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Inertial and gravity wave transmissions near radiative–convective boundaries

Published online by Cambridge University Press:  14 April 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
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Abstract

In this paper, we study inertial and gravity wave transmissions near radiative–convective boundaries on the f-plane. Two configurations have been considered: waves propagate from the convective layer to the radiative stratified stable layer, or the other way around. It has been found that waves prefer to survive at low latitudes when the stable layer is strongly stratified ($N^2/(2\varOmega )^2>1$). When the stable layer is weakly stratified ($N^2/(2\varOmega )^2 < 1$), however, waves can survive at any latitude if the meridional wavenumber is large. Then we have discussed transmission ratios for two buoyancy frequency structures: the uniform stratification and the continuously varying stratification. For the uniform stratification, we have found that the transmission is efficient when the rotation is rapid, or when the wave is near the critical colatitude. For the continuously varying stratification, we have discussed the transmission ratio when the square of buoyancy frequency is an algebraic function $N^2\propto z^{\nu } (\nu >0)$. We have found that the transmission can be efficient when the rotation is rapid, or when the wave is near the critical colatitude, or when the thickness of the stratification layer is far greater than the horizontal wavelength. The transmission ratio does not depend on the configurations (radiative layer sits above convective layer, or vice versa; wave propagates outward or inward), but only on characteristics of the wave (frequency and wavenumber) and the fluid (degree of stratification).

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Rotating flows Geophysical and Geological Flows: Stratified flows

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 916 , 10 June 2021 , A48
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© The Author(s), 2021. Published by Cambridge University Press

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