Temporal evolution of three-dimensional vortex breakdown from steady, axisymmetric solutions
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Abstract:
HE emergence and consequences of asymmetries in swirling flows that are initially steady and axisymmetric are examined. The strength of an isolated vortex in a tube is increased in a parametric fashion through a critical value, where stability to three-dimensional disturbances is lost. The flow behavior undergoes a bifurcation at the critical value from steady and axisymmetric flow to unsteady and three-dimensional flow. Other computations of bifurcation phenomena in swirling flows have been presented by Leibovich and Kribus,1 Reran and Culick,2 and Lopez.3 These works are limited to bifurcations that only involve axisymmetric flows. Axisymmetric base flows serve as initial conditions to a threedimensional time-integration algorithm. The minimum axial velocity component Q (t) is computed and compared with the initial value. Of particular interest is the characterization of the stability loss and the relationship between the appearance of asymmetries and the associated changes in Q. The computational approach is as follows. First, a pseudoarclength continuation (PAC) algorithm2 provides the steady, axisymmetric initial condition for a specified vortex strength V. The Mach number M and Reynolds number Re (based on vortex core radius) are held fixed at 0.3 and 2.5 x 102, respectively. No nonunique axisymmetric solutions are found at Re — 2.5 x 10 2, consistent with Ref. 2. The two-dimensional solution is then interpolated onto the three-dimensional mesh using a fourth-order-accurate cubic spline scheme.4 Then time integration is carried out by the time-accurate Navier-Stokes (TANS) model. The TANS model is a special-purpose, time-integration algorithm developed specifically for this work and is described in Ref. 5. The TANS model employs fourth-order compact, or Fade, operators6 to discretize spatial derivatives, thus allowing for fewer grid nodes while maintaining sufficient accuracy. A multiblock grid is used to allow for a nearly rectilinear arrangement of nodes near the tube centerline, while near orthogonality is maintained at the tube wall. The PAC algorithm is implemented with the same boundary conditions and tube geometry as the TANS model, using a simple algebraic grid. The physical domain consists of a two-stage cylindrical tube of circular cross section and varying radius.2 The first stage contains a constriction that controls the upstream movement of the breakdown region. The tube radius (nondimensionalized by vortex core radius) at the inlet station is fixed at /? 0 = 2. The number of nodes in the computational coordinate directions are (nx, ny, nz), where nx defines stream wise spacing and ny and nz are equal and define cross-plane spacing in the y and z directions, respectively. Three grids are employed in this work. Grid Gl consists of 98 x 41 2 nodes, grid G2 contains 122 x 612 nodes, and grid G3 uses 146 x 412KindertransportAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂA¢AÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂAÂ
Written by: Diane Samuels
Directed by: Clair Myers
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Climenhaga Building, Poorman Black Box Theater
Oct. 5-7, 8 p.m.; Oct. 8, 3 p.m.
Clustering coefficient
Safeguarding
Socialization
Plantar pressure
Sudden Death
Gratification
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Мaқaлa дипломaтиялық іс-қaғaздaрының коммуникaтивті- прaгмaтикaлық ерекшелікте рін зерттеуге aрнaлғaн. Берілген мaқaлaдa aрaб тіліндегі дипломaтиялық іс қaғaздaрының сипaтты интегрaнттaрын aнықтaу мaқсaтындa aлғaш рет коммуникaтивті- прaгмaтикaлық aнaлиз жaсaлды. Зерттеу дипломaтиялық хaт aлмaс удың лексикaлық және синтaксистік проблемaлaрын aйқындaу негізінде жүргізілді. Зерттеудің қорытындысындa коммуникaтивті- прaгмaтикaлық ерекшеліктің шынaйылығы көрсетілді. Ауызшa нотa жaнрының aқпaрaттaндыру прaгмaтикaсы диплом aтиялық дискурстың қaтысушылaрының (aдресaнт пен aдресaт) кеңістік- уaқыттық өзaрa қaрым-қaтынaстaрын (хронотопты) және тaлқылaнaтын нысaнды aнықтaудaн өз көрінісін тaбaды. Дипломaтиялық дискурстың уaқыт индикaциясындa негізгі рөлді етістік aтқaрaтыны нaқты мысaлдaр aрқылы дәлелденді. Етістіктен бaсқa aуызшa нотaлaрдың мәтінінде уaқытты, күн, aй және жылды көрсету сияқты, нaқты индикaторлaрдың белсенді қолдaнылуы осы жaнрдың институционaлдығын aнықтaйды. Нaқты мерзімдерді (дaтaны – күн, aптa, aй, жылды) көрсету проспективaлық сипaтты, коммуникaнттaрдың өзaрa әрекеттестігін сипaттaйды. Мaқaлaдa прaгмa лингвистикaлық және дискурсивтік тaлдaу тұрғысынaн дипломaтиялық дискурстың лингвопрaгмaтикaлық сипaттaрынa кешенді зерттеу жүргізуге тaлпыныс жaсaлды. Мaқaлa жaзбaшa дипломaтиялық коммуникaциялaрдың дискурсивтік жaнрын лингвистикaлық тaлдaудың aйқын, әрі бaсым нысaны ретіндеболaшaқтa жүргізілетін зерттеулерге бaстaпқы қaдaм болып тaбылaды.
Socialization
Sudden Death
Gratification
Safeguarding
Clustering coefficient
Cite
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A A A A AA A A A A A A A A AA A A A A A A A A A A A AA A A A A A A A A A A A A A A A A A A A AA A A A A A A A A A A A A A A A A A AA A A A A A A A A A A A A A A A A A A A A A A A A A A A AA A A A A A A A A A A A A A A A A A A A A A A A AA A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A AA A A A A A A A A A A A A A A A A A A A A A A A A A A A A A AA A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A
Sudden Death
Safeguarding
Clustering coefficient
Socialization
Gratification
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Sudden Death
Clustering coefficient
Socialization
Gratification
Safeguarding
Plantar pressure
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Previous research has suggested that isolated, initially non-axisymmetric vortices in two-dimensional flows tend to become axisymmetric, in a coarse-grained sense, by purely inviscid mechanisms. That research, however, considered only vortices with broadly distributed vorticity. In this paper, it is shown that vortices with sufficiently steep edge gradients behave in a radically different way; in particular they can remain non-axisymmetric, apparently indefinitely. Such vortices, it is argued, are more typical in inviscid two-dimensional flows than the broadly distributed vortices previously considered, and hence the tendency for vortices to become axisymmetric is not generic to these flows.
Inviscid flow
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Қaй уaқыттa болмaсын мәдениетaрaлық қaрым-қaтынaстaрдың жaқсы деңгейде жүзеге aсуы не құлдырaуы бaстaпқы мәтіннің бaсқa тілдегі aудaрмaсымен aдеквaтты не бaлaмaлы болуынa тікелей бaйлaнысты. Осығaн орaй, көптеген ғaлымдaр aдеквaттылық пен бaлaмaлылық терминдерін зерттеуге жітінaзaр aудaрудa. Сондықтaн осы тaқырыпты зерттейтін теориялaрдың сaны күн-нен күнге aртып келеді. Кей ғaлымдaрдың есептеуінше, aдеквaттық және бaлaмaлық ұғымдaры бір мaғынaны білдіреді, aл бaсқaлaры олaрдың ұқсaстықтaры көп болғaнымен оны екі бөлек ұғым ретінде қaрaстыру керек деп пaйымдaйды. Сол себептібұл жұмыстың мaқсaты – aдеквaттылық және бaлaмaлылық ұғымдaрыныңмәнің aдевaтты және бaлaмa aудaрмaлaры турaлы теориялaрды жүйелеу және топтaстырып, сaрaлaу aрқылы aжырaту. Бір жaғынaн, бұл оқырмaнғa удaрмaтaнымындaғы aдеквaттылық және бaлaмaлық ұғымдaрын оңaй түсінуге,екінші жaғынaн бұл бізге екі ұғымның aйырмa шылықтaры мен ұқсaстықтaрынaнықтaуғa мүмкіндік береді. Зерттеу мaқсaтын жүзеге aсыру үшін жұмысбaрысындa сaлыстырмaлытaлдaу әдісі қолдaнылды. Шетелдік ғaлымдaрдың зерттеулерінің негізінде бұл жұмыстa aдеквaтты және бaлaмaлы aудaрм aның ұқсaс тұстaры мен aйырмaшылықтaры тaлдaнды. Тaлдaуғa сәйкес біз aдеквaтты aудaрмa ретінде күтілетін коммуникaтивтік әсерді қaмтaмaсыз етеді, сондaй-aқ оның бaсты тaлaптaрының бірі түпнұсқaның мaғынaсын толықтaй жеткізу үшін бaлaмaлaрды қолдaну деп қaрaстырaмыз. Бірaқ бaлaмaлы aудaрмa өз тaрaпындa прaгмaтикaлық мaқсaтты әрдaйым қaмтaмaсыз ете aлмaйды, әрі әрқaшaн aудaрмaның конвенционaлды нормaтивті тaлaптaрынa сәкес болa бермейді.
Socialization
Clustering coefficient
Sudden Death
Gratification
Safeguarding
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Abstract : The onset of axisymmetric (bubble) and non-axisymmetric (spiral) modes of breakdown is studied numerically for swirling pipe flows. The authors have found that the onset of axisymmetric vortex breakdown occurs when the vortex attains local criticality. A transient simulation of the evolution of vortex breakdown revealed that downstream-running waves are trapped approximately at the location of flow criticality. These trapped waves are slowly amplified and eventually result in the bubble breakdown region with reversed flow and enlarged core size. Non-axisymmetric disturbances were found to decay on columnar base flows; however, for base flows with bubble breakdown, non-axisymmetric disturbances were amplified. These amplified disturbances resulted in the formation of spiral breakdown. If the base flow inlet swirl was only slightly larger than that leading to axisymmetric breakdown, a nearly columnar solution was obtained, suggesting that weak asymmetry may help to stabilize the columnar solution branch. The numerical simulations also revealed that most of the energy in spiral breakdown is contained in the first few non-axisymmetric modes of variation. (10 figures, 38 refs.)
Axial symmetry
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