1,360
Views
1
CrossRef citations to date
0
Altmetric
Research Article

Nonlinear interaction of gravity and acoustic waves

& ORCID Icon
Pages 1-17 | Received 05 Aug 2019, Accepted 09 Dec 2019, Published online: 10 Jan 2020

References

  • Andrews, D. G. 1981. A note on potential energy density in a stratified compressible fluid. J. Fluid Mech. 107, 227–236. doi:10.1017/S0022112081001754
  • Arnol’d, V. 1989. Mathematical Methods of Classical Mechanics. Graduate Texts in Mathematics. Springer, New York.
  • Bannon, P. R. 1995. Hydrostatic adjustment: Lamb’s problem. J. Atmos. Sci. 52, 1743–1752. doi:10.1175/1520-0469(1995)052<1743:HALP>2.0.CO;2
  • Bannon, P. R. 1996. Nonlinear hydrostatic adjustment. J. Atmos. Sci. 53, 3606–3617. doi:10.1175/1520-0469(1996)053<3606:NHA>2.0.CO;2
  • Benettin, G., Galgani, L. and Strelcyn, J.-M. 1976. Kolmogorov entropy and numerical experiments. Phys. Rev. A 14, 2338–2345. doi:10.1103/PhysRevA.14.2338
  • Bustamante, M. D., Quinn, B. and Lucas, D. 2014. Robust energy transfer mechanism via precession resonance in nonlinear turbulent wave systems. Phys. Rev. Letters. 113, 084502. doi:10.1103/PhysRevLett.113.084502
  • Chagnon, J. M. and Bannon, P. R. 2001. Hydrostatic and geostrophic adjustment in a compressible atmosphere: Initial response and final equilibrium to an instantaneous localized heating. J. Atmos. Sci. 58, 3776–3792. doi:10.1175/1520-0469(2001)058<3776:HAGAIA>2.0.CO;2
  • Chagnon, J. M. and Bannon, P. R. 2005a. Wave response during hydrostatic and geostrophic adjustment. Part I: Transient dynamics. J. Atmos. Sci. 62, 1311–1329. doi:10.1175/JAS3283.1
  • Chagnon, J. M. and Bannon, P. R. 2005b. Wave response during hydrostatic and geostrophic adjustment. Part II: Potential vorticity conservation and energy partitioning. J. Atmos. Sci. 62, 1330–1345. doi:10.1175/JAS3419.1
  • Connaughton, C., Nadiga, B. T., Nazarenko, S. and Quinn, B. 2010. Modulational instability of Rossby and drift waves and generation of zonal jets. J. Fluid Mech. 654, 207–231. doi:10.1017/S0022112010000510
  • Craik, A. D. D. 1988. Wave interactions and fluid flows. Cambridge Monographs on Mechanics and Applied Math. Cambridge University Press, Cambridge, UK.
  • Daley, R. 1988. The normal modes of the spherical nonhydrostatic equations with applications to the filterinf of acoustic modes. Tellus 40A, 96–106. doi:10.1111/j.1600-0870.1988.tb00409.x
  • Datseris, G. 2018. Dynamicalsystems.jl: A Julia software library for chaos and nonlinear dynamics. JOSS. 3, 598. doi:10.21105/joss.00598
  • Davies, T., Staniforth, A., Wood, N. and Thuburn, J. 2003. Validity of anelastic and other equation sets as inferred from normal-mode analysis. Q. J. R. Meteorol. Soc. 129, 2761–2775. doi:10.1256/qj.02.1951
  • Domaracki, A. and Lossch, A. Z. 1977. Nonlinear interactions among equatorial waves. J. Atmos. Sci. 34, 486–498. doi:10.1175/1520-0469(1977)034<0486:NIAEW>2.0.CO;2
  • Duffy, D. G. 1974. Resonant interactions of inertio-gravity and Rossby waves. J. Atmos. Sci. 31, 1218–1231. doi:10.1175/1520-0469(1974)031<1218:RIOIGA>2.0.CO;2
  • Duffy, D. G. 2003. Hydrostatic adjustment in nonisothermal atmospheres. J. Atmos. Sci. 60, 339–353. doi:10.1175/1520-0469(2003)060<0339:HAINA>2.0.CO;2
  • Eckart, C. 1960. Hydrodynamics of Oceans and Atmospheres. Pergamon Press, London.
  • Fanelli, P. F. and Bannon, P. R. 2005. Nonlinear atmospheric adjustment to thermal forcing. J. Atmos. Sci. 62, 4253–4272. doi:10.1175/JAS3517.1
  • Giraldo, F. X., Restelli, M. and Läuter, M. 2010. Semi-implicit formulations of the Navier-Stokes equations: Application to nonhydrostatic atmospheric modeling. SIAM J. Sci. Comput. 32, 3394–3425. doi:10.1137/090775889
  • Janssen, P. A. E. M. 2003. Nonlinear four-wave interactions and freak waves. J. Phys. Oceanogr. 33, 863–884. doi:10.1175/1520-0485(2003)33<863:NFIAFW>2.0.CO;2
  • Kasahara, A. 2003a. The roles of the horizontal component of the earth’s angular velocity in nonhydrostatic linear models. J. Atmos. Sci. 60, 1085–1095. doi:10.1175/1520-0469(2003)60<1085:TROTHC>2.0.CO;2
  • Kasahara, A. 2003b. On the nonhydrostatic atmospheric models with inclusion of the horizontal component of the earth’s angular velocity. JMSJ. 81, 935–950. doi:10.2151/jmsj.81.935
  • Kasahara, A. 2004. Free oscillations of deep nonhydrostatic global atmospheres: Theory and a test of numerical schemes. NCAR Tech. Rep. NCAR/TN-457 + STR, NCAR. University Corporation for Atmospheric Research, Boulder, CO.
  • Kasahara, A. and Gary, M. 2006. Normal modes of an incompressible and stratified fluid model including the vertical and horizontal components of Coriolis force. Tellus 58, 368–384. doi:10.1111/j.1600-0870.2006.00182.x
  • Kasahara, A. and Qian, J.-H. 2000. Normal modes of a global nonhydrostatic atmospheric model. Mon. Wea. Rev. 128, 3357–3375. doi:10.1175/1520-0493(2000)128<3357:NMOAGN>2.0.CO;2
  • Klein, R. 2009. Asymptotics, structure, and integration of sound-proof atmospheric flow equations. Theor. Comput. Fluid Dyn. 23, 161–195. doi:10.1007/s00162-009-0104-y
  • Klemp, J. B., Skamarock, W. C. and Ha, S. 2018. Damping acoustic modes in compressible horizontally explicit vertically implicit (HEVI) and split-explicit time integration schemes. Mon. Wea. Rev. 146, 1911–1923. doi:10.1175/MWR-D-17-0384.1
  • Loesch, A. Z. and Deininger, R. C. 1979. Dynamics of closed systems of resonantly interacting equatorial waves. J. Atmos. Sci. 36, 1490–1497. doi:10.1175/1520-0469(1979)036<1490:DOCSOR>2.0.CO;2
  • Majda, A. 2003. Introduction to PDEs and Waves for the Atmosphere and Ocean. Courant Lecture Notes in Mathematics Series. Courant Institute of Mathematical Sciences,.New York University, New York.
  • Majda, A. J. and Embid, P. 1998. Averaging over fast waves for geophysical flows with unbalanced initial data. Theor. Comput. Fluid Dyn. 11, 155–169. doi:10.1007/s001620050086
  • Pielke, R. 2002. Mesoscale Meteorological Modeling. International Geophysics Series. Academic Press, California. ISBN 9780125547666.
  • Qian, J.-H. and Kasahara, A. 2003. Nonhydrostatic atmospheric normal modes on beta-planes. Pure Appl. Geophys. 160, 1315–1358.
  • Raupp, C. F. M., Silva Dias, P. L., Tabak, E. G. and Milewski, P. 2008. Resonant wave interactions in the equatorial waveguide. J. Atmos. Sci. 65, 3398–3418. doi:10.1175/2008JAS2387.1
  • Raupp, C. F. M., Teruya, A. S. W. and Silva Dias, P. L. 2019. Linear and weakly nonlinear energetics of global nonhydrostatic normal modes. J. Atmos. Sci. 76, 3831–3846. doi:10.1175/JAS-D-19-0131.1
  • Ripa, P. 1981. On the theory of nonlinear wave-wave interactions among geophysical waves. J. Fluid Mech. 103, 87–115. doi:10.1017/S0022112081001250
  • Ripa, P. 1983a. Weak interactions of equatorial waves in a one-layer model. Part I: General properties. J. Phys. Oceanogr. 13, 1208–1226. doi:10.1175/1520-0485(1983)013<1208:WIOEWI>2.0.CO;2
  • Ripa, P. 1983b. Weak interactions of equatorial waves in a one-layer model. Part II: Applications. J. Phys. Oceanogr. 13, 1227–1240. doi:10.1175/1520-0485(1983)013<1227:WIOEWI>2.0.CO;2
  • Shepherd, T. D. 1990. Symmetries, conservation laws, and Hamiltonian structure in geophysical fluid dynamics. Adv. Geophys. 32, 287–338. doi:10.1016/S0065-2687(08)60429-X
  • Shepherd, T. G. 1993. A unified theory of available potential energy. Atmos. Ocean 31, 1–26. doi:10.1080/07055900.1993.9649460
  • Smith, L. M. and Lee, Y. 2005. On near resonances and symmetry breaking in forced rotating flows at moderate Rossby number. J. Fluid Mech. 535, 111–142. doi:10.1017/S0022112005004660
  • Taylor, G. I. 1936. The oscillations of the atmosphere. Proc. R. Soc. London 156, 318–326.
  • Thuburn, J. 2011. Some basic dynamics relevant to the design of atmospheric model dynamical cores. In: Numerical Techniques for Global Atmospheric Models (eds. P. H. Lauritzen, C. Jablonowski, M. A. Taylor and R. D. Nair) Vol. 80, Chapter 1, Springer, Berlin, pp. 3–27.
  • Tribbia, J. 1979. Non-linear initialization on an equatorial beta-plane. Mon. Wea. Rev. 107, 704–713. doi:10.1175/1520-0493(1979)107<0704:NIOAEB>2.0.CO;2
  • Vanneste, J. 2004. Inertia-gravity wave generation by balanced motion: revisiting the Lorenz-Krishnamurthy model. J. Atmos. Sci. 61, 224–234. doi:10.1175/1520-0469(2004)061<0224:IWGBBM>2.0.CO;2
  • Vanneste, J. and Vial, F. 1994. Nonlinear wave propagation on a sphere: Interaction between Rossby waves and gravity waves; stability of the Rossby waves. Geophys. Astrophys. Fluid Dyn. 76, 121–144. doi:10.1080/03091929408203662
  • Vanneste, J. and Yavneh, I. 2004. Exponentially small inertia-gravity waves and the breakdown of quasigeostrophic balance. J. Atmos. Sci. 61, 211–223. doi:10.1175/1520-0469(2004)061<0211:ESIWAT>2.0.CO;2
  • Weiland, J. and Wilhelmsson, H. 1977. Coherent Nonlinear Interaction of Waves in Plasmas. Pergamon, Oxford; Turkey.
  • White, A. A., Hoskins, B. J., Roulstone, I. and Staniforth, A. 2005. Consistent approximate models of the global atmosphere: Shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic. Q. J. R. Meteorol. Soc. 131, 2081–2107. doi:10.1256/qj.04.49
  • Zounes, R. and Rand, R. 1998. Transition curves for the quasi-periodic Mathieu equation. SIAM J. Appl. Math. 58, 1094–1115. doi:10.1137/S0036139996303877