Hostname: page-component-5d84bcc8dc-w56mk Total loading time: 0 Render date: 2026-09-04T19:50:49.002Z Has data issue: false hasContentIssue false
  • English
  • Français

Enhancement of wave transmissions in multiple radiative and convective zones

Published online by Cambridge University Press:  31 March 2021

Tao Cai Open the ORCID record for Tao Cai [Opens in a new window] ,
Cong Yu Open the ORCID record for Cong Yu [Opens in a new window]  and
Xing Wei Open the ORCID record for Xing Wei [Opens in a new window]
Tao Cai*
Affiliation:
State Key Laboratory of Lunar and Planetary Sciences, Macau University of Science and Technology, Macau, PR China
Cong Yu*
Affiliation:
State Key Laboratory of Lunar and Planetary Sciences, Macau University of Science and Technology, Macau, PR China School of Physics and Astronomy, Sun Yat-sen University, Zhuhai 519082, PR China
Xing Wei
Affiliation:
Department of Astronomy, Beijing Normal University, Beijing 100875, PR China
*
†Email addresses for correspondence: tcai@must.edu.mo, yucong@mail.sysu.edu.cn
†Email addresses for correspondence: tcai@must.edu.mo, yucong@mail.sysu.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we study wave transmission in a rotating fluid with multiple alternating convectively stable and unstable layers. We have discussed wave transmissions in two different circumstances: cases where the wave is propagative in each layer and cases where wave tunnelling occurs. We find that efficient wave transmission can be achieved by ‘resonant propagation’ or ‘resonant tunnelling’, even when stable layers are strongly stratified, and we call this phenomenon ‘enhanced wave transmission’. Enhanced wave transmission only occurs when the total number of layers is odd (embedding stable layers are alternatingly embedded within clamping convective layers, or vice versa). For wave propagation, the occurrence of enhanced wave transmission requires that the clamping layers have similar properties, the thickness of each clamping layer is close to a multiple of the half-wavelength of the corresponding propagative wave and the total thickness of the embedded layers is close to a multiple of the half-wavelength of the corresponding propagating wave (resonant propagation). For wave tunnelling, we have considered two cases: tunnelling of gravity waves and tunnelling of inertial waves. In both cases, efficient tunnelling requires that the clamping layers have similar properties, the thickness of each embedded layer is much smaller than the corresponding e-folding decay distance and the thickness of each clamping layer is close to a multiple-and-a-half of the half-wavelength (resonant tunnelling).

JFM classification

Geophysical and Geological Flows: Rotating flows Geophysical and Geological Flows: Stratified flows Geophysical and Geological Flows: Waves in rotating fluids

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A125
Check for updates
Copyright
© The Author(s), 2021. Published by 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.)

Article purchase

Temporarily unavailable

References

REFERENCES

Aerts, C., Mathis, S. & Rogers, T.M. 2019 Angular momentum transport in stellar interiors. Annu. Rev. Astron. Astrophys. 57, 35–78.CrossRefGoogle Scholar
André, Q., Barker, A.J. & Mathis, S. 2017 Layered semi-convection and tides in giant planet interiors-I. Propagation of internal waves. Astron. Astrophys. 605, A117.CrossRefGoogle Scholar
Belkacem, K., Marques, J.P., Goupil, M.J., Sonoi, T., Ouazzani, R.M., Dupret, M.-A., Mathis, S., Mosser, B. & Grosjean, M. 2015 a Angular momentum redistribution by mixed modes in evolved low-mass stars-I. Theoretical formalism. Astron. Astrophys. 579, A30.CrossRefGoogle Scholar
Belkacem, K., Marques, J.P., Goupil, M.J., Sonoi, T., Ouazzani, R.M., Dupret, M.-A., Mathis, S., Mosser, B. & Grosjean, M. 2015 b Angular momentum redistribution by mixed modes in evolved low-mass stars-II. Spin-down of the core of red giants induced by mixed modes. Astron. Astrophys. 579, A31.CrossRefGoogle Scholar
Belyaev, M.A., Quataert, E. & Fuller, J. 2015 The properties of g-modes in layered semiconvection. Mon. Not. R. Astron. Soc. 452 (3), 2700–2711.CrossRefGoogle Scholar
Cai, T. 2014 Numerical analysis of non-local convection. Mon. Not. R. Astron. Soc. 443 (4), 3703–3711.CrossRefGoogle Scholar
Cai, T., Yu, C. & Wei, X. 2021 Inertial and gravity wave transmissions near radiative-convective boundaries. J. Fluid Mech. (accepted) arXiv:2008.00205.Google Scholar
Fuller, J. 2014 Saturn ring seismology: evidence for stable stratification in the deep interior of saturn. Icarus 242, 283–296.CrossRefGoogle Scholar
Garaud, P. 2018 Double-diffusive convection at low Prandtl number. Annu. Rev. Fluid Mech. 50, 275–298.CrossRefGoogle Scholar
Gerkema, T. & Exarchou, E. 2008 Internal-wave properties in weakly stratified layers. J. Mar. Res. 66 (5), 617–644.CrossRefGoogle Scholar
Gerkema, T. & Shrira, V.I. 2005 a Near-inertial waves on the nontraditional $\beta$ plane. J. Geophys. Res.: Oceans 110, C10003.CrossRefGoogle Scholar
Gerkema, T. & Shrira, V.I. 2005 b Near-inertial waves in the ocean: beyond the “traditional approximation”. J. Fluid Mech. 529, 195–219.CrossRefGoogle Scholar
Ghaemsaidi, S.J., Dosser, H.V., Rainville, L. & Peacock, T. 2016 The impact of multiple layering on internal wave transmission. J. Fluid Mech. 789, 617–629.CrossRefGoogle Scholar
Goodman, J. & Lackner, C. 2009 Dynamical tides in rotating planets and stars. Astrophys. J. 696 (2), 2054–2067.CrossRefGoogle Scholar
Leconte, J. & Chabrier, G. 2012 A new vision of giant planet interiors: impact of double diffusive convection. Astron. Astrophys. 540, A20.CrossRefGoogle Scholar
Mihalas, D. & Mihalas, B.W. 2013 Foundations of Radiation Hydrodynamics. Courier Corporation.Google Scholar
Miralles, J.A., Urpin, V. & Van Riper, K. 1997 Convection in the surface layers of neutron stars. Astrophys. J. 480 (1), 358–363.CrossRefGoogle Scholar
Mirouh, G.M., Garaud, P., Stellmach, S., Traxler, A.L. & Wood, T.S. 2012 A new model for mixing by double-diffusive convection (semi-convection). I. The conditions for layer formation. Astrophys. J. 750 (1), 61.CrossRefGoogle Scholar
Moore, K. & Garaud, P. 2016 Main sequence evolution with layered semiconvection. Astrophys. J. 817 (1), 54.CrossRefGoogle Scholar
Ogilvie, G.I. & Lin, D.N.C. 2004 Tidal dissipation in rotating giant planets. Astrophys. J. 610 (1), 477–509.CrossRefGoogle Scholar
Pinçon, C., Belkacem, K., Goupil, M.J. & Marques, J.P. 2017 Can plume-induced internal gravity waves regulate the core rotation of subgiant stars? Astron. Astrophys. 605, A31.CrossRefGoogle Scholar
Pontin, C.M., Barker, A.J., Hollerbach, R., André, Q. & Mathis, S. 2020 Wave propagation in semiconvective regions of giant planets. Mon. Not. R. Astron. Soc. 493 (4), 5788–5806.CrossRefGoogle Scholar
Rainville, L. & Winsor, P. 2008 Mixing across the arctic ocean: microstructure observations during the beringia 2005 expedition. Geophys. Res. Lett. 35, L08606.CrossRefGoogle Scholar
Rieutord, M., Georgeot, B. & Valdettaro, L. 2001 Inertial waves in a rotating spherical shell: attractors and asymptotic spectrum. J. Fluid Mech. 435, 103–144.CrossRefGoogle Scholar
Rieutord, M. & Valdettaro, L. 1997 Inertial waves in a rotating spherical shell. J. Fluid Mech. 341, 77–99.CrossRefGoogle Scholar
Rogers, T.M., Lin, D.N.C. & Lau, H.H.B. 2012 Internal gravity waves modulate the apparent misalignment of exoplanets around hot stars. Astrophys. J. Lett. 758 (1), L6.CrossRefGoogle Scholar
Rogers, T.M., Lin, D.N.C., McElwaine, J.N. & Lau, H.H.B. 2013 Internal gravity waves in massive stars: angular momentum transport. Astrophys. J. 772 (1), 21.CrossRefGoogle Scholar
Shrira, V.I. & Townsend, W.A. 2010 Inertia-gravity waves beyond the inertial latitude. Part 1. Inviscid singular focusing. J. Fluid Mech. 664, 478–509.CrossRefGoogle Scholar
Silvers, L.J. & Proctor, M.R.E. 2007 The interaction of multiple convection zones in A-type stars. Mon. Not. R. Astron. Soc. 380 (1), 44–50.CrossRefGoogle Scholar
Singh, Y. 2010 Semiconductor Devices. IK International Pvt Ltd.Google Scholar
Sutherland, B.R. 1996 Internal gravity wave radiation into weakly stratified fluid. Phys. Fluids 8 (2), 430–441.CrossRefGoogle Scholar
Sutherland, B.R. 2016 Internal wave transmission through a thermohaline staircase. Phys. Rev. Fluids 1 (1), 013701.CrossRefGoogle Scholar
Sutherland, B.R. & Yewchuk, K. 2004 Internal wave tunnelling. J. Fluid Mech. 511, 125–134.CrossRefGoogle Scholar
Tellmann, S., Pätzold, M., Häusler, B., Bird, M.K. & Tyler, G.L. 2009 Structure of the venus neutral atmosphere as observed by the radio science experiment vera on venus express. J. Geophys. Res.: Planets 114, E00B36.Google Scholar
Wei, X. 2020 a Wave reflection and transmission at the interface of convective and stably stratified regions in a rotating star or planet. Astrophys. J. 890 (1), 20.CrossRefGoogle Scholar
Wei, X. 2020 b Erratum: wave reflection and transmission at the interface of convective and stably stratified regions in a rotating star or planet (APJ, 2020, 890, 20). Astrophys. J. 899 (1), 88.CrossRefGoogle Scholar
Wood, T.S., Garaud, P. & Stellmach, S. 2013 A new model for mixing by double-diffusive convection (semi-convection). II. The transport of heat and composition through layers. Astrophys. J. 768 (2), 157.CrossRefGoogle Scholar
Wu, Y. 2005 a Origin of tidal dissipation in Jupiter. I. Properties of inertial modes. Astrophys. J. 635 (1), 674–687.CrossRefGoogle Scholar
Wu, Y. 2005 b Origin of tidal dissipation in Jupiter. II. The value of Q. Astrophys. J. 635 (1), 688–710.CrossRefGoogle Scholar
Zhang, K. & Liao, X. 2017 Theory and Modeling of Rotating Fluids: Convection, Inertial Waves and Precession. Cambridge University Press.CrossRefGoogle Scholar