Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-28T06:40:54.395Z Has data issue: false hasContentIssue false

Gravity wave emission in an atmosphere-like configuration of the differentially heated rotating annulus experiment

Published online by Cambridge University Press:  08 October 2014

Sebastian Borchert*
Affiliation:
Institut für Atmosphäre und Umwelt, Goethe-Universität Frankfurt, Altenhöferallee 1, D-60438 Frankfurt am Main, Germany
Ulrich Achatz
Affiliation:
Institut für Atmosphäre und Umwelt, Goethe-Universität Frankfurt, Altenhöferallee 1, D-60438 Frankfurt am Main, Germany
Mark D. Fruman
Affiliation:
Institut für Atmosphäre und Umwelt, Goethe-Universität Frankfurt, Altenhöferallee 1, D-60438 Frankfurt am Main, Germany
*
Email address for correspondence: [email protected]

Abstract

A finite-volume model of the classic differentially heated rotating annulus experiment is used to study the spontaneous emission of gravity waves (GWs) from jet stream imbalances, which may be an important source of these waves in the atmosphere and for which no satisfactory parameterisation exists. Experiments were performed using a classic laboratory configuration as well as using a much wider and shallower annulus with a much larger temperature difference between the inner and outer cylinder walls. The latter configuration is more atmosphere-like, in particular since the Brunt–Väisälä frequency is larger than the inertial frequency, resulting in more realistic GW dispersion properties. In both experiments, the model is initialised with a baroclinically unstable axisymmetric state established using a two-dimensional version of the code, and a low-azimuthal-mode baroclinic wave featuring a meandering jet is allowed to develop. Possible regions of GW activity are identified by the horizontal velocity divergence and a modal decomposition of the small-scale structures of the flow. Results indicate GW activity in both annulus configurations close to the inner cylinder wall and within the baroclinic wave. The former is attributable to boundary layer instabilities, while the latter possibly originates in part from spontaneous GW emission from the baroclinic wave.

Type
Papers
Copyright
© 2014 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.)

References

Achatz, U. 2007 Modal and nonmodal perturbations of monochromatic high-frequency gravity waves: primary nonlinear dynamics. J. Atmos. Sci. 64, 19771994.Google Scholar
Afanasyev, Y. 2003 Spontaneous emission of gravity waves by interacting vortex dipoles in a stratified fluid: laboratory experiments. Geophys. Astrophys. Fluid Dyn. 97, 7995.Google Scholar
Alexander, M. J., Geller, M., McLandress, C., Polavarapu, S., Preusse, P., Sassi, F., Sato, K., Eckermann, S., Ern, M., Hertzog, A., Kawatani, Y., Pulido, M., Shaw, T. A., Sigmond, M., Vincent, R. & Watanabe, S. 2010 Recent developments in gravity-wave effects in climate models and the global distribution of gravity-wave momentum flux from observations and models. Q. J. R. Meteorol. Soc. 136, 11031124.CrossRefGoogle Scholar
Allen, J. S. 1972 Upwelling of a stratified fluid in a rotating annulus: steady state. Part 1. Linear theory. J. Fluid Mech. 56, 429445.Google Scholar
Arakawa, A. & Lamb, V. R. 1977 Computational design of the basic dynamical processes of the UCLA general circulation model. Methods Comput. Phys. 17, 173265.Google Scholar
Barcilon, V. & Pedlosky, J. 1967a Linear theory of rotating stratified fluid motions. J. Fluid Mech. 29, 116.Google Scholar
Barcilon, V. & Pedlosky, J. 1967b A unified linear theory of homogeneous and stratified rotating fluids. J. Fluid Mech. 29, 609621.Google Scholar
Bastin, M. E. & Read, P. L. 1998 Experiments on the structure of baroclinic waves and zonal jets in an internally heated, rotating, cylinder of fluid. Phys. Fluids 10 (2), 374389.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, 324337.Google Scholar
Beres, J. H., Garcia, R. R., Boville, B. A. & Sassi, F. 2005 Implementation of a gravity wave source spectrum parameterization dependent on the properties of convection in the Whole Atmosphere Community Climate Model (WACCM). J. Geophys. Res. 110, D10108.Google Scholar
Borchert, S., Achatz, U., Remmler, S., Hickel, S., Harlander, U., Vincze, M., Alexandrov, K. D., Rieper, F., Heppelmann, T. & Dolaptchiev, S. I. 2014 Finite-volume models with implicit subgrid-scale parameterization for the differentially heated rotating annulus. Meteorol. Z. (in press).Google Scholar
Bühler, O. & McIntyre, M. E. 2005 Wave capture and wave-vortex duality. J. Fluid Mech. 534, 6795.Google Scholar
Charney, J. G. 1948 On the scale of atmospheric motions. Geofys. Publ. Oslo 17, 117.Google Scholar
Chun, H.-Y. & Baik, J.-J. 1998 Momentum flux by thermally induced internal gravity waves and its approximation for large-scale models. J. Atmos. Sci. 55, 32993310.Google Scholar
Chun, H.-Y., Song, I.-S., Baik, J.-J. & Kim, Y.-J. 2004 Impact of a convectively forced gravity wave drag parameterization in NCAR CCM3. J. Clim. 17, 35303547.Google Scholar
Clapham, C. & Nicholson, J. 2009 The Concise Oxford Dictionary of Mathematics, 4th edn. Oxford University Press.Google Scholar
Danioux, E., Vanneste, J., Klein, P. & Sasaki, H. 2012 Spontaneous inertia-gravity-wave generation by surface-intensified turbulence. J. Fluid Mech. 699, 153173.Google Scholar
Douglas, H. A. & Mason, P. J. 1973 Thermal convection in a large rotating fluid annulus: some effects of varying the aspect ratio. J. Atmos. Sci. 30, 11241134.Google Scholar
Eady, E. T. 1949 Long waves and cyclone waves. Tellus 1, 3352.Google Scholar
Esler, J. G. & Polvani, L. M. 2004 Kelvin–Helmholtz instability of potential vorticity layers: a route to mixing. J. Atmos. Sci. 61, 13921405.Google Scholar
Farnell, L. & Plumb, R. A.1975 Numerical integration of flow in a rotating annulus I: axisymmetric model. Tech. Rep. Geophysical Fluid Dynamics Laboratory, UK Meteorological Office.Google Scholar
Farnell, L. & Plumb, R. A.1976 Numerical integration of flow in a rotating annulus II: three dimensional model. Tech. Rep. Geophysical Fluid Dynamics Laboratory, UK Meteorological Office.Google Scholar
Ferziger, J. H. & Perić, M. 2008 Numerische Strömungsmechanik. Springer (English: Computational Methods for Fluid Dynamics).Google Scholar
Ford, R. 1994a Gravity wave radiation from vortex trains in rotating shallow water. J. Fluid Mech. 281, 81118.Google Scholar
Ford, R. 1994b The instability of an axisymmetric vortex with monotonic potential vorticity in rotating shallow water. J. Fluid Mech. 280, 303334.Google Scholar
Ford, R. 1994c The response of a rotating ellipse of uniform potential vorticity to gravity wave radiation. Phys. Fluids 6, 36943704.Google Scholar
Fritts, D. C. & Alexander, M. J. 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, 681697.Google Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W. H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 17601765.Google Scholar
Gill, A. E. 1982 Atmosphere–Ocean Dynamics. Academic Press.Google Scholar
Grimshaw, R. 1975 Internal gravity waves: critical layer absorption in a rotating fluid. J. Fluid Mech. 70, 287304.Google Scholar
Guest, F. M., Reeder, M. J., Marks, C. J. & Karoly, D. J. 2000 Inertia-gravity waves observed in the lower stratosphere over Macquarie Island. J. Atmos. Sci. 57, 737752.Google Scholar
Harlander, U., von Larcher, Th., Wang, Y. & Egbers, Ch. 2011 PIV- and LDV-measurements of baroclinic wave interactions in a thermally driven rotating annulus. Exp. Fluids 51 (1), 3749.CrossRefGoogle Scholar
Harris, F. J. 1978 On the use of windows for harmonic analysis with the discrete Fourier transform. Proc. IEEE 66, 5183.Google Scholar
Hathaway, D. H. & Fowlis, W. W. 1986 Flow regimes in a shallow rotating cylindrical annulus with temperature gradients imposed on the horizontal boundaries. J. Fluid Mech. 172, 401418.Google Scholar
Hickel, S. & Adams, N. A. 2007 On implicit subgrid-scale modeling in wall-bounded flows. Phys. Fluids 19, 105106.Google Scholar
Hickel, S. & Adams, N. A. 2008 Implicit LES applied to zero-pressure-gradient and adverse-pressure-gradient boundary-layer turbulence. Intl J. Heat Fluid Flow 29, 626639.Google Scholar
Hickel, S., Adams, N. A. & Domaradzki, J. A. 2006 An adaptive local deconvolution method for implicit LES. J. Comput. Phys. 213, 413436.CrossRefGoogle Scholar
Hickel, S., Kempe, T. & Adams, N. A. 2008 Implicit large-eddy simulation applied to turbulent channel flow with periodic constrictions. Theor. Comput. Fluid Dyn. 22, 227242.Google Scholar
Hide, R. 1958 An experimental study of thermal convection in a rotating liquid. Phil. Trans. R. Soc. Lond. A 250, 441478.Google Scholar
Hide, R. 1967 Theory of axisymmetric thermal convection in a rotating fluid annulus. Phys. Fluids 10 (1), 5668.Google Scholar
Hide, R. & Mason, P. J. 1975 Sloping convection in a rotating fluid. Adv. Phys. 24 (1), 47100.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, 131154.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, 161181.Google Scholar
James, I. N., Jonas, P. R. & Farnell, L. 1981 A combined laboratory and numerical study of fully developed steady baroclinic waves in a cylindrical annulus. Q. J. R. Meteorol. Soc. 107, 5178.Google Scholar
Kim, Y.-J., Eckermann, S. D. & Chun, H.-Y. 2003 An overview of the past, present and future of gravity-wave drag parametrization for numerical climate and weather prediction models. Atmos.-Ocean 41, 6598.Google Scholar
Kwak, H. S. & Hyun, J. M. 1992 Baroclinic waves in a shallow rotating annulus with temperature gradients imposed on the horizontal boundaries. Geophys. Astrophys. Fluid Dyn. 66, 123.Google Scholar
von Larcher, Th. & Egbers, Ch. 2005 Experiments on transitions of baroclinic waves in a differentially heated rotating annulus. Nonlinear Process. Geophys. 12, 10331041.Google Scholar
Lighthill, M. J. 1952 On sound generated aerodynamically. I. General theory. Proc. R. Soc. Lond. 211, 564587.Google Scholar
Lovegrove, A. F., Read, P. L. & Richards, C. J. 1999 Generation of inertia-gravity waves by a time-dependent baroclinic wave in the laboratory. Phys. Chem. Earth B 24, 455460.Google Scholar
Lovegrove, A. F., Read, P. L. & Richards, C. J. 2000 Generation of inertia-gravity waves in a baroclinically unstable fluid. Q. J. R. Meteorol. Soc. 126, 32333254.Google 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, 104115.Google Scholar
McFarlane, N. A. 1987 The effect of orographically excited gravity wave drag on the general circulation of the lower stratosphere and troposphere. J. Atmos. Sci. 44, 17751800.Google Scholar
Meister, A. 2011 Numerik linearer Gleichungssysteme. Eine Einführung in moderne Verfahren. Vieweg+Teubner (English: Numerical Methods for Linear Systems of Equations. An Introduction to Modern Methods).Google Scholar
Miller, T. L. & Fowlis, W. W. 1986 Laboratory experiments in a baroclinic annulus with heating and cooling on the horizontal boundaries. Geophys. Astrophys. Fluid Dyn. 34, 283300.Google Scholar
Müller, P., Holloway, G., Henyey, F. & Pomphrey, N. 1986 Nonlinear interactions among internal gravity waves. Rev. Geophys. 24, 493536.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, 36953716.Google Scholar
Palmer, T. N., Shutts, G. J. & Swinbank, R. 1986 Alleviation of a systematic westerly bias in general circulation and numerical weather prediction models through an orographic gravity wave drag parametrization. Q. J. R. Meteorol. Soc. 112, 10011039.Google Scholar
Pavelin, E., Whiteway, J. A. & Vaughan, G. 2001 Observation of gravity wave generation and breaking in the lowermost stratosphere. J. Geophys. Res. 106, 51735179.Google Scholar
Plougonven, R. & Snyder, C. 2005 Gravity waves excited by jets: propagation versus generation. Geophys. Res. Lett. 32, L18802.Google Scholar
Plougonven, R. & Snyder, C. 2007 Inertia-gravity waves spontaneously generated by jets and fronts. Part I: different baroclinic life cycles. J. Atmos. Sci. 64, 25022520.Google Scholar
Plougonven, R., Snyder, C. & Zhang, F. 2009 Comments on “Application of the Lighthill–Ford theory of spontaneous imbalance to clear-air turbulence forecasting”. J. Atmos. Sci. 66, 25062510.Google 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 (D21), 4686.Google Scholar
Plougonven, R. & Zhang, F. 2014 Internal gravity waves from atmospheric jets and fronts. Rev. Geophys. 52, 3376.CrossRefGoogle Scholar
Randriamampianina, A. 2013 Caractéristiques d’ondes d’inertie gravité dans une cavité barocline (Inertia gravity wave characteristics within a baroclinic cavity). C. R. Méc. 341, 547552.Google Scholar
Read, P. L., Lewis, S. R. & Hide, R. 1997 Laboratory and numerical studies of baroclinic waves in an internally heated rotating fluid annulus: a case of wave/vortex duality? J. Fluid Mech. 337, 155191.Google Scholar
Remmler, S. & Hickel, S. 2012 Direct and large eddy simulation of stratified turbulence. Intl J. Heat Fluid Flow 35, 1324.Google Scholar
Richter, J. H., Sassi, F. & Garcia, R. R. 2010 Toward a physically based gravity wave source parameterization in a general circulation model. J. Atmos. Sci. 67, 136156.Google Scholar
Riehl, H. & Fultz, D. 1957 Jet stream and long waves in a steady rotating-dishpan experiment: structure of the circulation. Q. J. R. Meteorol. Soc. 83, 215231.Google Scholar
Rieper, F., Hickel, S. & Achatz, U. 2013 A conservative integration of the pseudo-incompressible equations with implicit turbulence parameterization. Mon. Weath. Rev. 141, 861886.Google Scholar
Rossby, C.-G. 1926 On the solution of problems of atmospheric motion by means of model experiments. Mon. Weath. Rev. 54 (6), 237240.Google Scholar
Rossby, C.-G. 1938 On the mutual adjustment of pressure and velocity distributions in certain simple current systems, II. J. Mar. Res. 2, 239263.Google Scholar
Sato, K., Watanabe, S., Kawatani, Y., Tomikawa, Y., Miyazaki, K. & Takahashi, M. 2009 On the origins of mesospheric gravity waves. Geophys. Res. Lett. 36, L19801.Google Scholar
Simmons, A. J. & Hoskins, B. J. 1975 A comparison of spectral and finite-difference simulations of a growing baroclinic wave. Q. J. R. Meteorol. Soc. 101, 551565.Google Scholar
Smith, L. M. & Waleffe, F. 2002 Generation of slow large scales in forced rotating stratified turbulence. J. Fluid Mech. 451, 145168.Google Scholar
Snyder, C., Muraki, D. J., Plougonven, R. & Zhang, F. 2007 Inertia-gravity waves generated within a dipole vortex. J. Atmos. Sci. 64, 44174431.Google Scholar
Snyder, C., Plougonven, R. & Muraki, D. J. 2009 Mechanisms for spontaneous gravity wave generation within a dipole vortex. J. Atmos. Sci. 66, 34643478.Google Scholar
Song, I.-S. & Chun, H.-Y. 2008 A Lagrangian spectral parameterization of gravity wave drag induced by cumulus convection. J. Atmos. Sci. 65, 12041224.Google Scholar
Uccellini, L. W. & Koch, S. E. 1987 The synoptic setting and possible energy sources for mesoscale wave disturbances. Mon. Weath. Rev. 115, 721729.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, 147172.Google Scholar
Vanneste, J. & Yavneh, I. 2004 Exponentially small inertia-gravity waves and the breakdown of quasigeostrophic balance. J. Atmos. Sci. 61, 211223.Google Scholar
Verein Deutscher Ingenieure, 2006 VDI-Wärmeatlas, 10th edn. Springer.Google Scholar
Viúdez, Á. & Dritschel, D. G. 2006 Spontaneous generation of inertia-gravity wave packets by balanced geophysical flows. J. Fluid Mech. 553, 107117.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, 14381455.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, 12941314.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, 723739.Google Scholar
Williams, G. P. 1967 Thermal convection in a rotating fluid annulus: Part 1. The basic axisymmetric flow. J. Atmos. Sci. 24, 144161.Google Scholar
Williams, G. P. 1969 Numerical integration of the three-dimensional Navier–Stokes equations for incompressible flow. J. Fluid Mech. 37, 727750.Google Scholar
Williams, G. P. 1971 Baroclinic annulus waves. J. Fluid Mech. 49, 417449.Google Scholar
Williams, P. D., Haine, T. W. N. & Read, P. L. 2005 On the generation mechanisms of short-scale unbalanced modes in rotating two-layer flows with vertical shear. J. Fluid Mech. 528, 122.Google Scholar
Williams, P. D., Haine, T. W. N. & Read, P. L. 2008 Inertia-gravity waves emitted from balanced flow: observations, properties, and consequences. J. Atmos. Sci. 65, 35433556.Google Scholar
Williams, P. D., Read, P. L. & Haine, T. W. N. 2003 Spontaneous generation and impact of inertia-gravity waves in a stratified, two-layer shear flow. Geophys. Res. Lett. 30 (24), 2255.Google Scholar
Williamson, J. H. 1980 Low-storage Runge–Kutta schemes. J. Comput. Phys. 35, 4856.Google Scholar
Zhang, F. 2004 Generation of mesoscale gravity waves in upper-tropospheric jet-front systems. J. Atmos. Sci. 61, 440457.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, 165183.Google Scholar