  10 January 2018

Steffen Hien Open the ORCID record for Steffen Hien [Opens in a new window] ,
Joran Rolland ,
Sebastian Borchert ,
Lena Schoon ,
Christoph Zülicke  and
Ulrich Achatz
Steffen Hien*
Affiliation:
Institut für Atmosphäre und Umwelt, Goethe-Universität Frankfurt am Main, Altenhöferallee 1, D-60438 Frankfurt am Main, Germany
Joran Rolland
Affiliation:
Institut für Atmosphäre und Umwelt, Goethe-Universität Frankfurt am Main, Altenhöferallee 1, D-60438 Frankfurt am Main, Germany
Sebastian Borchert
Affiliation:
Deutscher Wetterdienst, Frankfurter Straße 135, D-63067 Offenbach am Main, Germany
Lena Schoon
Affiliation:
Leibniz-Institut für Atmosphärenphysik, Schlossstraße 6, D-18225 Kühlungsborn, Germany
Christoph Zülicke
Affiliation:
Leibniz-Institut für Atmosphärenphysik, Schlossstraße 6, D-18225 Kühlungsborn, Germany
Ulrich Achatz
Affiliation:
Institut für Atmosphäre und Umwelt, Goethe-Universität Frankfurt am Main, Altenhöferallee 1, D-60438 Frankfurt am Main, Germany
*
†Email address for correspondence: hien@iau.uni-frankfurt.de
Get access Rights & Permissions [Opens in a new window]

Abstract

The source mechanism of inertia–gravity waves (IGWs) observed in numerical simulations of the differentially heated rotating annulus experiment is investigated. The focus is on the wave generation from the balanced part of the flow, a process presumably contributing significantly to the atmospheric IGW field. Direct numerical simulations are performed for an atmosphere-like configuration of the annulus and possible regions of IGW activity are characterised by a Hilbert-transform algorithm. In addition, the flow is separated into a balanced and unbalanced part, assuming the limit of a small Rossby number, and the forcing of IGWs by the balanced part of the flow is derived rigorously. Tangent-linear simulations are then used to identify the part of the IGW signal that is rather due to radiation by the internal balanced flow than to boundary-layer instabilities at the side walls. An idealised fluid set-up without rigid horizontal boundaries is considered as well, to investigate the effect of the identified balanced forcing unmasked by boundary-layer effects. The direct simulations of the realistic and idealised fluid set-ups show a clear baroclinic-wave structure exhibiting a jet–front system similar to its atmospheric counterparts, superimposed by four distinct IGW packets. The subsequent tangent-linear analysis indicates that three wave packets are radiated from the internal flow and a fourth one is probably caused by boundary-layer instabilities. The forcing by the balanced part of the flow is found to play a significant role in the generation of IGWs, so it supplements boundary-layer instabilities as a key factor in the IGW emission in the differentially heated rotating annulus.

JFM classification

Geophysical and Geological Flows: Baroclinic flows Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Internal waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 838 , 10 March 2018 , pp. 5 - 41
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

‡

Present address: Institut PPrime, UPR 3346, 86062 Chasseneuil-du-Poitou, France.

References

Achatz, U., Ribstein, B., Senf, F. & Klein, R. 2017 The interaction between synoptic-scale balanced flow and a finite-amplitude mesoscale wave field throughout all atmospheric layers: weak and moderately strong stratification. Q. J. R. Meteorol. Soc. 143, 342–361.Google Scholar
Arakawa, A. & Lamb, V. R. 1977 Computational design of the basic dynamical processes of the UCLA general circulation model. Meth. Comput. Phys. 17, 173–265.Google Scholar
Baldwin, M. P., Gray, L. J., Dunkerton, T. J., Hamilton, K., Haynes, P. H., Randel, W. J., Holton, J. R., Alexander, M. J., Hirota, I. & Horinouchi, T. 2001 The quasi-biennial oscillation. Rev. Geophys. 39 (2), 179–229.CrossRefGoogle Scholar
Beres, J. H., Alexander, M. J. & Holton, J. R. 2004 A method of specifying the gravity wave spectrum above convection based on latent heating properties and background wind. J. Atmos. Sci. 61, 324–337.Google Scholar
Borchert, S., Achatz, U. & Fruman, M. D. 2014 Gravity wave emission in an atmosphere-like configuration of the differentially heated rotating annulus experiment. J. Fluid Mech. 758, 287–311.Google Scholar
Borchert, S., Achatz, U., Remmler, S., Hickel, S., Harlander, U., Vincze, M., Alexandrov, K. D., Rieper, F., Heppelmann, T. & Dolaptchiev., S. I. 2015 Finite-volume models with implicit subgrid-scale parameterization for the differentially heated rotating annulus. Meteorol. Z. 23 (6), 561–580.Google Scholar
Bühler, O. & McIntyre, M. E. 2005 Wave capture and wave-vortex duality. J. Fluid Mech. 534, 67–95.CrossRefGoogle Scholar
Charney, J. G. 1948 On the Scale of Atmospheric Motions. Cammermeyer in Komm.Google Scholar
Danioux, E., Vanneste, J., Klein, P. & Sasaki., H. 2012 Spontaneous inertia-gravity-wave generation by surface-intensified turbulence. J. Fluid Mech. 699, 153–173.CrossRefGoogle Scholar
Davis, C. A. & Emanuel, K. A. 1991 Potential vorticity diagnostics of cyclogenesis. Mon. Weath. Rev. 119, 1929–1953.2.0.CO;2>CrossRefGoogle Scholar
Eady, E. T. 1949 Long waves and cyclone waves. Tellus 1, 33–52.CrossRefGoogle Scholar
Esler, J. G. & Polvani, L. M. 2004 Kelvin–Helmholtz instability of potential vorticity layers: a route to mixing. J. Atmos. Sci. 61, 1392–1405.Google Scholar
Fritts, D. C. & Alexander, J. M. 2003 Gravity wave dynamics and effects in the middle atmosphere. Rev. Geophys. 41 (1), 1003.Google Scholar
Fritts, D. C. & Luo, Z. 1992 Gravity wave excitation by geostrophic adjustment of the jet stream. Part I. Two-dimensional forcing. J. Atmos. Sci. 49, 681–697.2.0.CO;2>CrossRefGoogle Scholar
Früh, W. G. & Read, P. L. 1997 Wave interactions and the transition to chaos of baroclinic waves in a thermally driven rotating annulus. Phil. Trans. R. Soc. Lond. A 355 (1722), 101–153.Google Scholar
Fultz, D. 1991 Quantitative nondimensional properties of the gradient wind. J. Atmos. Sci. 48, 869–875.Google Scholar
Gray, D. D. & Giorgini, A. 1976 The validity of the Boussinesq approximation for liquids and gases. Intl J. Heat Mass Transfer 19, 545–551.Google Scholar
Harlander, U., Wenzel, J., Alexandrov, K., Wang, Y. & Egbers, C. 2012 Simultaneous PIV and thermography measurements of partially blocked flow in a differentially heated rotating annulus. Exp. Fluids 52 (4), 1077–1087.CrossRefGoogle Scholar
Haynes, P. H., McIntyre, M. E., Shepherd, T. G., Marks, C. J. & Shine, K. P. 1991 On the ‘downward control’ of extratropical diabatic circulations by eddy-induced mean zonal forces. J. Atmos. Sci. 48 (4), 651–678.2.0.CO;2>CrossRefGoogle Scholar
Hickel, S., Adams, N. A. & Domaradzki, J. A. 2006 An adaptive local deconvolution method for implicit LES. J. Comput. Phys. 213, 413–436.Google Scholar
Hide, R. 1967 Theory of axisymmetric thermal convection in a rotating fluid annulus. Phys. Fluids 10 (1), 56–68.Google Scholar
Hide, R. & Mason, P. J. 1975 Sloping convection in a rotating fluid. Adv. Phys. 24 (1), 47–100.Google Scholar
Hignett, P., White, A. A., Carter, R. D., Jackson, W. D. N. & Small, R. M. 1985 A comparison of laboratory measurements and numerical simulations of baroclinic wave flows in a rotating cylindrical annulus. Q. J. R. Meteorol. Soc. 111, 131–154.Google Scholar
Holton, J. R. 2004 An Introduction to Dynamic Meteorology, 4th edn. International Geophysics, vol. 88. Academic.Google Scholar
Hoskins, B. J., Draghici, I. & Davies, H. C. 1978 A new look at the omega-equation. Q. J. R. Meteorol. Sci. 104, 31–38.Google Scholar
Hoskins, B. J., McIntyre, M. E. & Robertson, A. W. 1985 On the use and significance of isentropic potential vorticity maps. Q. J. R. Meteorol. Sci. 111 (470), 877–946.Google Scholar
Jacoby, T. N. L., Read, P. L., Williams, P. D. & Young, R. M. B. 2011 Generation of inertia-gravity waves in the rotating thermal annulus by a localised boundary layer instability. Geophys. Astrophys. Fluid Dyn. 105, 161–181.Google Scholar
Lin, Y. & Zhang, F. 2008 Tracking gravity waves in baroclinic jet-front systems. J. Atmos. Sci. 65 (7), 2402–2415.CrossRefGoogle Scholar
Luo, Z. & Fritts, D. C. 1993 Gravity-wave excitation by geostrophic adjustment of the jet stream. Part II. Three-dimensional forcing. J. Atmos. Sci. 50, 104–115.Google Scholar
Marks, C. J. & Eckermann, S. D. 1995 A three-dimensional nonhydrostatic ray-tracing model for gravity waves: formulation and preliminary results for the middle atmosphere. J. Atmos. Sci. 52 (11), 1959–1984.2.0.CO;2>CrossRefGoogle Scholar
McIntyre, M. E. & Norton, W. A. 2000 Potential vorticity inversion on a hemisphere. J. Atmos. Sci. 57 (9), 1214–1235.Google Scholar
McWilliams, J. C. 1985 A uniformly valid model spanning the regimes of geostrophic and isotropic, stratified turbulence: balanced turbulence. J. Atmos. Sci. 42 (16), 1773–1774.Google Scholar
Mirzaei, M., Zülicke, C., Mohebalhojeh, A. R., Ahmadi-Givi, F. & Plougonven, R. 2014 Structure, energy, and parameterization of inertia-gravity waves in dry and moist simulations of a baroclinic wave life cycle. J. Atmos. Sci. 71 (7), 2390–2414.Google Scholar
Mohebalhojeh, A. R. & Dritschel, D. G. 2001 Hierarchies of balance conditions for the f-plane shallow-water equations. J. Atmos. Sci. 58, 2411–2426.Google Scholar
Muraki, D. J., Snyder, C. & Rotunno, R. 1999 The next-order corrections to quasigeostrophic theory. J. Atmos. Sci. 56 (11), 1547–1560.Google Scholar
O’Sullivan, D. & Dunkerton, T. J. 1995 Generation of inertia-gravity waves in a simulated life cycle of baroclinic instability. J. Atmos. Sci. 52, 3695–3716.Google Scholar
Pedlosky, J. 1987 Geophysical Fluid Dynamics. Springer.Google Scholar
Phillips, N. A. 1963 Geostrophic motion. Rev. Geophys. 1 (2), 123–176.CrossRefGoogle Scholar
Plougonven, R., Teitelbaum, H. & Zeitlin, V. 2003 Inertia gravity wave generation by the tropospheric midlatitude jet as given by the Fronts and Atlantic Storm–Track Experiment radio soundings. J. Geophys. Res. 108, 4686.Google Scholar
Plougonven, R. & Zhang, F. 2007 On the forcing of inertia-gravity waves by synoptic-scale flows. J. Atmos. Sci. 64, 1737–1742.Google Scholar
Plougonven, R. & Zhang, F. 2014 Internal gravity waves from atmospheric jets and fronts. Rev. Geophys. 52 (1), 33–76.Google Scholar
Randriamampianina, A. 2013 Caractéristiques d’ondes d’inertie gravité dans une cavité barocline (Inertia gravity waves characteristics within a baroclinic cavity). C. R. Méc. 341, 547–552.Google Scholar
Randriamampianina, A. & Crespo del Arco, E. 2015 Inertia-gravity waves in a liquid-filled, differentially heated, rotating annulus. J. Fluid Mech. 782, 144–177.Google Scholar
Sato, K., Kinoshita, T. & Okamoto, K. 2013 A new method to estimate three-dimensional residual-mean circulation in the middle atmosphere and its application to gravity wave-resolving general circulation model data. J. Atmos. Sci. 70 (12), 3756–3779.CrossRefGoogle Scholar
Scaife, A. A., Knight, J. R., Vallis, G. K. & Folland, C. K. 2005 A stratospheric influence on the winter NAO and North Atlantic surface climate. Geophys. Res. Lett. 32 (18), 1–5.Google Scholar
Schoon, L. & Zülicke, C. 2017 Diagnosis of local gravity wave properties during a sudden stratospheric warming. Atmos. Chem. Phys. Discuss. doi:10.5194/acp-2017-472.Google Scholar
Sitte, B. & Egbers, C. 2000 Higher Order Dynamics of Baroclinic Waves, pp. 355–375. Springer.Google Scholar
Smith, L. M. & Waleffe, F. 2002 Generation of slow large scales in forced rotating stratified turbulence. J. Fluid Mech. 451, 145–168.CrossRefGoogle Scholar
Snyder, C., Muraki, D. J., Plougonven, R. & Zhang, F. 2007 Inertia-gravity waves generated within a dipole vortex. J. Atmos. Sci. 64, 4417–4431.CrossRefGoogle Scholar
Snyder, C., Plougonven, R. & Muraki, D. J. 2009 Mechanisms for spontaneous gravity wave generation within a dipole vortex. J. Atmos. Sci. 66, 3464–3478.Google Scholar
Song, I.-S. & Chun, H.-Y. 2005 Momentum flux spectrum of convectively forced internal gravity waves and its application to gravity wave drag parameterization. Part I. Theory. J. Atmos. Sci. 62, 107–124.CrossRefGoogle Scholar
von Storch, H. & Zwiers, F. W. 2002 Statistical Analysis in Climate Research. Cambridge University Press.Google Scholar
Uccellini, L. W. & Koch, S. E. 1987 The synoptic setting and possible energy sources for mesoscale wave disturbances. Mon. Weath. Rev. 115, 721–729.Google Scholar
Vallis, G. K. 2006 Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-scale Circulation. Cambridge University Press.Google Scholar
Vanneste, J. 2013 Balance and spontaneous wave generation in geophysical flows. Annu. Rev. Fluid Mech. 45, 147–172.CrossRefGoogle Scholar
Vincze, M., Borchert, S., Achatz, U., Von Larcher, T., Baumann, M., Liersch, C., Remmler, S., Beck, T., Alexandrov, K. D. & Egbers, C. 2014 Benchmarking in a rotating annulus: a comparative experimental and numerical study of baroclinic wave dynamics. Meteorologische Zeitschrift 23 (6), 611–635.Google Scholar
Vincze, M., Borcia, I., Harlander, U. & Gal, P. L. 2016 Double-diffusive convection and baroclinic instability in a differentially heated and initially stratified rotating system: the barostrat instability. Fluid Dyn. Res. 48 (6), 1–21.Google Scholar
Viúdez, Á. 2007 The origin of the stationary frontal wave packet spontaneously generated in rotating stratified vortex dipoles. J. Fluid Mech. 593, 359–383.Google Scholar
Viúdez, Á. 2008 The stationary frontal wave packet spontaneously generated in mesoscale dipoles. J. Phys. Oceanogr. 38 (1), 243–256.Google Scholar
Viúdez, Á. & Dritschel, D. G. 2006 Spontaneous generation of inertia-gravity wave packets by balanced geophysical flows. J. Fluid Mech. 553, 107–117.Google Scholar
von Larcher, T. & Egbers, C. 2005 Experiments on transitions of baroclinic waves in a differentially heated rotating annulus. Nonlinear Process. Geophys. 12, 1033–1041.CrossRefGoogle Scholar
Van der Vorst, H. A. 1992 Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 13 (2), 631–644.Google Scholar
Wang, S. & Zhang, F. 2010 Source of gravity waves within a vortex-dipole jet revealed by a linear model. J. Atmos. Sci. 67 (5), 1438–1455.Google Scholar
Wang, S., Zhang, F. & Snyder, C. 2009 Generation and propagation of inertia-gravity waves from vortex dipoles and jets. J. Atmos. Sci. 66, 1294–1314.Google Scholar
Warn, T., Bokhove, O., Shepherd, T. G. & Vallis, G. K. 1995 Rossby number expansions, slaving principles, and balance dynamics. Q. J. R. Meteorol. Soc. 121, 723–739.Google Scholar
Williamson, J. H. 1980 Low-storage Runge–Kutta schemes. J. Comput. Phys. 35, 48–56.Google Scholar
Wilson, E. B. 1929 Vector Analysis: A Text-book for the Use of Students of Mathematics and Physics, Founded Upon the Lectures of J. Willard Gibbs. Yale University Press.Google Scholar
Wu, D. L. & Zhang, F. 2004 A study of mesoscale gravity waves over the North Atlantic with satellite observations and a mesoscale model. J. Geophys. Res. Atmos. 109 (22), 1–14.Google Scholar
Yasuda, Y., Sato, K. & Sugimoto, N. 2015 A theoretical study on the spontaneous radiation of inertia gravity waves using the renormalization group method. Part I. Derivation of the renormalization group equations. J. Atmos. Sci. 72 (3), 957–983.Google Scholar
Zdunkowski, W. & Bott, A. 2003 Dynamics of the Atmosphere: A Course in Theoretical Meteorology. Cambridge University Press.Google Scholar
Zhang, F. 2004 Generation of mesoscale gravity waves in upper-tropospheric jet–front systems. J. Atmos. Sci. 61, 440–457.Google Scholar
Zhang, F., Koch, S. E., Davis, C. A. & Kaplan, M. L. 2000 A survey of unbalanced flow diagnostics and their application. Adv. Atmos. Sci. 17 (2), 165–183.Google Scholar
Zimin, A. V., Szunyogh, I., Patil, D., Hunt, B. R. & Ott, E. 2003 Extracting envelopes of Rossby wave packets. Mon. Weather Rev. 131 (5), 1011–1017.Google Scholar
Zülicke, C. & Peters, D. 2006 Simulation of inertia–gravity waves in a poleward-breaking Rossby wave. J. Atmos. Sci. 63 (12), 3253–3276.Google Scholar