Abstract
Due to the ubiquitous steep continental shelf slope in the East China Sea, topographic Rossby waves are very common when the Kuroshio Current flows along the slope, and of great importance in the water and energy exchange between the open ocean and coastal sea. To examine the structural characteristics of topographic Rossby wave, we use stretching transform of time and space and perturbation method to get the analytic solution of potential vorticity equation with topography. For a given background flow v = v0 + δx, the effect of background flow shear is discussed. The main conclusions are drawn that background flow shear is required for the existence of solitary Rossby waves; for flow shear δ < 0 (δ > 0), anticyclonic (cyclonic) solitary Rossby waves exist and their zonal structure tilts eastward (westward); the phase speed of solitary Rossby waves is related to the amplitude and flow shear intensity; solitary Rossby waves are non-dispersive waves, and the width of solitary waves is inversely proportional to the intensity of the flow shear. Furthermore, these theoretical results are used to explain the propagation speeds and distributions of eddies along the Kuroshio Current in the East China Sea. In addition, these results could be applied to other areas with similar meridional current and topography.
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References
Benney DJ (1966) Long non-linear waves in fluid flows. Stud Appl Math 45(1–4):52–63
Boyd JP (1980) Equatorial solitary waves. Part I: Rossby solitons. J Phys Oceanogr 10(11):1699–1717
Challenor PG, Cipollini P, Cromwell D (2001) Use of the 3D Radon transform to examine the properties of oceanic Rossby waves. J Atmos Ocean Technol 18(9):1558–1566
Chelton DB, Schlax MG (1996) Global observations of oceanic Rossby waves. Science 272(5259):234
Chelton DB, Schlax MG, Samelson RM (2011) Global observations of nonlinear mesoscale eddies. Prog Oceanogr 91(2):167–216
Chelton DB, Schlax MG, Samelson RM, de Szoeke RA (2007) Global observations of large oceanic eddies. Geophys Res Lett. https://doi.org/10.1029/2007GL030812
Kamidaira Y, Uchiyama Y, Mitarai S (2016) Eddy-induced transport of the Kuroshio warm water around the Ryukyu Islands in the East China Sea. Cont Shelf Res 143:206–218
Liu Y, Dong C, Liu X, Dong J (2017) Antisymmetry of oceanic eddies across the Kuroshio over a shelfbreak. Sci Rep 7(1):6761
Long RR (1964) Solitary waves in the westerlies. J Atmos Sci 21(2):197–200
Louis JP, Petrie BD, Smith PC (1982) Observations of topographic Rossby waves on the continental margin off Nova Scotia. J Phys Oceanogr 12(1):47–55
Lu C, Fu C, Yang H (2018) Time-fractional generalized Boussinesq equation for Rossby solitary waves with dissipation effect in stratified fluid and conservation laws as well as exact solutions. Appl Math Comput 327:104–116
Oey L, Lee H (2002) Deep eddy energy and topographic Rossby waves in the Gulf of Mexico. J Phys Oceanogr 32(12):3499–3527
Ono H (1981) Algebraic Rossby wave soliton. J Oceanogr Soc Japan 50(8):2757–2761
Pedlosky J (1987) Geophysical fluid dynamics. Springer, New York
Qiu B (2001) Kuroshio and Oyashio currents. Academic Press, London
Redekopp LG (1977) On the theory of solitary Rossby waves. J Fluid Mech 82(4):725–745
Ribbe J, Toaspern L, Wolff JO, Ismail MFA (2018) Frontal eddies along a western boundary current. Cont Shelf Res 165:51–59
Sasaki YN, Minobe S, Asai T, Inatsu M (2012) Influence of the Kuroshio in the East China Sea on the early summer (baiu) rain. J Climate 25(19):6627–6645
Shi Y, Yang D, Feng X, Qi J, Yang H, Yin B (2018) One possible mechanism for eddy distribution in zonal current with meridional shear. Sci Rep 8(1):10106
Shi Y, Yang H, Yin B, Yang D, Xu Z, Feng X (2015) Dissipative nonlinear Schrodinger equation with external forcing in rotational stratified fluids and Its solution. Commun Theor Phys 64(4):464–472
Xu H, Xu M, Xie SP, Wang Y (2011) Deep atmospheric response to the spring Kuroshio over the East China Sea. J Climate 24(18):4959–4972
Yamagata T (1982) On nonlinear planetary waves: a class of solutions missed by the traditional quasi-geostrophic approximation. J Oceanogr Soc Japan 38(4):236–244
Yanagi T, Shimizu T, Lie HJ (1998) Detailed structure of the Kuroshio frontal eddy along the shelf edge of the East China Sea. Cont Shelf Res 18(9):1039–1056
Yang D, Yin B, Liu Z, Feng X (2011) Numerical study of the ocean circulation on the East China Sea shelf and a Kuroshio bottom branch northeast of Taiwan in summer. J Geophys Res. https://doi.org/10.1029/2010JC006777
Yang HW, Chen X, Guo M, Chen YD (2018) A new ZK–BO equation for three-dimensional algebraic Rossby solitary waves and its solution as well as fission property. Nonlinear Dyn 91(3):2019–2032
Zhang RG, Yang LG (2019) Nonlinear Rossby waves in zonally varying flow under generalized beta approximation. Dyn Atmos Oceans 85:16–27
Acknowledgements
This study was supported by the National Key Research, Development Program of China (Grant Numbers 2017YFC1404000, 2016YFC1401601, 2017YFA0604102); the Strategic Priority Research Program of Chinese Academy of Sciences (CAS; Grant Number XDA19060203); the National Natural Science Foundation of China (Grant Numbers 41576023, 41876019); Foundation for Innovative Research Groups of NSFC (Grant Number 41421005); NSFC-Shandong Joint Fund for Marine Science Research Centers (Grant Number U1406401); National Key Research and Development Plan Sino-Australian Center for Healthy Coasts (Grant Number 2016YFE0101500); Aoshan Sci-Tec Innovative Project of Qingdao National Laboratory for Marine Science and Technology (Grant Number 2016ASKJ02); Strategic Pioneering Research Program of the Chinese Academy of Sciences (Grant Numbers XDA11020104, XDA110203052); Open Fund of the Key Laboratory of Ocean Circulation and Waves, Chinese Academy of Sciences (Grant Number KLOCW1802); and the Startup Foundation for Introducing Talent of NUIST (Grant Number 2017r092).
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Shi, Y., Yang, D. & Yin, B. The effect of background flow shear on the topographic Rossby wave. J Oceanogr 76, 307–315 (2020). https://doi.org/10.1007/s10872-020-00546-6
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DOI: https://doi.org/10.1007/s10872-020-00546-6