Westward moving waves or eddies (Storms) on the Subtropical/Azores Front near 32.5°N? Interpretation of the Eulerian currents and temperature records at moorings 155 (35.5°W) and 156 (34.4°W)

Three Argos buoy-years of Lagrangian data in westward-moving cyclonic eddies, or Storms, near 32.5°N, together with hydrographic measurements, have shown that Storms move westward at nearly 3 km day⁻¹. Water in eddies can be trapped and moved westward by advection within the eddy or by phase propagation of the eddy pattern, so we cannot say that the flow field (or Eulerian mean) is 3 km day⁻¹ westward. Two moorings (155 and 156) deployed in the Storm Corridor have provided a further 8 instrument-years of Eulerian data. The temperature and current records confirmed that two Storms a year passed each mooring over the 2-year measurement period. As expected, there is a lag of 1.3 month at mooring 155 (which is 102 km to the west of mooring 156) with respect to conditions at mooring 156. The progressive vector diagrams (PVDs) derived from the current meter records exhibit fairly regular X (east or zonal) and Y (north or meridional) displacement scales that repeat with semi-annual periodicity (SAP). The dominant current signal is the north component of the SAP, which reaches an amplitude of 18 cm s⁻¹ for the upper layer or near surface current record (242-m depth). The geostrophic north component values derived from altimetry were in good agreement with the upper layer current meter measurements. The large north component amplitude was not interpreted as evidence for Rossby Waves but rather due to the passage of nine eddies (eight complete) of alternate sign (cyclonic, anticyclonic) passing the mooring rigs during the 2-year deployment period. The Y scale shows that the near surface characteristic or mean maximum azimuthal speed is about 35 cm s⁻¹ for cyclonic eddies or Storms, and that this value is reduced to 4 cm s⁻¹ at 1400-m depth. The residual or mean Eulerian currents range from 8 cm s⁻¹ for the upper layer currents to 1 cm s⁻¹ for the deeper currents at 1400-m depth and are predominantly westward. Simple theoretical considerations and idealised numerical simulations show that the mean westward Eulerian current depends markedly on whether the eddy centres pass to the north or south of the rigs. This raises the question as to what do we mean by Eulerian residual currents, even for relatively long records (2 years). It is shown that the strong near surface westward current (6 km day⁻¹) measured at mooring 155 is largely due to a westward-moving eddy field with variable centre offsets. The magnitude of the near surface east–west component of flow was estimated as eastward at 2 cm s⁻¹. The north–south component of mean flow was southward at 2 cm s⁻¹. The deeper records gave a weak westward flow of 1 cm s⁻¹ but did not show a significant southward component for the mean Eulerian flow field. 7.4 float-years of Lagrangian ALACE data in the Subtropical Front region near 740 dbar gave mean east–west flows that were <0.5 cm s⁻¹. Overall, it is shown that the eddy structures propagate westward mainly by phase propagation (i.e. a westward-moving pattern with no westward advection for the current meter to measure), though plane Rossby Wave dynamics appeared inappropriate. Theoretical and modeling considerations show that a speed of 3-km day⁻¹ westward is too large a value for the self-advection of eddies due to the beta effect.     

A simple vehicle dispatching policy with non-stationary stochastic arrival rates

This paper provides an impulsive stochastic control approach to the vehicle dispatching problem with non-stationary and stochastic arrival rates. Both necessary and sufficient conditions for optimal dispatches are given with proofs given in appendices. It is shown by means of examples that stationary solutions previously considered are a special case of the theory outlined here. In addition, a discussion of other dispatching rules is included in the conclusion together with their effect on the mathematical optimality of vehicle dispatching.