Impact of tropical cyclones on a baroclinic jet in the ocean

The initial evolution of a baroclinic jet under influence of a barotropic flow induced by the tropical cyclones is considered using a two-layer model and the thin-jet approximation. In spite of antisymmetric structure of the barotropic flow, the jet meander growth due to the barotropic flow advectio...

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Datum:	2013
Hauptverfasser:	Sutyrin, G., Ginis, I.
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Sprache:	English
Veröffentlicht:	Морський гідрофізичний інститут НАН України 2013
Schriftenreihe:	Морской гидрофизический журнал
Schlagworte:	Анализ результатов наблюдений и методы расчета гидрофизических полей океана
Online Zugang:	http://dspace.nbuv.gov.ua/handle/123456789/105098
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Zitieren:	Impact of tropical cyclones on a baroclinic jet in the ocean / G. Sutyrin, I. Ginis // Морской гидрофизический журнал. — 2013. — № 5. — С. 44-50. — Бібліогр.: 19 назв. — англ.

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spelling	irk-123456789-1050982016-08-07T03:02:29Z Impact of tropical cyclones on a baroclinic jet in the ocean Sutyrin, G. Ginis, I. Анализ результатов наблюдений и методы расчета гидрофизических полей океана The initial evolution of a baroclinic jet under influence of a barotropic flow induced by the tropical cyclones is considered using a two-layer model and the thin-jet approximation. In spite of antisymmetric structure of the barotropic flow, the jet meander growth due to the barotropic flow advection is shown to favor an anticyclonic meander to the right of the storm track. This enhancement of the anticyclonic meander is found to be related to the dispersion properties of frontal waves along the jet described by the thin-jet theory and coupling with deep eddies developing in the lower layer during the jet meandering. У рамках двошарової моделі та в наближенні тонкого струменя розглядається еволюція бароклинного струменя, викликаного баротропною течією, індукованою тропічним циклоном. Показано, що, не дивлячись на антисиметричну структуру баротропної течії, її адвекція призводить до меандрування бароклинного струменя та до зростання головним чином антициклонічного меандру праворуч від штормтрека. Знайдено, що посилення антициклонічного меандру пов'язане з дисперсійними властивостями фронтальних хвиль (які описуються у рамках теорії тонкого струменя) і з взаємодією з глибинними вихорами, які розвиваються в нижньому шарі океану при меандруванні бароклинного струменю. В рамках двухслойной модели и в приближении тонкой струи рассматривается эволюция бароклинной струи, вызванной баротропным течением, индуцированным тропическим циклоном. Показано, что, несмотря на антисимметричную структуру баротропного течения, его адвекция приводит к меандрированию бароклинной струи и к росту главным образом антициклонического меандра справа от штормтрека. Обнаружено, что усиление антициклонического меандра связано с дисперсионными свойствами фронтальных волн (описываемых в рамках теории тонкой струи) и с взаимодействием с глубинными вихрями, развивающимися в нижнем слое океана при меандрировании бароклинной струи. 2013 Article Impact of tropical cyclones on a baroclinic jet in the ocean / G. Sutyrin, I. Ginis // Морской гидрофизический журнал. — 2013. — № 5. — С. 44-50. — Бібліогр.: 19 назв. — англ. 0233-7584 http://dspace.nbuv.gov.ua/handle/123456789/105098 551.465 en Морской гидрофизический журнал Морський гідрофізичний інститут НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	Анализ результатов наблюдений и методы расчета гидрофизических полей океана Анализ результатов наблюдений и методы расчета гидрофизических полей океана
spellingShingle	Анализ результатов наблюдений и методы расчета гидрофизических полей океана Анализ результатов наблюдений и методы расчета гидрофизических полей океана Sutyrin, G. Ginis, I. Impact of tropical cyclones on a baroclinic jet in the ocean Морской гидрофизический журнал
description	The initial evolution of a baroclinic jet under influence of a barotropic flow induced by the tropical cyclones is considered using a two-layer model and the thin-jet approximation. In spite of antisymmetric structure of the barotropic flow, the jet meander growth due to the barotropic flow advection is shown to favor an anticyclonic meander to the right of the storm track. This enhancement of the anticyclonic meander is found to be related to the dispersion properties of frontal waves along the jet described by the thin-jet theory and coupling with deep eddies developing in the lower layer during the jet meandering.
format	Article
author	Sutyrin, G. Ginis, I.
author_facet	Sutyrin, G. Ginis, I.
author_sort	Sutyrin, G.
title	Impact of tropical cyclones on a baroclinic jet in the ocean
title_short	Impact of tropical cyclones on a baroclinic jet in the ocean
title_full	Impact of tropical cyclones on a baroclinic jet in the ocean
title_fullStr	Impact of tropical cyclones on a baroclinic jet in the ocean
title_full_unstemmed	Impact of tropical cyclones on a baroclinic jet in the ocean
title_sort	impact of tropical cyclones on a baroclinic jet in the ocean
publisher	Морський гідрофізичний інститут НАН України
publishDate	2013
topic_facet	Анализ результатов наблюдений и методы расчета гидрофизических полей океана
url	http://dspace.nbuv.gov.ua/handle/123456789/105098
citation_txt	Impact of tropical cyclones on a baroclinic jet in the ocean / G. Sutyrin, I. Ginis // Морской гидрофизический журнал. — 2013. — № 5. — С. 44-50. — Бібліогр.: 19 назв. — англ.
series	Морской гидрофизический журнал
work_keys_str_mv	AT sutyring impactoftropicalcyclonesonabaroclinicjetintheocean AT ginisi impactoftropicalcyclonesonabaroclinicjetintheocean
first_indexed	2025-07-07T16:19:09Z
last_indexed	2025-07-07T16:19:09Z
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fulltext	© G. Sutyrin, I. Ginis, 2013 Анализ результатов наблюдений и методы расчета гидрофизических полей океана UDC 551.465 G. Sutyrin, I. Ginis Impact of tropical cyclones on a baroclinic jet in the ocean The initial evolution of a baroclinic jet under influence of a barotropic flow induced by the tropi- cal cyclones is considered using a two-layer model and the thin-jet approximation. In spite of antisymmetric structure of the barotropic flow, the jet meander growth due to the barotropic flow advection is shown to favor an anticyclonic meander to the right of the storm track. This enhancement of the anticyclonic meander is found to be related to the dispersion properties of frontal waves along the jet described by the thin-jet theory and coupling with deep eddies developing in the lower layer during the jet meandering. Keywords: baroclinic jet, tropical cyclone, anticyclonic meander, thin-jet theory. Introduction Tropical cyclones (TC) provide the most intense atmospheric forcing to the ocean generating both barotropic and baroclinic currents. Here the barotropic cur- rent is defined as a depth-averaged flow. The baroclinic currents are what remain after substraction of the depth-averaged flow and are associated with the ocean stratification. J.E. Geisler [1] was the first to reveal distinctively different nature of the barotropic and baroclinic responses of the ocean to a moving TC because the barotropic gravity wave speed is much larger than the baroclnic one. Typically, the TC translation speed (5 m/s) is greater than the baroclinic wave speed and much smaller than the barotropic wave speed. Therefore, the baroclinic response is char- acterized by upwelling with oscillating narrow wake behind the TC, formed by slow propagating, near-inertial baroclinic waves, while fast propagating barotropic waves produce a broad barotropic flow. In a deep ocean, the depth-averaged TC-induced currents are essentially weak- er than the baroclinic currents concentrated in the upper ocean. Due to strong verti- cal shear, mixing processes and upwelling are able to reduce the surface tempera- ture by several degrees that was pointed out in pioneering works by A.I. Felzenbaum with colleagues (e.g., [2]). The TC-induced mixing and decrease of the ocean temperature was shown to be enhanced to the right from the storm track due to resonance between inertial oscillations and rotating wind direction during TC passage [3, 4]. Ocean cooling under TC provides an important negative feed- back to the TC intensity [5]. Therefore, coupled TC – ocean models are used now for prediction of TC evolution [6]. ISSN 0233-7584. Мор. гидрофиз. журн., 2013, № 5 44 The most important features of the ocean response to TC with initially hori- zontally homogeneous ocean conditions which have been widely studied as sum- marized by A.P. Khain and G.G. Sutyrin [7]. However, when a TC crosses frontal regions with strong ocean currents such as the Gulf Stream or Kuroshio, the ocean response is more complicated (e.g., [8 – 11]). Here we focus on a baroclinic jet meandering forced by a TC using a two-layer model and the thin-jet theory (see [12] and references therein). Formulation of the problem Let’s consider a TC uniformly moving in y-direction at the speed hU over a stratified ocean with a baroclinc jet flowing in the x-direction at the f-plane. As shown by I. Ginis and G. Sutyrin [13] for initially horizontally homogeneous ocean, the depth-averaged TC-induced flow behind the storm is antisymmetric, being positive to the right from the storm track (in the direction of TC motion) and negative to the left. It can be characterized by the depth-averaged velocity maxi- mum, mv and its distance from the storm track, mx : h L m UH Lav 00 1 ρ τ = , Laxm 2= , (1) where the characteristic TC scale L is defined as the radius where the wind stress torque dR reaches its maximum, Lτ is the wind stress at this radius, 0H is the ocean depth, 0ρ is the ocean density. It was found for several typical radial distri- butions of the wind stress in TC [14] that the coefficient 1a ranges between 2 and π , and 2a ranges between 0.65 and 1. Here we prescribe the typical cross-track distribution of the depth-averaged velocity as (thin line in Fig. 3) . 22 1exp 2 2       −= mmm x x x x v V (2) Evolution of an initially straight baroclinic jet is considered under influence of such barotropic ocean flow. Numerical simulations using a two-layer model For numerical simulations we use the two-layer intermediate geostrophic mod- el [15]. The initial setup includes an upper-layer jet without meanders plus the barotropic flow (2) in both layers over a flat bottom. The baroclinc jet in the upper layer is initialized by the potential vorticity jump at y = 0 along the x-axis. Choos- ing mx as the spatial scale and mv as the velocity scale, the flow evolution depends on three nondimensional parameters: the jet intensity, mu / mv , the jet width, md xR / , and the depth ratio 0/ HH , where mu is the maximum jet velocity, dR is the baroclinic radius of deformation, H is the upper layer depth. Typical results for ,8/ =mm vu ,2/1/ =md xR 6/1/ 0 =HH are shown in Fig. 1 for mm vxt /= and in Fig. 2 for mm vxt /2= . It can be seen that in spite of ISSN 0233-7584. Мор. гидрофиз. журн., 2013, № 5 45 antisymmetric structure of the barotropic flow (2), the jet meander growth due to the barotropic flow advection favors an anticyclonic meander to the right of the storm track in qualitative agreement with numerical simulations by S. Lee [11]. To evaluate physical mechanisms behind this effect we use a thin-jet theory. F i g. 1. The mid-jet path (thick line) superimposed by the stream function in the lower layer (dash line shows positive (anticyclonic) deep eddies) of the two-layer model for t = xm/vm; solution (11) – (13) is shown by a thin line F i g. 2. The mid-jet path (thick line) superimposed by the stream function in the lower layer (dash lines show positive (anticyclonic) deep eddies) of the two-layer model for t = 2xm/vm; solution (11) – (13) is shown by a thin line ISSN 0233-7584. Мор. гидрофиз. журн., 2013, № 5 46 Application of a thin-jet theory In works [16, 17] the authors investigated meandering of thin ocean jets using a reduced-gravity shallow water model (valid for small depth ratio) by expanding the governing equations in terms of a small parameter, the radius of deformation multiplied by the meander curvature. In the leading approximation, the mid-jet path: at the f-plane can be described by a self-contained set of equations: ,),(,),( jetjet YXU t XYXV t Y = ∂ ∂ = ∂ ∂ (3) s KaU s YV s X ∂ ∂ = ∂ ∂ − ∂ ∂ jetjet , (4) 1 22 =      ∂ ∂ +      ∂ ∂ s Y s X , 2 2 2 2 s X s Y s Y s XK ∂ ∂ ∂ ∂ − ∂ ∂ ∂ ∂ = , (5) where the jet velocity (U, V) is defined by (3), X and Y are Cartesian coordinates of the jet, s is the distance along the jet, K is the curvature, t is the time, and the coef- ficient a is defined by the cross-jet structure dn dn dhh hhf ga 2 21 2 2 )(       − ′ = ∫ , (6) where g′ is the reduced gravity, h is the layer thickness, h1 and h2 are the thickness values at both sides far from the jet, n is the cross-jet coordinate. Equation (4) indicates that the normal velocity of the baroclinic jet segment is proportional to the rate of change of centrifugal force along the path (∂K/∂s). Intro- ducing the local azimuth of the jet, so that ,,)sin(),cos( s K s Y s X ∂ ∂ == ∂ ∂ = ∂ ∂ θθθ (7) from equations (3) – (6) a single equation can be obtained: .)( 2 0 2 2 2 s tc s a s a t ∂ ∂ +      ∂ ∂ + ∂ ∂ = ∂ ∂ θθθθ (8) The function )(0 tc is determined by the boundary conditions at the inflow and /or by the initial condition. For an initial value problem in an unbounded do- main when a localized perturbation of the jet is considered, this equation can be further transformed into the modified Korteweg – de Vries (mKdV) equation for the curvature. The mKdV equation is known to describe a variety of long, nonline- ar waves, where the dispersive and nonlinear terms (the first and second terms in equation (8)) balance. The envelope solitary wave, or «breather», is particularly interesting as it describes a transformation of cyclonic meanders into anticyclonic ones and vise versa inside a breather [18]. ISSN 0233-7584. Мор. гидрофиз. журн., 2013, № 5 47 Taking into account motion in active lower layer when the depth ratio is not too small, the velocity in the lower layer has to be included into equations (3): .),(,),( jetjet y pYXU t X x pYXV t Y ∂ ∂ −= ∂ ∂ ∂ ∂ += ∂ ∂ (9) Here p is the geostrophic stream function in the lower layer. Developing meanders at the initial stage can be interpreted using the formulation (4), (5) and (9) where p is defined initially by the TC-induced velocity (2). When the meander amplitude \|Y\| remains small, a linearized version of (4), (5) can be considered assuming X ~ s: .)(2 2 sV s Ya t Y + ∂ ∂ = ∂ ∂ (10) Its solution can be found by Fourier transforms to describe forcing of dispersing meanders: ,)exp(),( 2 1),( dkikstkYtsY ∫=  π (11) ,)(]e1[ ω ω i kVY ti   −−= ,2ak=ω (12) dsikssVtkV )exp()(),( −= ∫  , (13) here hat denotes Fourier transforms, k is the wavenumber, ω is the frequency and i is the imaginary unit. In order to illustrate the asymmetry in developing meanders, we consider Taylor expansion in time. The first two orders show the meander growth proportionally to TC- induced velocity and modification of meanders due to dispersive effects ... 2 )(~ 2 22 ++ ds VdatstVY . (14) Fig. 3 shows mvV / according to equation (2) in comparison with the second term (dotted line) normalized by its extremum value to illustrate that the anticylonic meander growth is enhanced while the cyclonic meander growth is re- duced due to the dispersion properties of frontal waves along the jet. The linearized solution (11) – (13) agrees well with the numerical solution during an initial period up to mm vxt /= (Fig. 1). Advection of the jet by deep ed- dies coupled with meandering jet due to well-known baroclinic instability mecha- nism becomes noticeable in further enhancement of anticyclonic meander (Fig. 2). This kind of vertical coupling during growth of baroclinic meanders has been wide- ly investigated (see, e.g., [19] and references therein). ISSN 0233-7584. Мор. гидрофиз. журн., 2013, № 5 48 F i g. 3. TC-induced barotropic velocity (2) (thin line) and the normalized dispersive term in equation (14) (dotted line) Discussion and summary The initial evolution of a baroclinic jet under influence of the TC-induced barotropic flow is considered using a two-layer model and the thin-jet approxima- tion. In spite of antisymmetric structure of the barotropic flow, the jet meander growth due to the barotropic flow advection is shown to favor an anticyclonic me- ander to the right of the storm track in qualitative agreement with numerical simu- lations by S. Lee [11]. This enhancement of anticyclonic meander is found to be related to the dispersion properties of frontal waves along the jet described by the thin-jet theory during the initial stage. In order to consider further amplification of meander growth, the effects of vertical coupling have to be taken into account, e.g., using a two-layer model with both active layers as illustrated in Fig. 2. Acknowledgements This study was supported by the NSF grant OCE 1027573. REFERENCES 1. Geisler J.E. Linear theory of the response of a two layer-ocean to moving hurricane // Geophys. Fluid Dyn. – 1970. – 1. – P. 249 – 272. 2. Arseniev S.A., Sutyrin G.G., Felzenbaum A.I. On the response of the stratified ocean to a ty- phoon // Dokl. AN SSSR. Earth Sci. – 1976. – 231, № 3. – P. 567 – 570. 3. Price J.F. Upper ocean response to a hurricane // J. Phys. Oceanogr. – 1981. – 11. – P. 153 – 175. 4. Sutyrin G.G. The effect of tropical cyclones on the ocean // Dokl. AN SSSR. Earth Sci. – 1981. – 257. – P. 213 – 216. 5. Sutyrin G.G., Khain A.P. Interaction of the ocean and atmosphere in the region of translating tropical cyclone // Ibid. – 1979. – 249. – P. 211 – 213. 6. Ginis I. Tropical cyclone-ocean interactions // Atmosphere-Ocean Interactions / Ed. W. Perrie. – WIT Press, 2002. – 312 p. 7. Khain A.P., Sutyrin G.G. Tropical Cyclones and their Interaction with the Ocean. – Lenin- grad: Gidrometeoizdat, 1983. – 272 p. 8. Ichiye T. Response of a two-layer ocean with a baroclinic current to a moving storm. Part I // J. Oceanogr. Soc. Japan. – 1977. – 33. – P. 151 – 160. ISSN 0233-7584. Мор. гидрофиз. журн., 2013, № 5 49 9. Ichiye T. Response of a two-layer ocean with a baroclinic current to a moving storm. Part II // Ibid. – 1977. – 33. – P. 169 – 182. 10. Horton C.W. Surface front displacement in the Gulf Stream by Hurricane / Tropical Storm Dennis // J. Geophys. Res. – 1984. – 89, № C2. – P. 2005 – 2012. 11. Lee S. Tropical cyclone-ocean interaction in oceanic frontal regions / PhD thesis. – University of Rhode Island, 2011. – 136 p. 12. Flierl G.R. Thin jet and contour dynamics models of Gulf Stream meandering // Dyn. Atmos. Oceans. – 1999. – 29. – P. 189 – 215. 13. Ginis I., Sutyrin G. Hurricane-generated depth-averaged currents and sea surface elevation // J. Phys. Oceanogr. – 1995. – 25. – P. 1218 – 1242. 14. Holland G.J. An analytic model of the wind and pressure profiles in hurricanes // Mon. Wea. Rev. – 1980. – 108. – P. 1212 – 1218. 15. Sutyrin G., Rowe D., Rothstein L., Ginis I. Baroclinic-eddy interactions with continental slopes and shelves // J. Phys. Oceanogr. – 2003. – 33. – P. 283 – 291. 16. Nycander J., Dritschel D.G., Sutyrin G.G. The dynamics of long frontal waves in the shallow water equations // Phys. Fluids. – 1993. – A5. – P. 1089 – 1091. 17. Cushman-Roisin B., Pratt L., Ralph E. A general theory for equivalent barotropic thin jets // J. Phys. Oceanogr. – 1993. – 23. – P. 91 – 103. 18. Ralph E.A., Pratt L. Predicting eddy detachment for an equivalent barotropic thin jet // J. Nonlin. Sci. – 1994. – 4. – P. 355 – 374. 19. Greene A.D., Watts D.R., Sutyrin G.G. et al. Evidence of vertical coupling between the Kuroshio extension and topographically controlled deep eddies // J. Mar. Res. – 2012. – 70. – P. 719 – 747. Graduate School of Oceanography Received July 10, 2012 University of Rhode Island Narragansett, RI USA АНОТАЦІЯ У рамках двошарової моделі та в наближенні тонкого струменя розглядається еволюція бароклинного струменя, викликаного баротропною течією, індукованою тропічним циклоном. Показано, що, не дивлячись на антисиметричну структуру баротропної течії, її адвекція призводить до меандрування бароклинного струменя та до зростання головним чином антициклонічного меандру праворуч від штормтрека. Знайдено, що посилення антициклоніч- ного меандру пов'язане з дисперсійними властивостями фронтальних хвиль (які описуються у рамках теорії тонкого струменя) і з взаємодією з глибинними вихорами, які розвиваються в нижньому шарі океану при меандруванні бароклинного струменю. Ключові слова: бароклинний струмінь, тропічний циклон, антициклонічний меандр, тео- рія тонкого струменя. АННОТАЦИЯ В рамках двухслойной модели и в приближении тонкой струи рассматривается эволюция бароклинной струи, вызванной баротропным течением, индуцированным тропиче- ским циклоном. Показано, что, несмотря на антисимметричную структуру баротропного тече- ния, его адвекция приводит к меандрированию бароклинной струи и к росту главным образом антициклонического меандра справа от штормтрека. Обнаружено, что усиление антициклони- ческого меандра связано с дисперсионными свойствами фронтальных волн (описываемых в рамках теории тонкой струи) и с взаимодействием с глубинными вихрями, развивающимися в нижнем слое океана при меандрировании бароклинной струи. Ключевые слова: бароклинная струя, тропический циклон, антициклонический меандр, теория тонкой струи. ISSN 0233-7584. Мор. гидрофиз. журн., 2013, № 5 50

Impact of tropical cyclones on a baroclinic jet in the ocean

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