Range of validity of an extended WKB theory for atmospheric gravity waves: one-dimensional and two-dimensional case
A computational model of the pseudo-incompressible equations is used to probe the range of validity of an extended Wentzel–Kramers–Brillouin theory (XWKB), previously derived through a distinguished limit of a multiple-scale asymptotic analysis of the Euler or pseudo-incompressible equations of moti...
Gespeichert in:
Veröffentlicht in: | Journal of fluid mechanics 2013-08, Vol.729, p.330-363 |
---|---|
Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
container_end_page | 363 |
---|---|
container_issue | |
container_start_page | 330 |
container_title | Journal of fluid mechanics |
container_volume | 729 |
creator | Rieper, Felix Achatz, U. Klein, R. |
description | A computational model of the pseudo-incompressible equations is used to probe the range of validity of an extended Wentzel–Kramers–Brillouin theory (XWKB), previously derived through a distinguished limit of a multiple-scale asymptotic analysis of the Euler or pseudo-incompressible equations of motion, for gravity-wave packets at large amplitudes. The governing parameter of this analysis had been the scale-separation ratio
$\varepsilon $
between the gravity wave and both the large-scale potential-temperature stratification and the large-scale wave-induced mean flow. A novel feature of the theory had been the non-resonant forcing of higher harmonics of an initial wave packet, predominantly by the large-scale gradients in the gravity-wave fluxes. In the test cases considered a gravity-wave packet is propagating upwards in a uniformly stratified atmosphere. Large-scale winds are induced by the wave packet, and possibly exert a feedback on the latter. In the limit
$\varepsilon \ll 1$
all predictions of the theory can be validated. The larger
$\varepsilon $
is the more the transfer of wave energy to the mean flow is underestimated by the theory. The numerical results quantify this behaviour but also show that, qualitatively, XWKB remains valid even when the gravity-wave wavelength approaches the spatial scale of the wave-packet amplitude. This includes the prevalence of first and second harmonics and the smallness of harmonics with wave number higher than two. Furthermore, XWKB predicts for the vertical momentum balance an additional leading-order buoyancy term in Euler and pseudo-incompressible theory, compared with the anelastic theory. Numerical tests show that this term is relatively large with up to
$30\hspace{0.167em} \% $
of the total balance. The practical relevance of this deviation remains to be assessed in future work. |
doi_str_mv | 10.1017/jfm.2013.307 |
format | Article |
fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_1710619513</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cupid>10_1017_jfm_2013_307</cupid><sourcerecordid>3802044371</sourcerecordid><originalsourceid>FETCH-LOGICAL-c332t-86f55d9e14b1adf0e00bf70cdeb43140fd3e86922b82980c67dfe34a59ada10a3</originalsourceid><addsrcrecordid>eNptkMtKAzEUQIMoWB87PyAg7pzxJpmnOy2-UBBEcTncmdzUKZ1JTcbW_r0pFlFwlRDOPbkcxo4ExAJEfjY1XSxBqFhBvsVGIsnKKM-SdJuNAKSMhJCwy_a8n0KgoMxHzD9hPyFuDV_grNXtsFrfsef0OVCvSfPX-0s-vJF1K26s4zh01s_fyLUNnzhcrCeWuCB_zm1PkW476n1re5wFi-bD0v55a9DTAdsxOPN0uDn32cv11fP4Nnp4vLkbXzxEjVJyiIrMpKkuSSS1QG2AAGqTQ6OpTpRIwGhFRVZKWReyLKDJcm1IJZiWqFEAqn12_O2dO_v-QX6opvbDhS18JXIBmShToQJ1-k01znrvyFRz13boVpWAap21ClmrddYqZA34yUaKvsGZcdg3rf-ZkaF3magicPFGi13tWj2hX7__J_4CL3mIRA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1710619513</pqid></control><display><type>article</type><title>Range of validity of an extended WKB theory for atmospheric gravity waves: one-dimensional and two-dimensional case</title><source>Cambridge Journals - CAUL Collection</source><creator>Rieper, Felix ; Achatz, U. ; Klein, R.</creator><creatorcontrib>Rieper, Felix ; Achatz, U. ; Klein, R.</creatorcontrib><description>A computational model of the pseudo-incompressible equations is used to probe the range of validity of an extended Wentzel–Kramers–Brillouin theory (XWKB), previously derived through a distinguished limit of a multiple-scale asymptotic analysis of the Euler or pseudo-incompressible equations of motion, for gravity-wave packets at large amplitudes. The governing parameter of this analysis had been the scale-separation ratio
$\varepsilon $
between the gravity wave and both the large-scale potential-temperature stratification and the large-scale wave-induced mean flow. A novel feature of the theory had been the non-resonant forcing of higher harmonics of an initial wave packet, predominantly by the large-scale gradients in the gravity-wave fluxes. In the test cases considered a gravity-wave packet is propagating upwards in a uniformly stratified atmosphere. Large-scale winds are induced by the wave packet, and possibly exert a feedback on the latter. In the limit
$\varepsilon \ll 1$
all predictions of the theory can be validated. The larger
$\varepsilon $
is the more the transfer of wave energy to the mean flow is underestimated by the theory. The numerical results quantify this behaviour but also show that, qualitatively, XWKB remains valid even when the gravity-wave wavelength approaches the spatial scale of the wave-packet amplitude. This includes the prevalence of first and second harmonics and the smallness of harmonics with wave number higher than two. Furthermore, XWKB predicts for the vertical momentum balance an additional leading-order buoyancy term in Euler and pseudo-incompressible theory, compared with the anelastic theory. Numerical tests show that this term is relatively large with up to
$30\hspace{0.167em} \% $
of the total balance. The practical relevance of this deviation remains to be assessed in future work.</description><identifier>ISSN: 0022-1120</identifier><identifier>EISSN: 1469-7645</identifier><identifier>DOI: 10.1017/jfm.2013.307</identifier><identifier>CODEN: JFLSA7</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Atmosphere ; Earth, ocean, space ; Exact sciences and technology ; External geophysics ; Fluid mechanics ; General circulation. Atmospheric waves ; Gravity ; Gravity waves ; Meteorology ; Wave energy</subject><ispartof>Journal of fluid mechanics, 2013-08, Vol.729, p.330-363</ispartof><rights>2013 Cambridge University Press</rights><rights>2014 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c332t-86f55d9e14b1adf0e00bf70cdeb43140fd3e86922b82980c67dfe34a59ada10a3</citedby><cites>FETCH-LOGICAL-c332t-86f55d9e14b1adf0e00bf70cdeb43140fd3e86922b82980c67dfe34a59ada10a3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.cambridge.org/core/product/identifier/S0022112013003078/type/journal_article$$EHTML$$P50$$Gcambridge$$H</linktohtml><link.rule.ids>164,314,780,784,27915,27916,55619</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=27649438$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Rieper, Felix</creatorcontrib><creatorcontrib>Achatz, U.</creatorcontrib><creatorcontrib>Klein, R.</creatorcontrib><title>Range of validity of an extended WKB theory for atmospheric gravity waves: one-dimensional and two-dimensional case</title><title>Journal of fluid mechanics</title><addtitle>J. Fluid Mech</addtitle><description>A computational model of the pseudo-incompressible equations is used to probe the range of validity of an extended Wentzel–Kramers–Brillouin theory (XWKB), previously derived through a distinguished limit of a multiple-scale asymptotic analysis of the Euler or pseudo-incompressible equations of motion, for gravity-wave packets at large amplitudes. The governing parameter of this analysis had been the scale-separation ratio
$\varepsilon $
between the gravity wave and both the large-scale potential-temperature stratification and the large-scale wave-induced mean flow. A novel feature of the theory had been the non-resonant forcing of higher harmonics of an initial wave packet, predominantly by the large-scale gradients in the gravity-wave fluxes. In the test cases considered a gravity-wave packet is propagating upwards in a uniformly stratified atmosphere. Large-scale winds are induced by the wave packet, and possibly exert a feedback on the latter. In the limit
$\varepsilon \ll 1$
all predictions of the theory can be validated. The larger
$\varepsilon $
is the more the transfer of wave energy to the mean flow is underestimated by the theory. The numerical results quantify this behaviour but also show that, qualitatively, XWKB remains valid even when the gravity-wave wavelength approaches the spatial scale of the wave-packet amplitude. This includes the prevalence of first and second harmonics and the smallness of harmonics with wave number higher than two. Furthermore, XWKB predicts for the vertical momentum balance an additional leading-order buoyancy term in Euler and pseudo-incompressible theory, compared with the anelastic theory. Numerical tests show that this term is relatively large with up to
$30\hspace{0.167em} \% $
of the total balance. The practical relevance of this deviation remains to be assessed in future work.</description><subject>Atmosphere</subject><subject>Earth, ocean, space</subject><subject>Exact sciences and technology</subject><subject>External geophysics</subject><subject>Fluid mechanics</subject><subject>General circulation. Atmospheric waves</subject><subject>Gravity</subject><subject>Gravity waves</subject><subject>Meteorology</subject><subject>Wave energy</subject><issn>0022-1120</issn><issn>1469-7645</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNptkMtKAzEUQIMoWB87PyAg7pzxJpmnOy2-UBBEcTncmdzUKZ1JTcbW_r0pFlFwlRDOPbkcxo4ExAJEfjY1XSxBqFhBvsVGIsnKKM-SdJuNAKSMhJCwy_a8n0KgoMxHzD9hPyFuDV_grNXtsFrfsef0OVCvSfPX-0s-vJF1K26s4zh01s_fyLUNnzhcrCeWuCB_zm1PkW476n1re5wFi-bD0v55a9DTAdsxOPN0uDn32cv11fP4Nnp4vLkbXzxEjVJyiIrMpKkuSSS1QG2AAGqTQ6OpTpRIwGhFRVZKWReyLKDJcm1IJZiWqFEAqn12_O2dO_v-QX6opvbDhS18JXIBmShToQJ1-k01znrvyFRz13boVpWAap21ClmrddYqZA34yUaKvsGZcdg3rf-ZkaF3magicPFGi13tWj2hX7__J_4CL3mIRA</recordid><startdate>20130825</startdate><enddate>20130825</enddate><creator>Rieper, Felix</creator><creator>Achatz, U.</creator><creator>Klein, R.</creator><general>Cambridge University Press</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7TB</scope><scope>7U5</scope><scope>7UA</scope><scope>7XB</scope><scope>88I</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AEUYN</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>BKSAR</scope><scope>C1K</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>F1W</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>H8D</scope><scope>H96</scope><scope>HCIFZ</scope><scope>KR7</scope><scope>L.G</scope><scope>L6V</scope><scope>L7M</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PCBAR</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>Q9U</scope><scope>S0W</scope></search><sort><creationdate>20130825</creationdate><title>Range of validity of an extended WKB theory for atmospheric gravity waves: one-dimensional and two-dimensional case</title><author>Rieper, Felix ; Achatz, U. ; Klein, R.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c332t-86f55d9e14b1adf0e00bf70cdeb43140fd3e86922b82980c67dfe34a59ada10a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Atmosphere</topic><topic>Earth, ocean, space</topic><topic>Exact sciences and technology</topic><topic>External geophysics</topic><topic>Fluid mechanics</topic><topic>General circulation. Atmospheric waves</topic><topic>Gravity</topic><topic>Gravity waves</topic><topic>Meteorology</topic><topic>Wave energy</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Rieper, Felix</creatorcontrib><creatorcontrib>Achatz, U.</creatorcontrib><creatorcontrib>Klein, R.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Water Resources Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest One Sustainability</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection (ProQuest)</collection><collection>Natural Science Collection (ProQuest)</collection><collection>Earth, Atmospheric & Aquatic Science Collection</collection><collection>Environmental Sciences and Pollution Management</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ASFA: Aquatic Sciences and Fisheries Abstracts</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>Aerospace Database</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources</collection><collection>SciTech Premium Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) Professional</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Earth, Atmospheric & Aquatic Science Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><collection>DELNET Engineering & Technology Collection</collection><jtitle>Journal of fluid mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Rieper, Felix</au><au>Achatz, U.</au><au>Klein, R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Range of validity of an extended WKB theory for atmospheric gravity waves: one-dimensional and two-dimensional case</atitle><jtitle>Journal of fluid mechanics</jtitle><addtitle>J. Fluid Mech</addtitle><date>2013-08-25</date><risdate>2013</risdate><volume>729</volume><spage>330</spage><epage>363</epage><pages>330-363</pages><issn>0022-1120</issn><eissn>1469-7645</eissn><coden>JFLSA7</coden><abstract>A computational model of the pseudo-incompressible equations is used to probe the range of validity of an extended Wentzel–Kramers–Brillouin theory (XWKB), previously derived through a distinguished limit of a multiple-scale asymptotic analysis of the Euler or pseudo-incompressible equations of motion, for gravity-wave packets at large amplitudes. The governing parameter of this analysis had been the scale-separation ratio
$\varepsilon $
between the gravity wave and both the large-scale potential-temperature stratification and the large-scale wave-induced mean flow. A novel feature of the theory had been the non-resonant forcing of higher harmonics of an initial wave packet, predominantly by the large-scale gradients in the gravity-wave fluxes. In the test cases considered a gravity-wave packet is propagating upwards in a uniformly stratified atmosphere. Large-scale winds are induced by the wave packet, and possibly exert a feedback on the latter. In the limit
$\varepsilon \ll 1$
all predictions of the theory can be validated. The larger
$\varepsilon $
is the more the transfer of wave energy to the mean flow is underestimated by the theory. The numerical results quantify this behaviour but also show that, qualitatively, XWKB remains valid even when the gravity-wave wavelength approaches the spatial scale of the wave-packet amplitude. This includes the prevalence of first and second harmonics and the smallness of harmonics with wave number higher than two. Furthermore, XWKB predicts for the vertical momentum balance an additional leading-order buoyancy term in Euler and pseudo-incompressible theory, compared with the anelastic theory. Numerical tests show that this term is relatively large with up to
$30\hspace{0.167em} \% $
of the total balance. The practical relevance of this deviation remains to be assessed in future work.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/jfm.2013.307</doi><tpages>34</tpages></addata></record> |
fulltext | fulltext |
identifier | ISSN: 0022-1120 |
ispartof | Journal of fluid mechanics, 2013-08, Vol.729, p.330-363 |
issn | 0022-1120 1469-7645 |
language | eng |
recordid | cdi_proquest_journals_1710619513 |
source | Cambridge Journals - CAUL Collection |
subjects | Atmosphere Earth, ocean, space Exact sciences and technology External geophysics Fluid mechanics General circulation. Atmospheric waves Gravity Gravity waves Meteorology Wave energy |
title | Range of validity of an extended WKB theory for atmospheric gravity waves: one-dimensional and two-dimensional case |
url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-15T06%3A50%3A39IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Range%20of%20validity%20of%20an%20extended%20WKB%20theory%20for%20atmospheric%20gravity%20waves:%20one-dimensional%20and%20two-dimensional%20case&rft.jtitle=Journal%20of%20fluid%20mechanics&rft.au=Rieper,%20Felix&rft.date=2013-08-25&rft.volume=729&rft.spage=330&rft.epage=363&rft.pages=330-363&rft.issn=0022-1120&rft.eissn=1469-7645&rft.coden=JFLSA7&rft_id=info:doi/10.1017/jfm.2013.307&rft_dat=%3Cproquest_cross%3E3802044371%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1710619513&rft_id=info:pmid/&rft_cupid=10_1017_jfm_2013_307&rfr_iscdi=true |