Skip to main content Accessibility help
×
Home

Cyclone–anticyclone asymmetry in gravity wave radiation from a co-rotating vortex pair in rotating shallow water

  • Norihiko Sugimoto (a1), K. Ishioka (a2), H. Kobayashi (a1) and Y. Shimomura (a1)

Abstract

Cyclone–anticyclone asymmetry in spontaneous gravity wave radiation from a co-rotating vortex pair is investigated in an $f$ -plane shallow water system. The far field of gravity waves is derived analytically by analogy with the theory of aeroacoustic sound wave radiation (Lighthill theory). In the derived form, the Earth’s rotation affects not only the propagation of gravity waves but also their source. While the results correspond to the theory of vortex sound in the limit of $f\rightarrow 0$ , there is an asymmetry in gravity wave radiation between cyclone pairs and anticyclone pairs for finite values of $f$ . Anticyclone pairs radiate gravity waves more intensely than cyclone pairs due to the effect of the Earth’s rotation. In addition, there is a local maximum of intensity of gravity waves from anticyclone pairs at an intermediate $f$ . To verify the analytical solution, a numerical simulation is also performed with a newly developed spectral method in an unbounded domain. The novelty of this method is the absence of wave reflection at the boundary due to a conformal mapping and a pseudo-hyperviscosity that acts like a sponge layer in the far field of waves. The numerical results are in excellent agreement with the analytical results even for finite values of $f$ for both cyclone pairs and anticyclone pairs.

Copyright

Corresponding author

Email address for correspondence: nori@phys-h.keio.ac.jp

References

Hide All
Afanasyev, Y. D., Rhines, P. B. & Lindahl, E. G. 2008 Emission of inertial waves by baroclinically unstable flows: laboratory experiments with altimetric imaging velocimetry. J. Atmos. Sci. 65, 250262.
Bühler, O. & McIntyre, M. E. 2005 Wave capture and wave-vortex duality. J. Fluid Mech. 534, 6795.
Dritschel, D. G. & Vanneste, J. 2006 Instabilities of a shallow-water potential-vorticity front. J. Fluid Mech. 561, 237254.
Ford, R. 1994 Gravity wave radiation from vortex trains in rotating shallow water. J. Fluid Mech. 281, 81118.
Ford, R., McIntyre, M. E. & Norton, W. A. 2000 Balance and the slow quasimanifold: some explicit results. J. Atmos. Sci. 57, 12361254.
Fritts, D. C. & Alexander, M. J. 2003 Gravity wave dynamics and effects in the middle atmosphere. Rev. Geophys. 41, 159.
Gryanik, V. M. 1983 Emission of sound by linear vortical filaments. Izv. Atmos. Ocean. Phys. 19, 150152.
Harada, M. & Ishioka, K. 2011 Inertia–gravity wave radiation from an unstable Bickley jet in rotating two-layer shallow water. SOLA 7, 113116.
Holton, J. R., Haynes, P. H., McIntyre, M. E., Douglass, A. R., Road, R. B. & Pfister, L. 1995 Stratosphere–troposphere exchange. Rev. Geophys. 33, 403439.
Howe, M. S. 2003 Theory of Vortex Sound. Cambridge University Press.
Ishioka, K. 2008 A spectral method for unbounded domains and its application to wave equations in geophysical fluid dynamics. In IUTAM Symposium on Computational Physics and New Perspectives in Turbulence, pp. 291296. Springer.
Ishioka, K.2011 ispack-0.96. http://www.gfd-dennou.org/arch/ispack/, GFD Dennou Club 2011.
Jiménez, J. 1994 Hyperviscous vortices. J. Fluid Mech. 279, 169176.
Kitamura, Y. & Hirota, I. 1989 Small-scale disturbances in the lower stratosphere revealed by daily Rawin sonde observations. J. Met. Soc. Japan 67, 817831.
Knio, O. M., Collorec, L. & Juvé, D. 1995 Numerical study of sound emission by 2D regular and chaotic vortex configurations. J. Comput. Phys. 116, 226246.
Lahaye, N. & Zeitlin, V. 2012a Decaying vortex and wave turbulence in rotating shallow water mode, as follows from high-resolution direct numerical simulations. Phys. Fluids 24, 115106.
Lahaye, N. & Zeitlin, V. 2012b Shock modon: a new type of coherent structure in rotating shallow water. Phys. Rev. Lett. 108, 044502.
Lighthill, M. J. 1952 On the sound generated aerodynamically, I. Proc. R. Soc. Lond. A 211, 564587.
Mariotti, A., Legras, B. & Dritschel, D. G. 1994 Vortex stripping and the erosion of coherent structures in two-dimensional flows. Phys. Fluids 6, 39543962.
Matsushima, T. & Marcus, T. P. S. 1997 A spectral method for unbounded domains. J. Comput. Phys. 137, 321345.
May, P. T. 1996 The organization of convection in the rainbands of tropical cyclone Laurence. Mon. Weath. Rev. 124, 807815.
McIntyre, M. E. 2009 Spontaneous imbalance and hybrid vortex-gravity structures. J. Atmos. Sci. 66, 13151325.
Mitchell, B. E., Lele, S. K. & Moin, P. 1995 Direct computation of the sound from a compressible co-rotating vortex pair. J. Fluid Mech. 285, 181202.
Murakami, S.2008 Stability of the isolated vortex and gravity wave radiation in an $f$ -plane shallow water system. Master’s thesis, Kyoto University (in Japanese).
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.
Pfister, L. W., Chan, K. R., Bui, T. P., Bowen, S., Legg, M., Gary, B., Kelly, K., Proffitt, M. & Starr, W. 1993 Gravity waves generated by a tropical cyclone during the STEP Tropical Field Program: a case study. J. Geophys. Res. 98, 86118638.
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.
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.
Plougonven, R. & Zeitlin, V. 2002 Internal gravity wave emission from a pancake vortex: an example of wave–vortex interaction in strongly stratified flows. Phys. Fluids 14, 12591268.
Plougonven, R. & Zhang, F. 2014 Internal gravity waves from atmospheric jets and fronts. Rev. Geophys. 52, 3376.
Polvani, L. M., McWilliams, J. C., Spall, M. A. & Ford, R. 1994 The coherent strucutres of shallow water turbulence: deformation-radius effects, cyclone/anticyclone asymmetry and gravity wave generation. Chaos 4 (2), 177186.
Powell, A. 1964 Theory of vortex sound. J. Acoust. Soc. Am. 36, 177195.
Sato, K. 1994 A statistical study of the structure, saturation and sources of inertio-gravity waves in the lower stratosphere observed with the MU radar. J. Atmos. Terr. Phys. 56, 755774.
Sato, K. & Yoshiki, M. 2008 Gravity wave generation around the polar vortex in the stratosphere revealed by 3-hourly radiosonde observations at Syowa station. J. Atmos. Sci. 65, 37193735.
Saujani, S. & Shepherd, T. G. 2002 Comments on ‘Balance and the slow quasimanifold: some explicit results’. J. Atmos. Sci. 59, 28742877.
Schecter, D. A. & Montgomery, M. T. 2004 Damping and pumping of a vortex Rossby wave in a monotonic cyclone: critical layer stirring versus inertia-buoyancy wave emission. Phys. Fluids 16, 13341348.
Snyder, C., Muraki, D. J., Plougonven, R. & Zhang, F. 2007 Inertia–gravity waves generated within dipole vortex. J. Atmos. Sci. 64, 44174431.
Stegner, A. & Dritschel, D. G. 2000 A numerical investigation of the stability of isolated shallow water vortices. J. Phys. Oceanogr. 30, 25622573.
Sugimoto, N. & Ishii, K. 2012 Spontaneous gravity wave radiation in a shallow water system on a rotating sphere. J. Met. Soc. Japan 90 (1), 101125.
Sugimoto, N., Ishioka, K. & Ishii, K. 2008 Parameter sweep experiments on spontaneous gravity wave radiation from unsteady rotational flow in an $f$ -plane shallow water system. J. Atmos. Sci. 65, 249273.
Sugimoto, N., Ishioka, K. & Yoden, S. 2007a Balance regimes for the stability of a jet in an $f$ -plane shallow water system. Fluid Dyn. Res. 39, 353377.
Sugimoto, N., Ishioka, K. & Yoden, S. 2007b Gravity wave radiation from unsteady rotational flow in an $f$ -plane shallow water system. Fluid Dyn. Res. 39, 731754.
Sugimoto, N., Takagi, M. & Matsuda, Y. 2014 Baroclinic instability in the Venus atmosphere simulated by GCM. J. Geophys. Res. Planets 119, 19501968.
Uccelini, L. W. & Koch, S. E. 1987 The synoptic setting and possible energy sources for mesoscale wave disturbances. Mon. Weath. Rev. 115, 721729.
Vanneste, J. 2008 Exponential smallness of inertia–gravity wave generation at small Rossby number. J. Atmos. Sci. 65, 16221637.
Vanneste, J. 2013 Balance and spontanous wave generation in geophysical flows. Annu. Rev. Fluid Mech. 45, 147172.
Viúdez, Á. 2007 The origin of the stationary frontal wave packet spontaneously generated in rotating stratified vortex dipoles. J. Fluid Mech. 593, 359383.
Wang, S., Zhang, F. & Snyder, C. 2009 Generation and propagation of inertia–gravity waves from vortex dipoles and jets. J. Atmos. Sci. 66, 12941314.
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.
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, 34533556.
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, 2255.
Wu, D. L. & Eckermann, S. D. 2008 Global gravity wave variance from Aura MLS: characteristics and interpretation. J. Atmos. Sci. 65, 36953718.
Yao, H. B., Zabusky, N. J. & Dritschel, D. G. 1995 High gradient phenomena in two-dimensional vortex interactions. Phys. Fluids 7, 539548.
Yasuda, Y., Sato, K. & Sugimoto, N. 2015a 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, 957983.
Yasuda, Y., Sato, K. & Sugimoto, N. 2015b A theoretical study on the spontaneous radiation of inertia–gravity waves using the renormalization group method. Part II: verification of the theoretical equations by numerical simulation. J. Atmos. Sci. 72, 9841009.
Yoshiki, M. & Sato, K. 2000 A statistical study of gravity waves in the polar regions based on operational radiosonde data. J. Geophys. Res. 105, 1799518011.
Zeitlin, V. 1991 On the backreaction of acoustic radiation for distributed two-dimensional vortex structures. Phys. Fluids A3, 16771680.
Zeitlin, V. 2007 Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances. Elsevier.
Zhang, F. 2004 Generation of mesoscale gravity waves in upper tropospheric jet-front systems. J. Atmos. Sci. 61, 440457.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Cyclone–anticyclone asymmetry in gravity wave radiation from a co-rotating vortex pair in rotating shallow water

  • Norihiko Sugimoto (a1), K. Ishioka (a2), H. Kobayashi (a1) and Y. Shimomura (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed