A mesoscale eddy's trajectory and its interaction with topography under the
planetary
Eddies are common in oceans, both at surface and deep layers, including
mesoscale eddies (scale of 100 km) and sub-mesoscale eddies (scale of 10 km)
(Itoh et al., 2011; Oey, 2008; Olson et al., 2007). Eddies have gained
much attention since they are an important form of material and energy
transfer in the ocean (Zhang et al., 2011, 2013, 2014; Kersalé et al., 2013;
Waite et al., 2007; Jacob et al., 2002; Wang et al., 2005). Although isolated eddies in open oceans are
affected by different factors, many of them have similar kinematic
characteristics in general. As many researchers have pointed out, an
isolated warm eddy in open oceans moves southwestwards or moves northwards
along the western boundary in the northern hemisphere under the planetary
The eddy propagation in the ocean is directly affected by topography. The eddy trajectory and structure can be changed due to the interaction with a continental slope, an island or a seamount. The interaction between a warm eddy and a continental shelf slope has been investigated by many researchers based on satellite observations, laboratory and numerical model experiments (Hyun and Hogan, 2008; Rennie et al., 2007; Sutyrin and Grimshaw, 2010; Wei and Wang, 2009; Itoh and Sugimoto, 2001; Smith and O'Brien, 1983). A continental slope is often treated as a wall in the numerical model studies. Previous studies indicate that the eddy–wall collision can cause the eddy to leak water along the wall and generates along-wall jets which can be related to nonlinear Kelvin waves (Nof, 1988; Shi and Nof, 1994; Reznik and Sutyrin, 2005). When a patch of fast moving water catches up with a slower one, an eddy could be generated near the nose of the along-wall jet (Stern, 1986, 2010). Besides the jets and eddies, during the evolution of an isolated eddy near a wall, nonlinear Kelvin waves can be excited due to the geostrophic adjustment, which can trap and transform water along the wall (Umatani and Yamagata, 1987; Dorofeyev and Larichev, 1992). In contrast to the case with a continental slope, when eddies encounter an island or seamount, the eddy could split into two eddies because of the erosion by the isolated topography (Herbette et al., 2003, 2005; Simmons and Nof, 2002; Dewar, 2002; Luo and Liu, 2006; Cenedese, 2002).
Simmons and Nof (2000) obtained the essential conditions for a barotropic eddy splitting by using a wall moving into the eddy: even for infinitesimal splitting, which arises from weak collisions, the wall length must be at least a radius of the eddy. Drijfhout (2003) discussed the anticyclonic eddy splitting mechanism which is that anticyclones cannot split by barotropic processes alone, and baroclinic instability is a necessary ingredient for splitting to occur. Using an isopycnal ocean circulation model, Herbette et al. (2003) analysed the behaviour of a surface-intensified anticyclonic eddy encountering an isolated seamount, and the erosion often results in a subdivision of the eddy. Wang and Dewar (2003) studied the meddy–seamount interaction. The initial meddy splits into two meddies in their experiments, but meddies are able to survive as coherent vortices because of strong potential vorticity anomalies (PVAs). Numerical estimates of the transformed eddy structure indicate that topographic interactions provide powerful mechanisms for the baroclinic eddy evolution (Sutyrin et al., 2011).
There are plenty of mesoscale and sub-mesoscale eddies existing in the South China Sea (SCS), and most of them propagate to the southwest (Chang et al., 2012; Nan et al., 2011). In particular, mesoscale eddies occur frequently in the northern SCS (Hwang and Chen, 2000; Chang et al., 2012; Zhang et al., 2013; Nan et al., 2011; Wang et al., 2003, 2005), and the number of cold eddies is similar to that of warm eddies. Therefore, it is of importance to find out the difference between the cold and warm eddies.
Furthermore, the SCS is populated with numerous islands and seamounts. Therefore, most eddies are affected by the topography variation in their movement. The change of eddy structure over topography has an important influence on its dynamics, while it is an important means of energy transfer among different scales and affects the coastal ocean environment (Kersalé et al., 2013; Drijfhout, 2003; Dunphy and Lamb, 2014). Chang et al. (2012) found from satellite observations that an anticyclonic eddy (warm eddy) with a diameter of 120 km was split by the Dongsha atoll situated on the slope in the northern SCS. Because of difficulties in catching the entire process of eddy splitting by both satellite observations and in situ measurements, there are a few cases of eddy–island interactions found by satellite images so far. Particularly, the phenomenon of eddy-splitting reported in Dongsha in the SCS lacks sufficient measurement data to systematically describe the process of splitting (Chang et al., 2012). In addition, eddies may split during interaction with a curved continental slope. Kersalé et al. (2013) investigated a coastal anticyclonic eddy in the western part of the Gulf of Lion in the northwestern Mediterranean Sea, where eddies split in a similar pattern as in the case of the Dongsha atoll. This provides a wider application prospect for any eddy-splitting role in the interaction with topography. However, it is not clear whether an eddy can always be split by an island/seamount and how the scale of the isolated topography influences the eddy-splitting. Recently, Li et al. (2016) used the Genealogical Evolution Model (GEM) to track the dynamic evolution of mesoscale eddies in the ocean. They can distinguish between different dynamic processes including merging and splitting, but the special processes and characteristics of eddy splitting by an island have not been elucidated completely.
In this study, we constructed an idealized eddy in a numerical model according to the features of the observed eddies in the SCS to examine its kinematic characteristics and test eddy splitting processes using numerical simulations. Moreover, inspired by the eddy splitting near the Dongsha island in the SCS, we vary the island size and seamount submergence depth to investigate the influence of the island on the eddy, and then to analyse the effect of the island and the seamount on the mesoscale eddy evolution (weakening and destruction) as the eddy approaches the obstacles.
This paper is organized as follows: Sect. 2 describes the eddy structure used in the model and the method of eddy identification. Section 3 introduces the model. The model results, including a comparison of eddy trajectories between the warm eddy and cool eddy, and the effect of an island and seamount on eddy deformation will be presented in Sect. 4. A summary and discussion is given in Sect. 5.
An idealized mesoscale eddy is initialized with an axisymmetric
Gaussian-type profile based on long term moored observations (Zhang et
al., 2013), Argo float data and the merged data products of satellite
altimeters (Chen et al., 2010). Temperature profiles from observations
are fitted into an equation of
Initial velocity (m s
The eddy's initial velocity is calculated using the thermal wind balance
with zero velocity at the ocean bottom. The density distribution is obtained
from a state equation according to Jacket and Mcdougall (1995). Figure 1
shows the temperature and azimuthal velocity distribution on the cross
section through the eddy centre. The initial eddy is 60 km in diameter and
500 m in depth with a total water depth of 2000 m. The maximum surface
velocity is about 0.9 m s
There are different methods to identify an eddy and here we use the
Okubo–Weiss method (Okubo, 1970; Weiss, 1991) to identify the eddy that
we constructed in the model and define the boundary of the eddy. The
Okubo–Weiss parameter
Because the velocity field within an eddy is dominated by its rotation,
ocean eddies are generally characterized by negative values of
The MITgcm (MIT General Circulation Model; Adcroft et al., 2011) is used in this study. Its
non-hydrostatic formulation enables us to simulate fluid phenomena over a
wide range of scales. However, we only use the hydrostatic form of the model
as we expect that the non-hydrostatic dynamics play minor roles in our
problem (to capture the non-hydrostatic dynamics we would have to use a much
finer resolution than used here). The model domain is 500 km
In the model, both the warm eddy and the cold eddy are initialized with an
axisymmetric Gaussian-type profile described in Sect. 2. The temperature
decreases with the depth in the upper 1000 m and is set to a constant value
of 4
For the model with flat topography, the eddy is located at the centre of the model domain to test the difference between warm- and cold-eddy trajectories. In the cases studying the interaction between an eddy and an island/seamount, the island/seamount with different sizes/depths is located in the central path of the eddy, and all islands and seamounts are cylinder shaped. We run the model from the initial state of rest for 50 days in order to compare different effects of obstacles on eddies.
Our main attention is on eddy-splitting due to the interaction between
eddies and obstacles, and a series of experiments based on the idealized
eddy structure in the SCS have been carried out (Table 1). The eddy
diameter is 60 km, and the initial location of the eddy centre is
We first examine the eddy trajectories and its characteristics without any island/seamount. Then we focus on the interaction between the eddy and the island/seamount, and the sensitivity of eddy-splitting to the island size and seamount depth.
List of different topography used in the experiments.
Eddy trajectory over a flat bottom ocean:
The speed of eddies over a flat bottom ocean. Solid lines: time series of speed; dashed lines: the speed averaged over 50 days.
In our first set of numerical experiments, an eddy (warm or cold) is located
at the centre (
The process of eddy-splitting induced by the interaction with an island
of 20 km in diameter over 50 days. A time series of snapshots of temperature
at 100 m depth is shown in colour.
With a cold eddy (cyclonic eddy in the northern hemisphere) in the same
situation, the movement direction is northwest under
When an isolated eddy propagates in open oceans with a flat bottom, while
the
The influence of an island on the eddy deformation is explored in this study. According to the eddy-splitting at Dongsha island in the SCS (Chang et al., 2012), we set an island on the path of the warm eddy based on the first case we have examined. The diameter of the island is 20 km. At the beginning of the model integration, the eddy is not influenced by the island because the distance between the eddy and the island is not sufficiently close. As the eddy moves towards the island along its trajectory, the eddy eventually interacts with the island.
The warm eddy splits into two eddies during the interaction with an island of 20 km in diameter on day 50 (the results shown are at 100 m depth).
The cold eddy splits into two eddies during the interaction with an
island of 20 km in diameter on day 50 (the temperature
The temporal evolution of the eddy in the interaction with an island of 20 km in diameter. The colours represent the temperature at 100 m depth and the solid lines are temperature contours.
The temporal evolution of the eddy in the interaction with an island of 20 km in diameter. The colours represent the potential vorticity anomaly (PVA) at 100 m depth.
It is evident from Fig. 4 when the eddy collides with the island, that there is
another weak warm eddy formed on the other side of the island. The two
eddies have similar diameters but the secondary eddy is weaker than the
main one, which can be seen from sea surface height (SSH), temperature, potential
vorticity anomaly (PVA), and
As mentioned previously, when an eddy collides with an island, the eddy can
split into two eddies with similar rotation characters. Here we examine the
evolution of the eddy-splitting process. Figure 7 shows the temperature field
evolution of an anticyclonic eddy colliding with an island with a diameter
of 20 km. The eddy is initially located at 40 km northeast of the
island. Then the eddy moves towards the island at 0.023 m s
As the inertia and
The radius of the newly formed anticyclone is about 25 km, which is similar with the parent eddy, but its strength is weaker. Under the boundary effect, both eddies move away from the island. As a result, the parent anticyclonic eddy splits into two anticyclonic eddies during the interaction with the island.
For a better understanding of the mechanism of the eddy-splitting process, the
PVA field is analysed, which is shown in Fig. 8. The eddy is composed by two
parts: one is the inner part with negative PVA and the other is the outer
annulus with positive PVA. As shown in the figure, from
The position of the newly formed anticyclone is controlled by the separation point of the jet and the island boundary and therefore is influenced by the boundary curvature, which is a function of the island scale. As the island scale increases, the azimuthal angle (clockwise is positive) of the new anticyclonic eddy to the parent eddy decreases. The relationship between the positions of the eddies and the island will be discussed in Sect. 4.3.
When the eddy encounters an obstacle, the trajectories and speed are usually drastically altered. The results show that the speed of the eddy decreases significantly when the eddy interacts with the island. Shi and Nof (1994) pointed out that the image effect and the rocket effect (caused by the jet) usually dominate when colliding with a solid obstacle, and the effect would change the original movement trend combined with the boundary effect. At the same time, the generation of a weak cyclonic eddy during the interaction of warm eddies with an island/seamount adds a significant effect to the eddy propagation.
The potential vorticity anomaly (PVA) distributions of the interaction between the warm eddy (anticyclonic eddy) and the island of 60 km in diameter at 100 m (upper panels) and 1000 m (lower panels) at day 30 and 50. The colours represent the PVA and the solid lines being the PVA contours.
Actually, an anticyclonic eddy can never split on its own. Nof (1990)
demonstrated this by applying the conservation law of integrated angular momentum (IAM). As a result, when a warm eddy splits, the IAM has to
increase as the newly formed eddies move away from their original centre.
When a warm eddy is forced by the solid boundary of an island or the lower
layer of a seamount, there has to be a transfer of IAM from the surrounding
fluid to the core region of the eddy (Drijfhout, 2003). In order to show
the change of IAM before and after the eddy
interacts with the island, the PVA at the surface layer (depth
Observational data, including satellite images and in situ measurements,
indicate that when an eddy collides with a continental slope or a small
island there is no eddy-splitting, only changes to its trajectory (Jacob et
al., 2002; Nan et al., 2011; Wei and Wang, 2009). In order to find
out the parameter ranges of eddy-splitting, we use a series of islands with
different diameters at the same location in the model. Before that,
interactions of different sized islands and eddies were investigated. Take,
for example, the eddies with 90 km (Eddy
We, therefore, define two dimensionless parameters
Comparison of the interactions between different sized islands and
eddies
The results of the eddy–island interaction after 50 days for islands
with different diameters
Sketch illustrating the position relationship of the two split eddies.
When the eddy (eddy 1) encounters the island, the secondary eddy (eddy 2) splits-off at angle
The eddy collides with the islands in 20 days and interacts with them as we
have described previously. Figure 11 shows when the island is small enough,
namely
Distribution of relative angle (rad) with island size (
Eddy evolution in the case of the interaction with a seamount of 60 km
in diameter at 100 m depth for different submergence depths
From the eddy-splitting processes with different sizes of islands, we can
find that the locations of the secondary eddy split-off are related to the
island size. Figure 12 shows the position relationship of the two eddies and
the island. The angle (
In natural oceans, islands are just part of the topography and there are more seamounts which are submerged under the sea surface. The effect of seamounts on ocean dynamics is different from that of islands. The submergence depth and the size of a seamount are key factors in the eddy-splitting. During the interaction between an eddy and a seamount, the lower part of the eddy is affected directly by the solid seamount while the upper part is not, then the vertical structure of the eddy is deformed significantly. As a result, its trajectory and splitting process is different from that of the interaction between an eddy and an island.
Here we investigate the effect of seamount submergence depth on
eddy-splitting. The experiments are set up based on the cases of
Eddy evolution at 100 m depth during the interaction with different
size seamounts with a submergence depth of 100 m.
When the seamount submergence depth is 200 m, the effect of the seamount on
the eddy structure has weakened greatly compared with the seamount
submergence depth of 100 m. Apart from the filament shedding, there is no
significant change in the main structure of the eddy. The result also shows
that the seamount with
From the results of the numerical experiments, we find that eddy-splitting
happens roughly in the range of
When an eddy collides with a seamount, the effect of the seamount on eddy-splitting is weaker than that of an island. The effect of the seamount on eddy-splitting is not only determined by the submergence depth but also influenced by the seamount horizontal scale. Here we test three different sized seamounts with the same submergence depth (Fig. 15). During the interaction between the eddy and the seamount with 15 km diameter, the eddy does not split, and when the seamount diameter is 60 km a small eddy is split-off while the main eddy deforms. For the seamount with 120 km diameter, intense deformation occurs in the eddy without splitting.
For a seamount, the eddy-splitting happens in a narrower band of horizontal scale compared with an island. As the seamount submergence depth increases, the influence of the seamount on eddy deformation decreases. Therefore the band of seamount horizontal scale for which the eddy-splitting occurs becomes narrower and narrower as the submergence depth increases.
Concerning eddy evolution in the ocean, we have explored the effect of topography such as islands and seamounts on eddy-splitting. According to the results we obtained, the dependence of eddy-splitting on the parameters R and S is summarized in Fig. 16. This diagram illustrates the main settings of the experiments and the red area is where eddy-splitting occurs.
Motivated by the eddy-splitting near Dongsha island in the SCS, we have
explored the eddy's trajectory and effect of topography on an idealized eddy
evolution. The MITgcm is used in the study of the effect of topography on eddy
evolution including eddy trajectory and its structure, particularly the
eddy-splitting when the eddy collides with an island/seamount. The
topography used in the numerical experiments includes a flat bottom, islands
with different diameters and seamounts with different submergence depths.
Eddies colliding with the topography all have the same initial structure.
The simulation results of PVA, SSH, temperature and the
The model eddies (both warm and cold) move at a speed of 2.4 km day
The range of
Because observational data of eddy-splitting in oceans is scarce, we need
more comprehensive measurement data in combination with numerical models
to explore the dynamic mechanisms of eddy-splitting further. In addition to
the dimensionless parameters
All of the data and the model can be obtained by contacting the authors.
The authors declare that they have no conflict of interest.
The authors would like to express their sincere gratitude to the insightful comments from J. Huthnance of NOC (UK). The very constructive comments from the editor (Eric J. M. Delhez) and referees, in particular, Y. Lu (Bedford Institute of Oceanography, Fisheries and Oceans Canada), J. Berntsen (University of Bergen) and an anonymous referee have greatly helped to improve the manuscript. This work was supported by the National Key Basic Research Program of China (program 973, grant 2014CB745001), the Environmental Protection Special Funds for Public Welfare (201309006), the Shenzhen Special Funds for Future Industry Development (201411201645511650) and S. Chen is supported by the China Postdoctoral Science Foundation (2016M591159). Edited by: Eric J. M. Delhez Reviewed by: Jarle Berntsen, Youyu Lu, and one anonymous referee