Unstable jets generated by a sphere descending in a very strongly stratified fluid
The flow around a sphere descending at constant speed in a very strongly stratified fluid ( $Fr\lesssim 0.2$ ) is investigated by the shadowgraph method and particle image velocimetry. Unlike the flow under moderately strong stratification ( $Fr\gtrsim 0.2$ ), which supports a thin cylindrical jet,...
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| Veröffentlicht in: | Journal of fluid mechanics 2019-05, Vol.867, p.26-44 |
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| creator | Akiyama, Shinsaku Waki, Yusuke Okino, Shinya Hanazaki, Hideshi |
| description | The flow around a sphere descending at constant speed in a very strongly stratified fluid (
$Fr\lesssim 0.2$
) is investigated by the shadowgraph method and particle image velocimetry. Unlike the flow under moderately strong stratification (
$Fr\gtrsim 0.2$
), which supports a thin cylindrical jet, the flow generates an unstable jet, which often develops into turbulence. The transition from a stable jet to an unstable jet occurs for a sufficiently low Froude number
$Fr$
that satisfies
$Fr/Re |
| doi_str_mv | 10.1017/jfm.2019.123 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2216660390</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cupid>10_1017_jfm_2019_123</cupid><sourcerecordid>2216660390</sourcerecordid><originalsourceid>FETCH-LOGICAL-c368t-1953b67660fc2b71c1d005c8960df6215b93d2540b4ef78f69e87b501753d6a03</originalsourceid><addsrcrecordid>eNptkE1LxDAQhoMouK7e_AEBr7ZOkjZtjrL4BYIg7jkkzaS2dLtr0hX235t1F7x4mmF45h3mIeSaQc6AVXe9X-UcmMoZFydkxgqpskoW5SmZAXCeMcbhnFzE2AMwAaqakfflGCdjB6Q9TpG2OGIwEzpqd9TQuPnEgNRhbHB03djSbkzjbww7GqewHtvhtzFT57u05Idt5y7JmTdDxKtjnZPl48PH4jl7fXt6Wdy_Zo2Q9ZQxVQorKynBN9xWrGEOoGxqJcF5yVlplXC8LMAW6KvaS4V1Zcv0ZymcNCDm5OaQuwnrry3GSffrbRjTSc05kylYqD11e6CasI4xoNeb0K1M2GkGem9NJ2t6b00nawnPj7hZ2dC5Fv9S_134AYFhbg0</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2216660390</pqid></control><display><type>article</type><title>Unstable jets generated by a sphere descending in a very strongly stratified fluid</title><source>Cambridge University Press Journals Complete</source><creator>Akiyama, Shinsaku ; Waki, Yusuke ; Okino, Shinya ; Hanazaki, Hideshi</creator><creatorcontrib>Akiyama, Shinsaku ; Waki, Yusuke ; Okino, Shinya ; Hanazaki, Hideshi</creatorcontrib><description>The flow around a sphere descending at constant speed in a very strongly stratified fluid (
$Fr\lesssim 0.2$
) is investigated by the shadowgraph method and particle image velocimetry. Unlike the flow under moderately strong stratification (
$Fr\gtrsim 0.2$
), which supports a thin cylindrical jet, the flow generates an unstable jet, which often develops into turbulence. The transition from a stable jet to an unstable jet occurs for a sufficiently low Froude number
$Fr$
that satisfies
$Fr/Re<1.57\times 10^{-3}$
. The Froude number
$Fr$
here is in the range of
$0.0157<Fr<0.157$
or lower, while the Reynolds number
$Re$
is in the range of
$10\lesssim Re\lesssim 100$
for which the homogeneous fluid shows steady and axisymmetric flows. Since the radius of the jet can be estimated by the primitive length scale of the stratified fluid, i.e.
$l_{\unicode[STIX]{x1D708}}^{\ast }=\sqrt{\unicode[STIX]{x1D708}^{\ast }/N^{\ast }}$
or
$l_{\unicode[STIX]{x1D708}}^{\ast }/2a^{\ast }=\sqrt{Fr/2Re}$
, this predicts that the jet becomes unstable when it becomes thinner than approximately
$l_{\unicode[STIX]{x1D708}}^{\ast }/2a^{\ast }=0.028$
, where
$N^{\ast }$
is the Brunt–Väisälä frequency,
$a^{\ast }$
the radius of the sphere and
$\unicode[STIX]{x1D708}^{\ast }$
the kinematic viscosity of the fluid. The instability begins when the boundary-layer thickness becomes thin, and the disturbances generated by shear instabilities would be transferred into the jet. When the flow is marginally unstable, two unstable states, i.e. a meandering jet and a turbulent jet, can appear. The meandering jet is thin with a high vertical velocity, while the turbulent jet is broad with a much smaller velocity. The meandering jet may persist for a long time, or develop into a turbulent jet in a short time. When the instability is sufficiently strong, only the turbulent jet could be observed.</description><identifier>ISSN: 0022-1120</identifier><identifier>EISSN: 1469-7645</identifier><identifier>DOI: 10.1017/jfm.2019.123</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Brunt-Vaisala frequency ; Carbon ; Density stratification ; Fluid dynamics ; Fluid flow ; Froude number ; Instability ; Investigations ; JFM Papers ; Kelvin-Helmholtz instability ; Kinematic viscosity ; Laboratories ; Meandering ; Particle image velocimetry ; Plankton ; Reynolds number ; Salinity ; Stratification ; Thickness ; Turbulence ; Turbulent jets ; Velocity ; Velocity measurement ; Viscosity</subject><ispartof>Journal of fluid mechanics, 2019-05, Vol.867, p.26-44</ispartof><rights>2019 Cambridge University Press</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c368t-1953b67660fc2b71c1d005c8960df6215b93d2540b4ef78f69e87b501753d6a03</citedby><cites>FETCH-LOGICAL-c368t-1953b67660fc2b71c1d005c8960df6215b93d2540b4ef78f69e87b501753d6a03</cites><orcidid>0000-0002-0306-1971 ; 0000-0002-8371-3641</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.cambridge.org/core/product/identifier/S002211201900123X/type/journal_article$$EHTML$$P50$$Gcambridge$$H</linktohtml><link.rule.ids>164,314,780,784,27924,27925,55628</link.rule.ids></links><search><creatorcontrib>Akiyama, Shinsaku</creatorcontrib><creatorcontrib>Waki, Yusuke</creatorcontrib><creatorcontrib>Okino, Shinya</creatorcontrib><creatorcontrib>Hanazaki, Hideshi</creatorcontrib><title>Unstable jets generated by a sphere descending in a very strongly stratified fluid</title><title>Journal of fluid mechanics</title><addtitle>J. Fluid Mech</addtitle><description>The flow around a sphere descending at constant speed in a very strongly stratified fluid (
$Fr\lesssim 0.2$
) is investigated by the shadowgraph method and particle image velocimetry. Unlike the flow under moderately strong stratification (
$Fr\gtrsim 0.2$
), which supports a thin cylindrical jet, the flow generates an unstable jet, which often develops into turbulence. The transition from a stable jet to an unstable jet occurs for a sufficiently low Froude number
$Fr$
that satisfies
$Fr/Re<1.57\times 10^{-3}$
. The Froude number
$Fr$
here is in the range of
$0.0157<Fr<0.157$
or lower, while the Reynolds number
$Re$
is in the range of
$10\lesssim Re\lesssim 100$
for which the homogeneous fluid shows steady and axisymmetric flows. Since the radius of the jet can be estimated by the primitive length scale of the stratified fluid, i.e.
$l_{\unicode[STIX]{x1D708}}^{\ast }=\sqrt{\unicode[STIX]{x1D708}^{\ast }/N^{\ast }}$
or
$l_{\unicode[STIX]{x1D708}}^{\ast }/2a^{\ast }=\sqrt{Fr/2Re}$
, this predicts that the jet becomes unstable when it becomes thinner than approximately
$l_{\unicode[STIX]{x1D708}}^{\ast }/2a^{\ast }=0.028$
, where
$N^{\ast }$
is the Brunt–Väisälä frequency,
$a^{\ast }$
the radius of the sphere and
$\unicode[STIX]{x1D708}^{\ast }$
the kinematic viscosity of the fluid. The instability begins when the boundary-layer thickness becomes thin, and the disturbances generated by shear instabilities would be transferred into the jet. When the flow is marginally unstable, two unstable states, i.e. a meandering jet and a turbulent jet, can appear. The meandering jet is thin with a high vertical velocity, while the turbulent jet is broad with a much smaller velocity. The meandering jet may persist for a long time, or develop into a turbulent jet in a short time. When the instability is sufficiently strong, only the turbulent jet could be observed.</description><subject>Brunt-Vaisala frequency</subject><subject>Carbon</subject><subject>Density stratification</subject><subject>Fluid dynamics</subject><subject>Fluid flow</subject><subject>Froude number</subject><subject>Instability</subject><subject>Investigations</subject><subject>JFM Papers</subject><subject>Kelvin-Helmholtz instability</subject><subject>Kinematic viscosity</subject><subject>Laboratories</subject><subject>Meandering</subject><subject>Particle image velocimetry</subject><subject>Plankton</subject><subject>Reynolds number</subject><subject>Salinity</subject><subject>Stratification</subject><subject>Thickness</subject><subject>Turbulence</subject><subject>Turbulent jets</subject><subject>Velocity</subject><subject>Velocity measurement</subject><subject>Viscosity</subject><issn>0022-1120</issn><issn>1469-7645</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</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>eNptkE1LxDAQhoMouK7e_AEBr7ZOkjZtjrL4BYIg7jkkzaS2dLtr0hX235t1F7x4mmF45h3mIeSaQc6AVXe9X-UcmMoZFydkxgqpskoW5SmZAXCeMcbhnFzE2AMwAaqakfflGCdjB6Q9TpG2OGIwEzpqd9TQuPnEgNRhbHB03djSbkzjbww7GqewHtvhtzFT57u05Idt5y7JmTdDxKtjnZPl48PH4jl7fXt6Wdy_Zo2Q9ZQxVQorKynBN9xWrGEOoGxqJcF5yVlplXC8LMAW6KvaS4V1Zcv0ZymcNCDm5OaQuwnrry3GSffrbRjTSc05kylYqD11e6CasI4xoNeb0K1M2GkGem9NJ2t6b00nawnPj7hZ2dC5Fv9S_134AYFhbg0</recordid><startdate>20190525</startdate><enddate>20190525</enddate><creator>Akiyama, Shinsaku</creator><creator>Waki, Yusuke</creator><creator>Okino, Shinya</creator><creator>Hanazaki, Hideshi</creator><general>Cambridge University Press</general><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>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><orcidid>https://orcid.org/0000-0002-0306-1971</orcidid><orcidid>https://orcid.org/0000-0002-8371-3641</orcidid></search><sort><creationdate>20190525</creationdate><title>Unstable jets generated by a sphere descending in a very strongly stratified fluid</title><author>Akiyama, Shinsaku ; Waki, Yusuke ; Okino, Shinya ; Hanazaki, Hideshi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c368t-1953b67660fc2b71c1d005c8960df6215b93d2540b4ef78f69e87b501753d6a03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Brunt-Vaisala frequency</topic><topic>Carbon</topic><topic>Density stratification</topic><topic>Fluid dynamics</topic><topic>Fluid flow</topic><topic>Froude number</topic><topic>Instability</topic><topic>Investigations</topic><topic>JFM Papers</topic><topic>Kelvin-Helmholtz instability</topic><topic>Kinematic viscosity</topic><topic>Laboratories</topic><topic>Meandering</topic><topic>Particle image velocimetry</topic><topic>Plankton</topic><topic>Reynolds number</topic><topic>Salinity</topic><topic>Stratification</topic><topic>Thickness</topic><topic>Turbulence</topic><topic>Turbulent jets</topic><topic>Velocity</topic><topic>Velocity measurement</topic><topic>Viscosity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Akiyama, Shinsaku</creatorcontrib><creatorcontrib>Waki, Yusuke</creatorcontrib><creatorcontrib>Okino, Shinya</creatorcontrib><creatorcontrib>Hanazaki, Hideshi</creatorcontrib><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 Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>Natural Science Collection</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>Akiyama, Shinsaku</au><au>Waki, Yusuke</au><au>Okino, Shinya</au><au>Hanazaki, Hideshi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Unstable jets generated by a sphere descending in a very strongly stratified fluid</atitle><jtitle>Journal of fluid mechanics</jtitle><addtitle>J. Fluid Mech</addtitle><date>2019-05-25</date><risdate>2019</risdate><volume>867</volume><spage>26</spage><epage>44</epage><pages>26-44</pages><issn>0022-1120</issn><eissn>1469-7645</eissn><abstract>The flow around a sphere descending at constant speed in a very strongly stratified fluid (
$Fr\lesssim 0.2$
) is investigated by the shadowgraph method and particle image velocimetry. Unlike the flow under moderately strong stratification (
$Fr\gtrsim 0.2$
), which supports a thin cylindrical jet, the flow generates an unstable jet, which often develops into turbulence. The transition from a stable jet to an unstable jet occurs for a sufficiently low Froude number
$Fr$
that satisfies
$Fr/Re<1.57\times 10^{-3}$
. The Froude number
$Fr$
here is in the range of
$0.0157<Fr<0.157$
or lower, while the Reynolds number
$Re$
is in the range of
$10\lesssim Re\lesssim 100$
for which the homogeneous fluid shows steady and axisymmetric flows. Since the radius of the jet can be estimated by the primitive length scale of the stratified fluid, i.e.
$l_{\unicode[STIX]{x1D708}}^{\ast }=\sqrt{\unicode[STIX]{x1D708}^{\ast }/N^{\ast }}$
or
$l_{\unicode[STIX]{x1D708}}^{\ast }/2a^{\ast }=\sqrt{Fr/2Re}$
, this predicts that the jet becomes unstable when it becomes thinner than approximately
$l_{\unicode[STIX]{x1D708}}^{\ast }/2a^{\ast }=0.028$
, where
$N^{\ast }$
is the Brunt–Väisälä frequency,
$a^{\ast }$
the radius of the sphere and
$\unicode[STIX]{x1D708}^{\ast }$
the kinematic viscosity of the fluid. The instability begins when the boundary-layer thickness becomes thin, and the disturbances generated by shear instabilities would be transferred into the jet. When the flow is marginally unstable, two unstable states, i.e. a meandering jet and a turbulent jet, can appear. The meandering jet is thin with a high vertical velocity, while the turbulent jet is broad with a much smaller velocity. The meandering jet may persist for a long time, or develop into a turbulent jet in a short time. When the instability is sufficiently strong, only the turbulent jet could be observed.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/jfm.2019.123</doi><tpages>19</tpages><orcidid>https://orcid.org/0000-0002-0306-1971</orcidid><orcidid>https://orcid.org/0000-0002-8371-3641</orcidid></addata></record> |
| fulltext | fulltext |
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| ispartof | Journal of fluid mechanics, 2019-05, Vol.867, p.26-44 |
| issn | 0022-1120 1469-7645 |
| language | eng |
| recordid | cdi_proquest_journals_2216660390 |
| source | Cambridge University Press Journals Complete |
| subjects | Brunt-Vaisala frequency Carbon Density stratification Fluid dynamics Fluid flow Froude number Instability Investigations JFM Papers Kelvin-Helmholtz instability Kinematic viscosity Laboratories Meandering Particle image velocimetry Plankton Reynolds number Salinity Stratification Thickness Turbulence Turbulent jets Velocity Velocity measurement Viscosity |
| title | Unstable jets generated by a sphere descending in a very strongly stratified fluid |
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