Linear development of quasi- geostrophic baroclinic disturbances with condensational heating.

Peter R. Bannon

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

This paper presents the linear solution to the initial value problem for the Eady model of baroclinic instability including condensational heating using a wave-CISK formulation with a uniform heating profile in the vertical. As in the dry case, the continuous spectrum completes the class of free mode solutions but is asymptotically stable. In the moist case, both the dry and the moist normal modes contribute to the solution to the initial value problem. Analysis of the moist Eady dispersion relation indicates that the heating increases the growth rate and the wavenumber of the most unstable mode and of the short-wave cutoff. For all values of the heating amplitude, the growth rate is bounded, both wavenumbers are finite, and the very short waves are always stable. Shallow clouds, however, increase both wavenumbers more than deep clouds. Four sufficiently large values of the heating amplitude, the free modes display unphysical behaviour with steering levels either above the rigid-lid tropopause or below the ground. The absence of any free modes when the wind shear vanishes implies that no free, inviscid, quasi-geostrophic, wave-CISK disturbances exist on the f-plane. The temporal and spatial structure of the most unstable moist Eady wave with shallow convective heating compares favourably to observations of intermediate scale disturbances on tshe Baiu front. The Appendix treats the case of condensational heating from large-scale ascent in an atmosphere with a saturated layer.-Author

Original languageEnglish (US)
Pages (from-to)2261-2274
Number of pages14
JournalJournal of the Atmospheric Sciences
Volume43
Issue number20
DOIs
StatePublished - Jan 1 1986

Fingerprint

heating
disturbance
display behavior
baroclinic instability
wind shear
tropopause
atmosphere

All Science Journal Classification (ASJC) codes

  • Atmospheric Science

Cite this

@article{d1608c26cc5b4748a527f7df9ee1ed33,
title = "Linear development of quasi- geostrophic baroclinic disturbances with condensational heating.",
abstract = "This paper presents the linear solution to the initial value problem for the Eady model of baroclinic instability including condensational heating using a wave-CISK formulation with a uniform heating profile in the vertical. As in the dry case, the continuous spectrum completes the class of free mode solutions but is asymptotically stable. In the moist case, both the dry and the moist normal modes contribute to the solution to the initial value problem. Analysis of the moist Eady dispersion relation indicates that the heating increases the growth rate and the wavenumber of the most unstable mode and of the short-wave cutoff. For all values of the heating amplitude, the growth rate is bounded, both wavenumbers are finite, and the very short waves are always stable. Shallow clouds, however, increase both wavenumbers more than deep clouds. Four sufficiently large values of the heating amplitude, the free modes display unphysical behaviour with steering levels either above the rigid-lid tropopause or below the ground. The absence of any free modes when the wind shear vanishes implies that no free, inviscid, quasi-geostrophic, wave-CISK disturbances exist on the f-plane. The temporal and spatial structure of the most unstable moist Eady wave with shallow convective heating compares favourably to observations of intermediate scale disturbances on tshe Baiu front. The Appendix treats the case of condensational heating from large-scale ascent in an atmosphere with a saturated layer.-Author",
author = "Bannon, {Peter R.}",
year = "1986",
month = "1",
day = "1",
doi = "10.1175/1520-0469(1986)043<2261:LDOQGB>2.0.CO;2",
language = "English (US)",
volume = "43",
pages = "2261--2274",
journal = "Journals of the Atmospheric Sciences",
issn = "0022-4928",
publisher = "American Meteorological Society",
number = "20",

}

Linear development of quasi- geostrophic baroclinic disturbances with condensational heating. / Bannon, Peter R.

In: Journal of the Atmospheric Sciences, Vol. 43, No. 20, 01.01.1986, p. 2261-2274.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Linear development of quasi- geostrophic baroclinic disturbances with condensational heating.

AU - Bannon, Peter R.

PY - 1986/1/1

Y1 - 1986/1/1

N2 - This paper presents the linear solution to the initial value problem for the Eady model of baroclinic instability including condensational heating using a wave-CISK formulation with a uniform heating profile in the vertical. As in the dry case, the continuous spectrum completes the class of free mode solutions but is asymptotically stable. In the moist case, both the dry and the moist normal modes contribute to the solution to the initial value problem. Analysis of the moist Eady dispersion relation indicates that the heating increases the growth rate and the wavenumber of the most unstable mode and of the short-wave cutoff. For all values of the heating amplitude, the growth rate is bounded, both wavenumbers are finite, and the very short waves are always stable. Shallow clouds, however, increase both wavenumbers more than deep clouds. Four sufficiently large values of the heating amplitude, the free modes display unphysical behaviour with steering levels either above the rigid-lid tropopause or below the ground. The absence of any free modes when the wind shear vanishes implies that no free, inviscid, quasi-geostrophic, wave-CISK disturbances exist on the f-plane. The temporal and spatial structure of the most unstable moist Eady wave with shallow convective heating compares favourably to observations of intermediate scale disturbances on tshe Baiu front. The Appendix treats the case of condensational heating from large-scale ascent in an atmosphere with a saturated layer.-Author

AB - This paper presents the linear solution to the initial value problem for the Eady model of baroclinic instability including condensational heating using a wave-CISK formulation with a uniform heating profile in the vertical. As in the dry case, the continuous spectrum completes the class of free mode solutions but is asymptotically stable. In the moist case, both the dry and the moist normal modes contribute to the solution to the initial value problem. Analysis of the moist Eady dispersion relation indicates that the heating increases the growth rate and the wavenumber of the most unstable mode and of the short-wave cutoff. For all values of the heating amplitude, the growth rate is bounded, both wavenumbers are finite, and the very short waves are always stable. Shallow clouds, however, increase both wavenumbers more than deep clouds. Four sufficiently large values of the heating amplitude, the free modes display unphysical behaviour with steering levels either above the rigid-lid tropopause or below the ground. The absence of any free modes when the wind shear vanishes implies that no free, inviscid, quasi-geostrophic, wave-CISK disturbances exist on the f-plane. The temporal and spatial structure of the most unstable moist Eady wave with shallow convective heating compares favourably to observations of intermediate scale disturbances on tshe Baiu front. The Appendix treats the case of condensational heating from large-scale ascent in an atmosphere with a saturated layer.-Author

UR - http://www.scopus.com/inward/record.url?scp=0022841453&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022841453&partnerID=8YFLogxK

U2 - 10.1175/1520-0469(1986)043<2261:LDOQGB>2.0.CO;2

DO - 10.1175/1520-0469(1986)043<2261:LDOQGB>2.0.CO;2

M3 - Article

AN - SCOPUS:0022841453

VL - 43

SP - 2261

EP - 2274

JO - Journals of the Atmospheric Sciences

JF - Journals of the Atmospheric Sciences

SN - 0022-4928

IS - 20

ER -