Rotation Numbers Of Invariant Manifolds Around Unstable Periodic Orbits For The Diamagnetic Kepler Problem

In this paper, a method to construct topological template in terms of symbolic dynamics for the diamagnetic Kepler problem is proposed. To confirm the topological template, rotation numbers of invariant manifolds around unstable periodic orbits in a phase space are taken as an object of comparison. The rotation numbers are determined from the definition and connected with symbolic sequences encoding the periodic orbits in a reduced Poincare section. Only symbolic codes with inverse ordering in the forward mapping can contribute to the rotation of invariant manifolds around the periodic orbits. By using symbolic ordering, the reduced Poincare section is constricted along stable manifolds and a topological template, which preserves the ordering of forward sequences and can be used to extract the rotation numbers, is established. The rotation numbers computed from the topological template are the same as those computed from their original definition.

A method to find unstable periodic orbits for the diamagnetic Kepler problem

A method to determine the admissibility of symbolic sequences and to find the unstable periodic orbits corresponding to allowed symbolic sequences for the diamagnetic Kepler problem is proposed by using the ordering of stable and unstable manifolds. By investigating the unstable periodic orbits up to length 6, a one to one correspondence between the unstable periodic orbits and their corresponding symbolic sequences is shown under the system symmetry decomposition.

Dynamics of intraseasonal sea level and thermocline variability in the equatorial Atlantic during 2002-03

Satellite and in situ observations in the equatorial Atlantic Ocean during 2002-03 show dominant spectral peaks at 40-60 days and secondary peaks at 10-40 days in sea level and thermocline within the intraseasonal period band (10-80 days). A detailed investigation of the dynamics of the intraseasonal variations is carried out using an ocean general circulation model, namely, the Hybrid Coordinate Ocean Model (HYCOM). Two parallel experiments are performed in the tropical Atlantic Ocean basin for the period 2000-03: one is forced by daily scatterometer winds from the Quick Scatterometer (QuikSCAT) satellite together with other forcing fields, and the other is forced by the low-passed 80-day version of the above fields. To help in understanding the role played by the wind-driven equatorial waves, a linear continuously stratified ocean model is also used. Within 3 degrees S-3 degrees N of the equatorial region, the strong 40-60-day sea surface height anomaly (SSHA) and thermocline variability result mainly from the first and second baroclinic modes equatorial Kelvin waves that are forced by intraseasonal zonal winds, with the second baroclinic mode playing a more important role. Sharp 40-50-day peaks of zonal and meridional winds appear in both the QuikSCAT and Pilot Research Moored Array in the Tropical Atlantic (PIRATA) data for the period 2002-03, and they are especially strong in 2002. Zonal wind anomaly in the central-western equatorial basin for the period 2000-06 is significantly correlated with SSHA across the equatorial basin, with simultaneous/ lag correlation ranging from-0.62 to 0.74 above 95% significance. Away from the equator (3 degrees-5 degrees N), however, sea level and thermocline variations in the 40-60-day band are caused largely by tropical instability waves (TIWs). On 10-40-day time scales and west of 10 degrees W, the spectral power of sea level and thermocline appears to be dominated by TIWs within 5 degrees S-5 degrees N of the equatorial region. The wind-driven circulation, however, also provides a significant contribution. Interestingly, east of 10 W, SSHA and thermocline variations at 10 40- day periods result almost entirely from wind-driven equatorial waves. During the boreal spring of 2002 when TIWs are weak, Kelvin waves dominate the SSHA across the equatorial basin (2 degrees S-2 degrees N). The observed quasi-biweekly Yanai waves are excited mainly by the quasi-biweekly meridional winds, and they contribute significantly to the SSHA and thermocline variations in 1 degrees-5 degrees N and 1 degrees-5 degrees S regions.

The Obduction of Equatorial 13 degrees C Water in the Pacific Identified by a Simulated Passive Tracer

The obduction of equatorial 13 degrees C Water in the Pacific is investigated using a simulated passive tracer of the Consortium for Estimating the Circulation and Climate of the Ocean (ECCO). The result shows that the 13 degrees C Water initialized in the region 8 degrees N-8 degrees S, 130 degrees-90 degrees W enters the surface mixed layer in the eastern tropical Pacific, mainly through upwelling near the equator, in the Costa Rica Dome, and along the coast of Peru. Approximately two-thirds of this obduction occurs within 10 years after the 13 degrees C Water being initialized, with the upper portion of the water mass reaching the surface mixed layer in only about a month. The obduction of the 13 degrees C Water helps to maintain a cool sea surface temperature year-round, equivalent to a surface heat flux of about -6.0 W m(-2) averaged over the eastern tropical Pacific (15 degrees S-15 degrees N, 130 degrees W-eastern boundary) for the period of integration (1993-2006). During El Nino years, when the thermocline deepens as a consequence of the easterly wind weakening, the obduction of the 13 degrees C Water is suppressed, and the reduced vertical entrainment generates a warming anomaly of up to 10 W m(-2) in the eastern tropical Pacific and in particular along the coast of Peru, providing explanations for the warming of sea surface temperature that cannot be accounted for by local winds alone. The situation is reversed during La Nina years.

Origin and Pathway of Equatorial 13 degrees C Water in the Pacific Identified by a Simulated Passive Tracer and Its Adjoint

The origin and pathway of the thermostad water in the eastern equatorial Pacific Ocean, often referred to as the equatorial 13 degrees C Water, are investigated using a simulated passive tracer and its adjoint, based on circulation estimates of a global general circulation model. Results demonstrate that the source region of the 13 degrees C Water lies well outside the tropics. In the South Pacific, some 13 degrees C Water is formed northeast of New Zealand, confirming an earlier hypothesis on the water's origin. The South Pacific origin of the 13 degrees C Water is also related to the formation of the Eastern Subtropical Mode Water (ESTMW) and the Sub-Antarctic Mode Water (SAMW). The portion of the ESTMW and SAMW that eventually enters the density range of the 13 degrees C Water (25.8 < sigma(theta) < 26.6 kg m(-3)) does so largely by mixing. Water formed in the subtropics enters the equatorial region predominantly through the western boundary, while its interior transport is relatively small. The fresher North Pacific ESTMW and Central Mode Water (CMW) are also important sources of the 13 degrees C Water. The ratio of the southern versus the northern origins of the water mass is about 2 to 1 and tends to increase with time elapsed from its origin. Of the total volume of initially tracer-tagged water in the eastern equatorial Pacific, approximately 47.5% originates from depths above sigma(theta) = 25.8 kg m(-3) and 34.6% from depths below sigma(theta) = 26.6 kg m(-3), indicative of a dramatic impact of mixing on the route of subtropical water to becoming the 13 degrees C Water. Still only a small portion of the water formed in the subtropics reaches the equatorial region, because most of the water is trapped and recirculates in the subtropical gyre.

Bifurcation of Pacific North Equatorial Current at the surface

The grid altimetry data between 1993 and 2006 near the Philippines were analyzed by the method of Empirical Orthogonal Function (EOF) to study the variation of bifurcation of the North Equatorial Current at the surface of the Pacific. The relatively short-term signals with periods of about 6 months, 4 months, 3 months and 2 months are found besides seasonal and interannual variations mentioned in previous studies. Local wind stress curl plays an important role in controlling variation of bifurcation latitude except in the interannual timescale. The bifurcation latitude is about 13.3A degrees N in annual mean state and it lies at the northernmost position (14.0A degrees N) in January, at the southernmost position (12.5A degrees N) in July. The amplitude of variation of bifurcation latitude in a year is 1.5A degrees, which can mainly be explained as the contributions of the signals with periods of about 1 year (1.2A degrees) and 0.5 year (0.3A degrees).

Interannual horizontal heat advection in the surface mixed layer over the equatorial Pacific Ocean: assimilation versus TAO analysis

The interannual anomalies of horizontal heat advection in the surface mixed layer over the equatorial Pacific Ocean in an assimilation experiment are studied and compared with existing observational analyses. The assimilation builds upon a hindcast study that has produced a good simulation of the observed equatorial currents and optimizes the simulation of the Reynolds sea surface temperature (SST) data. The comparison suggests that the assimilation has improved the simulation of the interannual horizontal heat advection of the surface mixed layer significantly. During periods of interrupted current measurements, the assimilation is shown to produce more meaningful anomalies of the heat advection than the interpolation of the observational data does. The assimilation also shows that the eddy heat flux due to the correlation between high-frequency current and SST variations, which is largely overlooked by the existing observational analyses, is important for the interannual SST balance over the equatorial Pacific. The interannual horizontal heat advection anomalies are found to be sensitive to SST errors where oceanic currents are strong, which is a challenge for ENSO prediction. The study further suggests that the observational analyses of the tropical SST balance based on the TAO and the Reynolds SST data contain significant errors due to the large gradient errors in the Reynolds SST data, which are amplified into the advection anomalies by the large equatorial currents.