1. Tsuchiya Jets: A tropical arrested front? Jay McCreary A short course on: Modeling IO processes and phenomena University of Tasmania Hobart, Tasmania May 4–7, 2009

2. References 1)McCreary, J.P., P. Lu, and Z. Yu, 2002: Dynamics of the Pacific subsurface countercurrents. J. Phys. Oceanogr., 32, 2379–2404. 2)Furue, R., J.P. McCreary, Z. Yu, and D. Wang, 2007: Dynamics of the Southern Tsuchiya Jet. J. Phys. Oceanogr., 37 (3), 531–553. 3)Furue, R., J.P. McCreary, and Z. Yu, 2009: Dynamics of the northern Tsuchiya Jet. J. Phys. Oceanogr., in press.

3. Introduction 1)Background 2)Layer ocean model (LOM) solutions 3)OGCM solutions 4)Summary

4. Background

5. Observed Tsuchiya Jets Johnson et al. (2002) Eq. 8S8N 165ºE (west)155ºW (center) 110ºW (east) u T TJs Thermostad There often appear to be two southern TJs The TJs and the EUC both rise and lighten to the east, and the TJs diverge from the equator

6. Theories TJ? Remote forcing Linear wave dynamics (McPhaden 1984) Inertial jet (Johnson & Moore 1997) Arrested front (McCreary et al. 2002). Local (y-z) forcing Conservation of angular momentum (Marin et al. 2000, 2003; Hua et al. 2003) Eddy forcing (Jochum & Malanotte-Rizzoli 2004; Ishida et al. 2005)

7. LOM solutions

8. Equations: Equations of motion for the analytic model are: where the pressure gradients are and If h 1 become less than h e1, w 1 instantly adjusts it back to h e1. (1) 2½-layer model The interesting features of the solutions discussed below all happen because of the nonlinear terms. For example, n = 2 Rossby waves no longer propagate only westward.

9. h equation: Neglecting horizontal mixing and in regions where w' 1 = 0, (1) can be solved for a single equation in h, yielding where (2) are the depth-averaged geostrophic currents associated with the Sverdrup circulation, and is the speed of the n = 2 Rossby waves, is the Sverdrup transport streamfunction. h t + In a 2-layer model, one can retain h t, modifying (2) as indicated. In this form, it is clear that baroclinic Rossby waves don’t propagate due westward. An additional component of their propagation velocity is the geostrophic current of the background Sverdrup flow. 2½-layer model

10. Characteristics: Equation (2) can be solved by finding the characteristic curves, x c and y c, which are integrations of where s is a time-like parameter. The solution follows from the property that h is constant along characteristics. Boundary conditions: The solution requires knowledge of h and h 1 at some boundary of the domain. where H 1 and H are values of h 1 and h at the eastern boundary, x e. Interior h 1 : To evaluate c r, h 1 must also be known in the interior ocean. It is determined from the constraint (3) 2½-layer model

11. Geostrophic streamlines: The characteristic curves are parallel to h isolines. Thus, in regions where h varies on the domain boundary, h contours are geostrophic streamlines for the layer-2 flow. Arrested fronts and shocks: Stationary fronts (shocks) form wherever characteristics converge and intersect in the interior ocean (Dewar, 1991, 1992). Rossby waves: In transient situations, n = 1 Rossby waves propagate westward, as expected from linear theory. In contrast, n = 2 Rossby waves propagate along characteristics. 2½-layer model

12. Characteristics change markedly depending on model parameters. As the nonlinearities strengthen, they bend more equatorward, eventually intersecting to form a shock. H = 1000 m τyτy H = 300 m T 1 = 29ºC 2½-layer model

13. H = 1000 m H = 300 m T 1 = 29ºC τ y Numerical analogs of the analytic solutions are driven by wind stress and inflow into layer 2 and outflow from layer 1. The outflow drains water from layer 1 until h 1 becomes less than h e1 somewhere in the domain. Eventually, mass balance is attained in which inflow = upwelling = outflow. As nonlinear terms strengthen, the model TJ becomes narrower and hence swifter, but its transport is unchanged.

14. 2½-layer model The TJ is not visible in the total transport field (h 1 v 1 + h 2 v 2 ), which is in Sverdrup balance, with boundary layers along the equator and 30ºS. There is strengthened westward flow in layer 1 that compensates for the eastward TJ, an indication that it is generated by a signal like the second baroclinic mode. There appears to be an analog to this situation in the subtropical SIO. There, subduction (the reverse of upwelling) generates a stronger than expected (i.e., stronger than Sverdrup) subsurface westward flow, which is compensated for by near-surface eastward flow.

15. H = 1000 m τxeτxe H = 300 m T 1 = 29ºC 2½-layer model Characteristics change markedly depending on model parameters. As the nonlinearities strengthen, they bend more equatorward, eventually intersecting to form a shock.

16. 2½-layer model H = 1000 m H = 300 m T 1 = 29ºC τ x e Numerical analogs of the analytic solutions are driven by wind stress and inflow into layer 2 and outflow from layer 1. The outflow drains water from layer 1 until h 1 becomes less than h e1 somewhere in the domain. Eventually, mass balance is attained in which inflow = upwelling = outflow. As nonlinear terms strengthen, the model TJ becomes narrower and hence swifter, but its transport is unchanged.

17. Meridional section at 140ºW from the 4½-layer solution. Each layer represents a specific water-mass type. The solution is forced by Hellerman and Rosenstein winds and by an ITF transport of 10 Sv. The model develops a realistic equatorial thermal structure, including thermal fronts at the edge a thermostad (layer 3). 4½-layer model thermostad

18. 4½-layer model The TJs still exist in layer 3 of a more realistic model forced by realistic winds, and with a realistic upper-ocean circulation. The outflow drains water from layers 1 and 2 water until h 1 and h 2 become less than h e1 and h e2, in which case water upwells from layer 3 into layer 2. There are NP and SP STCs in layers 1 and 2, with subduction in the subtropics and upwelling in the eastern, tropics.

19. OGCM solutions

20. Configuration COCO 3.4 (Hasumi at CCSR, U Tokyo): level model; primitive equations on spherical coordinates. 2 o ×1 o ×36 levels → no eddies Constant salinity Box ocean: 100 o ×(40 o S– 10 o N) × 4000 m for southern TJ OGCM solutions Mixing To minimize diffusion, we set K V0 = 0 in the P-P vertical diffusion, and … … only allow isopycnal diffusion (10 7 cm 2 /s) when |dz/dx| > a critical slope Third-order upstream advection scheme is weakly diffusive. Laplacian horizontal viscosity (10 8 cm 2 /s) with 20×10 8 cm 2 /s in the WBL. Eq 10N 40S 100 o Forcing Idealized τ x, τ y Inflow of cool water (7.5 Sv; 6 o C–14 o C) thru s.b. Outflow of warm water from 2 o N–6 o N thru w.b. Relax SST to T*(y) = 15 o C–25 o C.

21. Layer 2 is defined by the integral Without wind, there is no interior Sverdrup flow. As a result, water flows directly from the inflow to the outflow port. 14 o C–6 o C, yr 120 Hierarchy of solutions No wind

22.  y without curl (zonally uniform) Because of  y, upwelling shifts to the eastern boundary. Because  y has no curl, there is still no interior Sverdrup flow and hence no v g. So, layer-2 water flows zonally across the basin to supply water for the upwelling.  y =  0 Y(y)  0 = 1 dyn/cm 2 14 o C–6 o C, yr 120 Hierarchy of solutions

23.  y with curl Because  y has curl, there is an interior Sverdrup flow with a northward v g. Now, layer-2 water bends equatorward to the west to form an interior jet, the model TJ. 14 o C–6 o C, year 120 u, T 14 o C–6 o C, yr 120 Hierarchy of solutions 0 dyn/cm 2 vgvg

24.   x  y (control run) Because of the additional zonal wind, v g increases. As a result, the model TJ bends more equatorward, narrows, and strengthens. 14 o C–6 o C, yr 120  x =  0 X(x)Y(y)  0 = 0.5 dyn/cm 2 u, T Hierarchy of solutions

25. TJ pathways (control run) The deep part of the TJ at 50ºE, shifts southward and weakens to the east. By 80ºE, it lies outside the main jet. 10 o C–9 o C 12 o C–11 o C The shallow part of the TJ at 50ºE, shifts southward to join the top of the TJ at 80ºE Due to these processes, both the TJ and EUC rise and warm to the east, consistent with the observed TJ.

26. TJ pathways (higher resolution run) PV & (uh, vh) PV, hv 1º×¼º near the equator, and low viscosity Now, EUC water first reverses to flow westward before joining the TJ What happens as resolution is increased further, and the system enters an eddy- resolving regime?

27. No I/O No inflow/outflow Control The TJ weakens, and its core temperature rises by 2.5°C.

28. Southern TJ in a global model OpenClosed A southern TJ exists in a global GCM (1°×1°×40 levels; Nakano, 2000) with both open and closed IT passages With closed passages, the TJ has almost the same strength but its core is 1°C warmer 130°W These properties suggest that the model TJ is supplied primarily by an overturning cell internal to the Pacific, one that is somewhat broader and deeper than the STCs.

29. Summary

30. 1)The TJs are driven by off-equatorial upwelling in the tropics. The upwelling for the southern TJ occurs along the South American coast. The upwelling for the northern TJ occurs in the in the eastern ocean in the ITCZ band (6ºN to 12ºN), most notably in the Costa Rica dome. 2)Our solutions indicate that the TJs are geostrophic currents flowing along arrested fronts. Arrested fronts are generated when characteristics, associated with different h values, converge or intersect in the interior ocean. As a result, h jumps across the front. 3)The top of the TJs are fed in part by the bottom of the EUC. As a result, both the EUC and the TJs rise in the water column and shift to lighter densities toward the east. 4)The TJs weaken and warm when there is no IT. This happens because the IT drains water from the upper layers, intensifying the upwelling from the TJ layer.

32. In steady state, the total thickness field, h = h 1 + h 2, satisfies where u g and v g are geostrophic components of Sverdrup flow and c r is the speed on a non-dispersive, n = 2, Rossby wave. Arrested fronts in a 2½-layer model Forced by winds like those in the South Pacific, v g bends characteristics meridionally. Consistent with the observed TJ, an arrested front occurs where characteristics overlap and the front shifts southward to the east. vgvg Eq. 30°S 100° 0°0° A numerical solution illustrates the characteristic solution. It is forced by 1) winds and 2) by an inflow into layer 2 and an ouflow from layer 1. Layer-1 water is drained from the system, and hence there is eastern-boundary upwelling. An analogous solution exists for the northern TJ. In this case, there is upwelling in the Costa Rica dome.