SIMPLE STREAMFUNCTION MODEL

The fraction of the Mindanao Current and SEC, which make up the throughflow, in Fig. 2 can be calculated from the simple, streamfunction model of Wajsowicz (1993). Nondimensionalising the streamfunction ψ on the magnitude of the throughflow, a channel operator, M is defined as

M(ψa) = median(0, ψa, 1) ≡ A.

The operator, therefore, determines whether the streamline with value ψ_a is a candidate for making up the throughflow, which contains streamlines with values between 0 and 1. If ψ_n is the value of the streamfunction at the interior edge of the Pacific western boundary layer at the latitude y_N (to be defined below), then streamlines of the Mindanao Current with values between 0 and N = M(ψ_n) and of the SEC with values between N and 1 make up the throughflow. The fractional composition, therefore, is

C_NP=N, C_SP=1-N,　　(1)

The latitude y_N is crucial in determining the throughflow composition. If relative vorticity is destroyed at the latitude of creation, then y_N is the latitude of the northern tip of the Australian continent, which in a GCM is Irian Jaya, or Halmahera if the Halmahera Sea not resolved. Wajsowicz (1999a) showed that _yN Should be more generally defined as the northern extent of the SEC retroflection, so taking into account such nonlinear features as overshooting of the western boundary currents and deflection of the streamlines by the Mindanao and Halmahera Eddies. Their effect is to shift y_N about 2° to 4° of latitude further north.

Fig. 4　The dimensional form of the theoretical fractional composition relationship (1) is contoured as a function of throughflow magnitude and streamfunction value at the interior edge of the west Pacific boundary layer at y_N. The scale for the grey tones is given on the r. h. s.

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