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Chuan Shi and Doron Nof


Since midocean eddies Migrate westward, they eventually reach the western boundaries. It is, therefore, of interest to find out what happens after the eddies collide with the walls. An isopycnic, two-layer, primitive equation model on a β plane and a simple analytical model on an f plane are constructed to investigate the meridional migration of an oceanic eddy along a western wall.

On a β plane, three factors determine the eddy's migration along a western meridional wall. First, the image effect pushes an anticyclonic (cyclonic) eddy northward (southward). Second, the β force (resulting from the larger Coriolis force on the northern side of the eddy) pulls an anticyclonic (cyclonic) eddy southward (northward). Third, after an anticyclonic (cyclonic) eddy collides with the wall, parts of the anticyclonic eddy's interior fluid leak out southward (northward) along the wall forming a thin jet. In an analogy to a rocket, this jet pushes the eddy northward (southward). Our aim is to investigate in which direction the eddy ultimately migrates along the will (i.e., to determine which of the above three processes dominates).

The combined effect of the three processes is a rather complicated process and the results are counterintuitive. For instance, imagine a lenslike anticyclonic eddy situated on a sloping bottom (analogous to β). This highly nonlinear eddy migrates with shallow water on its right (“westward”) and encounters a meridional wall. Intuitively, it is expected that, once the “westward” migration is arrested by the wall, gravity will pull the eddy downhill (southward) so that the eddy will migrate toward deep water (i.e., toward the equator). Surprisingly, however, the authors’ numerical computations show that the eddy migrates uphill. This bizarre behavior results from the leakage along the wall that, in terms of the eddy energy, compensates for the uphill drift. Namely, the leakage plays a crucial role in the eddy-wall interaction process because it allows the uphill migration. Eventually, it causes a destruction of the lens by completely draining its fluid.

The above highly nonlinear experiments are supplemented by quasigeostrophic analytical solutions and iso-pycnic numerical experiments of cyclones and anticyclones. It is found that, in contrast to the situation with the lens, the leakage does not play a crucial role in quasigeostrophic eddies. However, all of these experiments show that the image effect is the most dominant process. It turns out that, as the eddy responds to the presence of the wall, it is transformed into a half-circular shape that is very different from its original preinteraction circular shape. This results from the fact that, even though the westward β-induced speed (forcing the eddy into the wall) is small, it is active over an extended period of time so that its final effect is relatively large. The final half-circular eddy that migrates along the wall is nearly independent of β as long as the eddy is not extremely far from its original latitude. This is demonstrated by both our numerical solution (of the primitive equations) as well as our quasigeostrophic analytical solution. The authors term this final migrating eddy a wodon as it represents a combination of a wall and a modon.

Possible applications of these models to various oceanic situations are discussed.

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Doron Nof and Chuan Shi


A two-layer analytical model of cold- and warm-core rings has been constructed to explore steady interactions of isolated eddies with horizontally sheared flows around and below the eddies. Steady inviscid solutions to the quasi-geostrophic equations are found by assuming that the environmental sheer is weak compared to the ring's shear.

It is found that such interactions lead to elliptical rings in contrast to our expectations, the eccentricity of the rings is caused solely by the lower layer shear and is independent of the surrounding upper shear. Namely, when there is no shear in the lower layer, the ring's shape is circular, even though there may exist a surrounding upper shear. When the flow inside the ring rotates in the same direction as the lower shear, the elliptical ring in aligned along the lower layer flow. On the other hand, when the flow inside the ring rotates in the opposite direction to that of the lower shear, the elliptical ring is aligned across the lower-layer flow.

Surprisingly, when the surrounding upper flow shear rotates in the opposite direction to that of the flow below the ring, a chain of weak vortices is generated outside the ring in the upper layer. This chain of vortices is a result of trapped planetary waves. When the surrounding upper flow and the lower layer flow rotate in the same sense, there are no such ambient vortices. Instead, U-turned flows on both sides of the ring are established.

Possible applications of this theory to both warm- and cold-core rings are mentioned.

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Yonghui Lei, Jiancheng Shi, Chuan Xiong, and Dabin Ji


In this study, the net water flux (precipitation minus evaporation) over the Tibetan Plateau (TP) and its 12 drainage basins is estimated using ERA5. The terrestrial branch of the water cycle is investigated using the total water storage anomalies (TWSAs) derived from GRACE (Gravity Recovery and Climate Experiment) data and daily streamflow records collected in Zhimenda and Tangnaihai (two hydrological stations located in the upper Yangtze River Basin and upper Yellow River Basin). This work provides a preliminary assessment of discrepancies between model-derived and space-based observations in the atmospheric–terrestrial water cycle over the TP and its drainage basins. The results show that the net water fluxes occurring over the TP and the scale of its drainage basins are closely tied to local dynamics and physical processes and to large-scale circulation and atmospheric water vapor. ERA5 maintains the atmospheric water balance over the TP. ERA5-derived net water flux anomalies constitute a major component of the water cycle and correspond to GRACE-derived TWSAs. The water budget–based approach with the ERA5 and ITSG-Grace2018 datasets constrains the atmospheric–terrestrial water cycle over the TP and its drainage basins. Both the ERA5- and GRACE-derived estimates contain consistent long- and short-term variations over the TP. Discrepancies are evident at the drainage basin, while the ratio of signal to noise in both the ERA5 and GRACE datasets might cause discrepancies between estimates over relatively small or arid basins. Nevertheless, the observed good correspondence between ERA5- and GRACE-derived atmospheric–terrestrial water cycles over the TP highlights the potential value of the rational application of water resource information.

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