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Using hydrographic data and box models, it is shown that the presently discussed diversion of rivers such as the Yellow or the Yangtze for agricultural use is likely to cause the renewal of Bottom Water formation in the Japan/East Sea. Such formation was common (near the Siberian coast) in the 1930s, 1940s, and 1950s, but subsided since that time due to a warming trend (accompanied by a decreased salinity due to the melting of ice). Since a diversion of freshwater is analogous to evaporation, a (diversion induced) increase of salinity is expected and the increase is large enough to allow Bottom Water formation even at the present-day cooling rates. Even a modest diversion of “merely” 3000 m^{3} s−1 (which is 10% of the total freshwater flux) will probably cause Bottom Water formation at a rate of roughly 750 000 m^{3} s−1. This is the first study that predicts anthropogenic *reversal* of an existing vertical structure in a semienclosed sea.

Using hydrographic data and box models, it is shown that the presently discussed diversion of rivers such as the Yellow or the Yangtze for agricultural use is likely to cause the renewal of Bottom Water formation in the Japan/East Sea. Such formation was common (near the Siberian coast) in the 1930s, 1940s, and 1950s, but subsided since that time due to a warming trend (accompanied by a decreased salinity due to the melting of ice). Since a diversion of freshwater is analogous to evaporation, a (diversion induced) increase of salinity is expected and the increase is large enough to allow Bottom Water formation even at the present-day cooling rates. Even a modest diversion of “merely” 3000 m^{3} s−1 (which is 10% of the total freshwater flux) will probably cause Bottom Water formation at a rate of roughly 750 000 m^{3} s−1. This is the first study that predicts anthropogenic *reversal* of an existing vertical structure in a semienclosed sea.

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## Abstract

A different way of examining the meridional flux of warm and intermediate water (*σ*
_{
θ
} < 27.50) from the Southern Ocean into the South Atlantic is proposed. The method considers the Americas to be a “pseudo island” in the sense that the continent is entirely surrounded by water but has no circulation around it. It is shown that, although the northern connection between the Atlantic and the Pacific (via the Bering Strait) is weak, it imposes severe limitations on the sea level in the Atlantic basin: so much so that it allows one to compute the meridional transport without finding the detailed solution to the complete wind–thermohaline problem. The method employs an integration of the linearized momentum equations along a closed contour containing the Americas, Greenland, the Atlantic, and parts of the Arctic Ocean.

First, an idealized rectangular model involving three layers, an active continuously stratified upper layer containing both thermocline (*σ*
_{
θ
} < 26.80) and intermediate water (26.80 < *σ*
_{
θ
} < 27.80), an inert deep layer (27.80 < *σ*
_{
θ
} < 27.90), and a southward moving bottom layer (*σ*
_{
θ
} > 27.90) is considered. In this idealized model, the Americas are represented by the pseudo island. Deep-water formation is allowed (in the northern part of the basin east of the Americas and south of the gap connecting the Atlantic–Arctic basin to the Pacific), but the cooling rate need not be specified. The basin is subject to both zonal winds and heat exchange with the atmosphere [i.e., *ρ* = *ρ*(*x, y, z*)], but, for simplicity, (temporarily) meridional winds are not allowed. A simple analytical expression for the transport of the meridional overturning cell is derived, and process-oriented numerical experiments that were conducted (using a primitive equation layer-and-a-half isopycnic model) are in excellent agreement with the theory.

The theory is then extended to a more convoluted geography subject to both zonal and meridional winds. The surprising result is found that, even for the complex situation, the northward transport of upper and intermediate water is given simply by [fy917,1]) *τ*
^{
l
}
*dl*/*ρ*/*f*
_{0}, where *f*
_{0} is the average Coriolis parameter along a line connecting the southern tip of the Americas with the southern tip of Africa and *τ*
^{
l
} is the wind stress along the integration path (*l*). This implies that, although the amount of high-latitude cooling is responsible for the location and manner in which bottom water is formed, it has very limited effect on the net meridional mass flux (which constitutes the so-called conveyor).

Detailed application of the above formula to the Atlantic using actual geography and spherical coordinates as well as actual meridional and zonal winds (adopted from 40-yr averages given by NCEP) gives the reasonable estimate of 9 Sv (Sv ≡ 10^{6} m^{3} s^{−1}) for the transport of the conveyor upper limb.

## Abstract

A different way of examining the meridional flux of warm and intermediate water (*σ*
_{
θ
} < 27.50) from the Southern Ocean into the South Atlantic is proposed. The method considers the Americas to be a “pseudo island” in the sense that the continent is entirely surrounded by water but has no circulation around it. It is shown that, although the northern connection between the Atlantic and the Pacific (via the Bering Strait) is weak, it imposes severe limitations on the sea level in the Atlantic basin: so much so that it allows one to compute the meridional transport without finding the detailed solution to the complete wind–thermohaline problem. The method employs an integration of the linearized momentum equations along a closed contour containing the Americas, Greenland, the Atlantic, and parts of the Arctic Ocean.

First, an idealized rectangular model involving three layers, an active continuously stratified upper layer containing both thermocline (*σ*
_{
θ
} < 26.80) and intermediate water (26.80 < *σ*
_{
θ
} < 27.80), an inert deep layer (27.80 < *σ*
_{
θ
} < 27.90), and a southward moving bottom layer (*σ*
_{
θ
} > 27.90) is considered. In this idealized model, the Americas are represented by the pseudo island. Deep-water formation is allowed (in the northern part of the basin east of the Americas and south of the gap connecting the Atlantic–Arctic basin to the Pacific), but the cooling rate need not be specified. The basin is subject to both zonal winds and heat exchange with the atmosphere [i.e., *ρ* = *ρ*(*x, y, z*)], but, for simplicity, (temporarily) meridional winds are not allowed. A simple analytical expression for the transport of the meridional overturning cell is derived, and process-oriented numerical experiments that were conducted (using a primitive equation layer-and-a-half isopycnic model) are in excellent agreement with the theory.

The theory is then extended to a more convoluted geography subject to both zonal and meridional winds. The surprising result is found that, even for the complex situation, the northward transport of upper and intermediate water is given simply by [fy917,1]) *τ*
^{
l
}
*dl*/*ρ*/*f*
_{0}, where *f*
_{0} is the average Coriolis parameter along a line connecting the southern tip of the Americas with the southern tip of Africa and *τ*
^{
l
} is the wind stress along the integration path (*l*). This implies that, although the amount of high-latitude cooling is responsible for the location and manner in which bottom water is formed, it has very limited effect on the net meridional mass flux (which constitutes the so-called conveyor).

Detailed application of the above formula to the Atlantic using actual geography and spherical coordinates as well as actual meridional and zonal winds (adopted from 40-yr averages given by NCEP) gives the reasonable estimate of 9 Sv (Sv ≡ 10^{6} m^{3} s^{−1}) for the transport of the conveyor upper limb.

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## Abstract

The author considers two oceanic basins separated by a meridional wall. The wall contains a gap that is initially blocked by a gate; westward winds are allowed to blow over the two-layered oceans creating western boundary currents and a sea level difference between the basins. The conceptual gate is then removed and the resulting nonlinear flow is computed.

The analytical calculations are based on a simple wind-driven general circulation model and a nonlinear integrated momentum constraint. Two classes of nonlinear solutions are constructed. One corresponds to a situation where the flow through the gap originates from the right-hand side (looking upstream) of the inner Pacific basin and the other to a situation where the flow originates from the left-hand side. It is suggested that the actual Indonesian Throughflow is composed of both of these classes of flows; that is, the throughflow corresponds to an exchange via *two* adjacent gaps.

Computations suggest that approximately 6 Sv (Sv ≡ 10^{6} m^{3} s^{−1}) enter the passages from the North Pacific and 1 Sv from the South Pacific giving a total of 7 Sv. This may resolve the apparent difficulty associated with existing linear theories (and nonlinear theories that neglect western boundary currents), which predict that without strong turbulent diffusion only South Pacific water can enter the passages.

## Abstract

The author considers two oceanic basins separated by a meridional wall. The wall contains a gap that is initially blocked by a gate; westward winds are allowed to blow over the two-layered oceans creating western boundary currents and a sea level difference between the basins. The conceptual gate is then removed and the resulting nonlinear flow is computed.

The analytical calculations are based on a simple wind-driven general circulation model and a nonlinear integrated momentum constraint. Two classes of nonlinear solutions are constructed. One corresponds to a situation where the flow through the gap originates from the right-hand side (looking upstream) of the inner Pacific basin and the other to a situation where the flow originates from the left-hand side. It is suggested that the actual Indonesian Throughflow is composed of both of these classes of flows; that is, the throughflow corresponds to an exchange via *two* adjacent gaps.

Computations suggest that approximately 6 Sv (Sv ≡ 10^{6} m^{3} s^{−1}) enter the passages from the North Pacific and 1 Sv from the South Pacific giving a total of 7 Sv. This may resolve the apparent difficulty associated with existing linear theories (and nonlinear theories that neglect western boundary currents), which predict that without strong turbulent diffusion only South Pacific water can enter the passages.

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## Abstract

A simplified two-layer analytical model describing the interaction between a longshore current and a thin lenslike eddy is considered. The eddy is situated near a vertical wall and is embedded in a frictional boundary current which is flowing from one latitude to another. Attention is focused on the conditions under which the boundary current compensates for the tendency of the eddy is drift due to β so that the eddy is stationary. The model incorporates movements resulting from the circulation within the eddy, the longshore flow and β. Both the upper and lower layer are taken to be active; diffusion is neglected but bottom friction is included. Although our model is simplified, the movements within the eddy are not constrained to be quasi-geostrophic, in the sense that the Rossby number can be relatively large and the interface surfaces at a finite distance from the center. The desired solutions are constructed analytically.

It is found that a thin lenslike eddy adjacent to a western boundary can remain in a fixed position if the current in which it is embedded is *flowing from low to high latitudes* at a (“critical”) speed which depends on β, the inclination of the coastline, the frictional coefficient along the bottom of the ocean and the eddy's size, intensity and volume. Presumably, a northward flowing current whose speed is ten than “critical” will allow the eddy to drift *upstream* (southward), whereas a current whose speed is stronger than the *critical* will sweep the current *downstream* (northward).

In contrast to western boundaries, thin eddies embedded in eastern longshore flows can never be stationary regardless of the current's characteristics. This difference between western and eastern boundaries exists because as the current flows, it exert two forces on the eddy. One is parallel to the coastline (and can compensate for the eddy's β-induced force) and the other is perpendicular to the wall. In the western boundary case, the cross-stream force pushes the eddy toward the boundary causing it to lean against the wall. In the eastern boundary case, on the other hand, the force pushes the eddy away from the wall causing it to accelerate toward the open ocean.

## Abstract

A simplified two-layer analytical model describing the interaction between a longshore current and a thin lenslike eddy is considered. The eddy is situated near a vertical wall and is embedded in a frictional boundary current which is flowing from one latitude to another. Attention is focused on the conditions under which the boundary current compensates for the tendency of the eddy is drift due to β so that the eddy is stationary. The model incorporates movements resulting from the circulation within the eddy, the longshore flow and β. Both the upper and lower layer are taken to be active; diffusion is neglected but bottom friction is included. Although our model is simplified, the movements within the eddy are not constrained to be quasi-geostrophic, in the sense that the Rossby number can be relatively large and the interface surfaces at a finite distance from the center. The desired solutions are constructed analytically.

It is found that a thin lenslike eddy adjacent to a western boundary can remain in a fixed position if the current in which it is embedded is *flowing from low to high latitudes* at a (“critical”) speed which depends on β, the inclination of the coastline, the frictional coefficient along the bottom of the ocean and the eddy's size, intensity and volume. Presumably, a northward flowing current whose speed is ten than “critical” will allow the eddy to drift *upstream* (southward), whereas a current whose speed is stronger than the *critical* will sweep the current *downstream* (northward).

In contrast to western boundaries, thin eddies embedded in eastern longshore flows can never be stationary regardless of the current's characteristics. This difference between western and eastern boundaries exists because as the current flows, it exert two forces on the eddy. One is parallel to the coastline (and can compensate for the eddy's β-induced force) and the other is perpendicular to the wall. In the western boundary case, the cross-stream force pushes the eddy toward the boundary causing it to lean against the wall. In the eastern boundary case, on the other hand, the force pushes the eddy away from the wall causing it to accelerate toward the open ocean.

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## Abstract

In this paper an analytical method is proposed for calculating the nonlinear β-induced translation of isolated baroclinic eddies. The study focuses on frictionless anticyclonic eddies with a uniform anomalous density and a lens-like cross section which translates steadily in a resting Ocean. The depth of these eddies vanishes along the outer edge so that as they translate westward their entire mass anomaly is caused along with them.

The proposed method for calculating the translation speed incorporates the nonlinear equations of motion in an integrated form and a simple perturbation scheme. It relates the translation of the eddy to its intensity, size and volume, but requires only an approximate knowledge of the corresponding numerical values.

The power and usefulness of the proposed method is demonstrated by its application to a class of simply-structured eddies whose swirl velocity increases monotonically with the distance from the center. It is found that the translation of these eddies is considerably smaller than that of a simple Rossby wave. A small Rossby number eddy whose swirl velocity increases monotonically with the distance from the center translates westward at approximately *R*
_{
d
}
^{2}
*R*
_{
d
}, is the deformation radius), whereas the most nonlinear eddy (whose negative relative vorticity approaches the vorticity of the earth) translates at *R*
_{
d
}
^{2}

The proposed method is tested by its application to more complicated anticyclonic eddies representing those shed by the Loop Current in the Gulf of Mexico. For these eddies, the predicted westward translation speed is *R*
_{
d
}
^{2}

## Abstract

In this paper an analytical method is proposed for calculating the nonlinear β-induced translation of isolated baroclinic eddies. The study focuses on frictionless anticyclonic eddies with a uniform anomalous density and a lens-like cross section which translates steadily in a resting Ocean. The depth of these eddies vanishes along the outer edge so that as they translate westward their entire mass anomaly is caused along with them.

The proposed method for calculating the translation speed incorporates the nonlinear equations of motion in an integrated form and a simple perturbation scheme. It relates the translation of the eddy to its intensity, size and volume, but requires only an approximate knowledge of the corresponding numerical values.

The power and usefulness of the proposed method is demonstrated by its application to a class of simply-structured eddies whose swirl velocity increases monotonically with the distance from the center. It is found that the translation of these eddies is considerably smaller than that of a simple Rossby wave. A small Rossby number eddy whose swirl velocity increases monotonically with the distance from the center translates westward at approximately *R*
_{
d
}
^{2}
*R*
_{
d
}, is the deformation radius), whereas the most nonlinear eddy (whose negative relative vorticity approaches the vorticity of the earth) translates at *R*
_{
d
}
^{2}

The proposed method is tested by its application to more complicated anticyclonic eddies representing those shed by the Loop Current in the Gulf of Mexico. For these eddies, the predicted westward translation speed is *R*
_{
d
}
^{2}

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## Abstract

Shock waves are discontinuities (in the physical properties of a fluid) which behave in an organized manner. The possibility that such waves may occur in oceanic boundary currents is examined with a nonlinear two-layer analytical model. Attention is focused on separated boundary currents (i.e., light currents whose lower interface strikes the free surface or heavy currents whose upper interface intersects the floor) with zero potential vorticity. The shocks result from an increase in the upstream transport; they correspond to abrupt and violent changes in depth and velocity accompanied by a local energy loss. Nonlinear solutions for steadily translating shocks are constructed analytically by connecting the upstream and downstream fields without solving for the complicated region in the immediate vicinity of the shock.

It is found that, while stationary shocks are impossible, steadily propagating shocks can always occur. There are no special requirements on the boundary currents in question and the only necessary condition for steadily advancing shocks to occur is that the upstream depth is increased. Once formed the shocks propagate downstream at a speed greater than that of a Kelvin wave associated with the increased up-stream flow.

Possible application of this theory to the Mediterranean outflow is discussed. For this purpose, the results of the two-layer model are extended to a three-layer model corresponding to a wedge-like boundary current “sandwiched” between two infinitely deep layers. With the aid of this model it is suggested that the abrupt changes in temperature and depth observed in the Mediterranean outflow are a result of a shock wave advancing downstream. The observed changes in this region are so abrupt and violent that no other known kind of wave ran explain them.

## Abstract

Shock waves are discontinuities (in the physical properties of a fluid) which behave in an organized manner. The possibility that such waves may occur in oceanic boundary currents is examined with a nonlinear two-layer analytical model. Attention is focused on separated boundary currents (i.e., light currents whose lower interface strikes the free surface or heavy currents whose upper interface intersects the floor) with zero potential vorticity. The shocks result from an increase in the upstream transport; they correspond to abrupt and violent changes in depth and velocity accompanied by a local energy loss. Nonlinear solutions for steadily translating shocks are constructed analytically by connecting the upstream and downstream fields without solving for the complicated region in the immediate vicinity of the shock.

It is found that, while stationary shocks are impossible, steadily propagating shocks can always occur. There are no special requirements on the boundary currents in question and the only necessary condition for steadily advancing shocks to occur is that the upstream depth is increased. Once formed the shocks propagate downstream at a speed greater than that of a Kelvin wave associated with the increased up-stream flow.

Possible application of this theory to the Mediterranean outflow is discussed. For this purpose, the results of the two-layer model are extended to a three-layer model corresponding to a wedge-like boundary current “sandwiched” between two infinitely deep layers. With the aid of this model it is suggested that the abrupt changes in temperature and depth observed in the Mediterranean outflow are a result of a shock wave advancing downstream. The observed changes in this region are so abrupt and violent that no other known kind of wave ran explain them.

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## Abstract

The nonlinear leakage of Kuroshio water (via the Tsushima Strait) into the Sea of Japan is examined using a “reduced gravity” analytical model. The flow in our conceptual model results from the zonal sea level difference between the Pacific Ocean and the Sea of Japan. The landmasses separating the Pacific from the adjacent Sea of Japan are represented by thin walls and the Tsushima Strait, whose width is larger than the Rossby radius, is represented by a gap. The gap is initially closed and the problem is treated as an adjustment process resulting from an abrupt opening of the gap.

Steady analytical solutions for the final state associated with the adjustment are constructed using the integrated momentum equation on a *β* plane, conservation of energy, and potential vorticity. Also, a perturbation expansion in ε≡*βL*/*f*
_{0} (the ratio of the change in the Coriolis parameter, as one moves from the gap to the boundary current separation latitude, to the Coriolis parameter at the center of the gap) is used.

*H*, and the “reduced gravity,”

*g*Δρ/ρ). As other studies for flows through broad gaps have demonstrated, the transport is controlled by the geostrophic flows upstream and downstream. However, in addition to the so-called “geostrophic control,” the flow is also controlled by

*β*and, therefore, we term it “beta control.” Specifically, the penetration flux is given by

^{6}m

^{3}s

^{−1}). This computed flux is much greater than the linear transport,

## Abstract

The nonlinear leakage of Kuroshio water (via the Tsushima Strait) into the Sea of Japan is examined using a “reduced gravity” analytical model. The flow in our conceptual model results from the zonal sea level difference between the Pacific Ocean and the Sea of Japan. The landmasses separating the Pacific from the adjacent Sea of Japan are represented by thin walls and the Tsushima Strait, whose width is larger than the Rossby radius, is represented by a gap. The gap is initially closed and the problem is treated as an adjustment process resulting from an abrupt opening of the gap.

Steady analytical solutions for the final state associated with the adjustment are constructed using the integrated momentum equation on a *β* plane, conservation of energy, and potential vorticity. Also, a perturbation expansion in ε≡*βL*/*f*
_{0} (the ratio of the change in the Coriolis parameter, as one moves from the gap to the boundary current separation latitude, to the Coriolis parameter at the center of the gap) is used.

*H*, and the “reduced gravity,”

*g*Δρ/ρ). As other studies for flows through broad gaps have demonstrated, the transport is controlled by the geostrophic flows upstream and downstream. However, in addition to the so-called “geostrophic control,” the flow is also controlled by

*β*and, therefore, we term it “beta control.” Specifically, the penetration flux is given by

^{6}m

^{3}s

^{−1}). This computed flux is much greater than the linear transport,

^{ }

## Abstract

The analytical results for the splitting conditions of isolated barotropic eddies and the associated final equilibrium state are extended to: 1) nonlinear baroclinic eddies; 2) a group of four nonlinear closely packed eddies, two of which are cyclonic and two of which are anticyclonic (i.e., multiple eddies); and 3) joint nonlinear eddies (i.e., a system consisting of two eddies situated one above the other). The final equilibrium state associated with the group (of four) fission is related to a nonlinear version or geostrophic turbulence and, therefore, is referred to as *ageostrophic turbulence*.

Taking into account that inviscid fission may involve loss of energy via waves radiation, the breakup process is examined by conserving integrated angular momentum, potential vorticity, and mass. The analytical expressions for the conservation of these three properties provide a set of algebraic equations that are solved numerically.

For baroclinic eddies embedded in an infinitely deep lower layer, it is found that, as in the barotropic case, only intense cyclones can break up. This results from the fact that, despite the large amplitude of the nonlinear baroclinic eddies, the offspring are still forced a considerable distance away from their original prebirth center of rotation as is the case with the barotropic eddies. This causes a large gain in angular momentum implying that only eddies whose angular momentum is relatively large to begin with are capable of being potential parents. Again, as in the barotropic case, it turns out that only intense cyclones have large enough angular momentum to allow splitting (because the cyclonic orbital speed is in the same direction as the earth's rotation).

In ageostrophic turbulence, the cyclones break up and the anticyclones merge. Namely, the fission of the cyclones provides the energy necessary for the fusion of the anticyclones. Hence, the final result is a nonlinear system resembling a “Mickey Mouse”(with one large anticyclone and four small cyclones) whose total energy is identical to the total initial energy prior to the fission.

The impossibility of baroclinic anticyclones to break up appears initially to be in contradiction with classical laboratory experiments which show what seems to be an anticyclonic fission. The solution for joint eddies consisting of a cyclone situated above an anticyclone suggests, however, that what really really breaks up in the laboratory is the cyclone on top rather than the anticyclone underneath. (Recall that the generation of anticyclone in the laboratory is often accompanied by the formation of a cyclone on top due to convergence.)

It is suggested that the impossibility of baroclinic anticyclones to break up and the tendency of cyclones to split may provide an explanation for the relative abundance of anticyclones in the ocean.

## Abstract

The analytical results for the splitting conditions of isolated barotropic eddies and the associated final equilibrium state are extended to: 1) nonlinear baroclinic eddies; 2) a group of four nonlinear closely packed eddies, two of which are cyclonic and two of which are anticyclonic (i.e., multiple eddies); and 3) joint nonlinear eddies (i.e., a system consisting of two eddies situated one above the other). The final equilibrium state associated with the group (of four) fission is related to a nonlinear version or geostrophic turbulence and, therefore, is referred to as *ageostrophic turbulence*.

Taking into account that inviscid fission may involve loss of energy via waves radiation, the breakup process is examined by conserving integrated angular momentum, potential vorticity, and mass. The analytical expressions for the conservation of these three properties provide a set of algebraic equations that are solved numerically.

For baroclinic eddies embedded in an infinitely deep lower layer, it is found that, as in the barotropic case, only intense cyclones can break up. This results from the fact that, despite the large amplitude of the nonlinear baroclinic eddies, the offspring are still forced a considerable distance away from their original prebirth center of rotation as is the case with the barotropic eddies. This causes a large gain in angular momentum implying that only eddies whose angular momentum is relatively large to begin with are capable of being potential parents. Again, as in the barotropic case, it turns out that only intense cyclones have large enough angular momentum to allow splitting (because the cyclonic orbital speed is in the same direction as the earth's rotation).

In ageostrophic turbulence, the cyclones break up and the anticyclones merge. Namely, the fission of the cyclones provides the energy necessary for the fusion of the anticyclones. Hence, the final result is a nonlinear system resembling a “Mickey Mouse”(with one large anticyclone and four small cyclones) whose total energy is identical to the total initial energy prior to the fission.

The impossibility of baroclinic anticyclones to break up appears initially to be in contradiction with classical laboratory experiments which show what seems to be an anticyclonic fission. The solution for joint eddies consisting of a cyclone situated above an anticyclone suggests, however, that what really really breaks up in the laboratory is the cyclone on top rather than the anticyclone underneath. (Recall that the generation of anticyclone in the laboratory is often accompanied by the formation of a cyclone on top due to convergence.)

It is suggested that the impossibility of baroclinic anticyclones to break up and the tendency of cyclones to split may provide an explanation for the relative abundance of anticyclones in the ocean.

^{ }

## Abstract

The breakup of a long strip of dense fluid flowing over a sloping bottom is examined with the aid of a nonlinear two-layer analytical model. The inviscid strip is bounded by the sloping bottom from below and an interface (that intersects the bottom along the two edges) from the top. The infinitely deep upper layer in which the filament is embedded contains a uniform flow and is taken to be passive. Such flows represent an idealization of currants that result from various outflows and deep water spreading.

It is shown analytically that a dense filament can break up to a discrete set or closely packed anticyclonic eddies (lenses) propagating steadily along the isobaths. The lenses are arranged in a zig-zag manner with the e4cs of each tens touching its neighboring tens. Such a pattern results from the fact that the eddies are too large to fit into the area freed by the straight filament so that they push each other to the sides during the breakup. The solution for this pack of eddies is computed without solving for the detailed breakup process. As in other adjustment problems, the final and initial states are connected via known conservation properties even though the problem is highly nonlinear. Specifically, conservation of potential vorticity, integrated angular momentum and mass am applied. These conservation laws illustrate that about 10% of the initial energy is ,radiated away (via long gravity waves) during the breakup.

The theory suggest that some of the actual filaments in the ocean, such as the Mediterranean outflow, may not consist at a single continuous flow but rather of a stream of closely packed lenses translating steadily along the bottom.

## Abstract

The breakup of a long strip of dense fluid flowing over a sloping bottom is examined with the aid of a nonlinear two-layer analytical model. The inviscid strip is bounded by the sloping bottom from below and an interface (that intersects the bottom along the two edges) from the top. The infinitely deep upper layer in which the filament is embedded contains a uniform flow and is taken to be passive. Such flows represent an idealization of currants that result from various outflows and deep water spreading.

It is shown analytically that a dense filament can break up to a discrete set or closely packed anticyclonic eddies (lenses) propagating steadily along the isobaths. The lenses are arranged in a zig-zag manner with the e4cs of each tens touching its neighboring tens. Such a pattern results from the fact that the eddies are too large to fit into the area freed by the straight filament so that they push each other to the sides during the breakup. The solution for this pack of eddies is computed without solving for the detailed breakup process. As in other adjustment problems, the final and initial states are connected via known conservation properties even though the problem is highly nonlinear. Specifically, conservation of potential vorticity, integrated angular momentum and mass am applied. These conservation laws illustrate that about 10% of the initial energy is ,radiated away (via long gravity waves) during the breakup.

The theory suggest that some of the actual filaments in the ocean, such as the Mediterranean outflow, may not consist at a single continuous flow but rather of a stream of closely packed lenses translating steadily along the bottom.

^{ }

## Abstract

The interaction of two isolated lens-like eddies is examined with the aid of an inviscid nonlinear model. The barotropic layer in which the lenses are embedded is infinitely deep so that there is no interaction between the eddies unless their edges touch each other. It is assumed that the latter is brought about by a mean flow which relaxes after pushing the eddies against each other and forming a “figure 8” structure.

Using qualitative arguments (based on continuity and conservation of energy along the eddies’ edge) it is shown that, once a “figure 8” shape is established, intrusions along the eddies’ peripheries are generated. These intrusions resemble “arms” or “tentacles” and their structure gives the impression that one vortex is “hugging” the other. As time goes on the tentacles become longer and longer and, ultimately, the eddies are entirely converted into very long spiral-like tentacles. These spiraled tentacles are adjacent to each other so that the final result is a *single* vortex containing the fluid of the two parent eddies. It is speculated that the above process leads to the actual merging of lens-like eddies in the ocean.

Because of the inherent nonlinearity and the fact that the problem is three-dimensional (*x*, *y*, *t*), the complete details of the above process cannot be described analytically. Therefore, one cannot prove in a rigorous manner that the above process is the only possible merging mechanism. It is, however, possible to rigorously show analytically and experimentally that the intrusions and tentacles are *inevitable*. For this purpose, one of the interacting eddies is conceptually replaced by a solid cylinder. Initially, the cylinder drifts toward the eddy; subsequently, it is pushed slightly into the eddy and is then held fixed. The subsequent events are examined in a rigorous mathematical and experimental manner.

It is found that as the cylinder is forced into the eddy, a band of eddy water starts enveloping the cylinder in the clockwise direction. This tentacle continues to intrude along the cylinder parameter until it ultimately reattaches itself to the eddy, forming a “padlock” flow. Simple laboratory experiments on a rotating table clearly demonstrate that a “padlock” flow is indeed established when a lens is interacting with a solid cylinder. Using the details of this process it is argued that, in the actual eddy–eddy interaction case, intrusions must be established and that, consequently, merging of the two eddies is inevitable.

## Abstract

The interaction of two isolated lens-like eddies is examined with the aid of an inviscid nonlinear model. The barotropic layer in which the lenses are embedded is infinitely deep so that there is no interaction between the eddies unless their edges touch each other. It is assumed that the latter is brought about by a mean flow which relaxes after pushing the eddies against each other and forming a “figure 8” structure.

Using qualitative arguments (based on continuity and conservation of energy along the eddies’ edge) it is shown that, once a “figure 8” shape is established, intrusions along the eddies’ peripheries are generated. These intrusions resemble “arms” or “tentacles” and their structure gives the impression that one vortex is “hugging” the other. As time goes on the tentacles become longer and longer and, ultimately, the eddies are entirely converted into very long spiral-like tentacles. These spiraled tentacles are adjacent to each other so that the final result is a *single* vortex containing the fluid of the two parent eddies. It is speculated that the above process leads to the actual merging of lens-like eddies in the ocean.

Because of the inherent nonlinearity and the fact that the problem is three-dimensional (*x*, *y*, *t*), the complete details of the above process cannot be described analytically. Therefore, one cannot prove in a rigorous manner that the above process is the only possible merging mechanism. It is, however, possible to rigorously show analytically and experimentally that the intrusions and tentacles are *inevitable*. For this purpose, one of the interacting eddies is conceptually replaced by a solid cylinder. Initially, the cylinder drifts toward the eddy; subsequently, it is pushed slightly into the eddy and is then held fixed. The subsequent events are examined in a rigorous mathematical and experimental manner.

It is found that as the cylinder is forced into the eddy, a band of eddy water starts enveloping the cylinder in the clockwise direction. This tentacle continues to intrude along the cylinder parameter until it ultimately reattaches itself to the eddy, forming a “padlock” flow. Simple laboratory experiments on a rotating table clearly demonstrate that a “padlock” flow is indeed established when a lens is interacting with a solid cylinder. Using the details of this process it is argued that, in the actual eddy–eddy interaction case, intrusions must be established and that, consequently, merging of the two eddies is inevitable.