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tokens: λ , to dimensionalize our expressions. It is thus, in Equation ( 26 ), that we use to formally eliminate a . We assume that the horizontal motion of the open flux has deflected it by some small angle, say 10°, relative to the stationary and undeflected arcade flux. This angular difference, ±5°, produces the tangential discontinuity that is the secondary CS. The field strength in the vicinity of the flare ribbon region was estimated by BLQ to be 150 G. The single-sided 10° deflection will therefore produce a reconnecting component of 150 sin (5°) = 13 G. Assuming a typical electron density of gives the value v a = 500 km s −1 , which was used in our nondimensionalization. The sawtooth pattern is observed to propagate with phase velocity perpendicular to the IRIS slit of km s −1 . This was found in the plane of the sky (primed coordinates) but applied to horizontal motion some 40° from disk center. Foreshortening effects will reduce the velocity V in the horizontal x- direction to an apparent velocitywhere is the horizontal distance from disk center. The observed phase velocity of 15 km s −1 thus corresponds to a real horizontal velocity of km s −1 . Scaling this to the reconnection-component Alfvén speed, v a = 500 km s −1 , yields . 3.3. The Saturated State We use these dimensions to construct a synthetic observation from the velocity structure of our model. We do so by first using the velocity structure given by the linear eigenmode, , discussed above. We construct the stream function by superposing this using the amplitude, , in Equations ( 24 ) and ( 25 ). Figure 6 shows the magnetic field lines (black) and stream lines (red) of the resulting construction. This specific eigenfunction results from and , which has a growth rate of in agreement with Equation ( 26 ). The green contour shows the trajectory of a fluid element that begins at . Figure 6. Contours of TM/KH eigenfunctions for , and with . The green contour shows the trajectory of a particle that started at . Because the growing linear eigenmode has been used in the nonlinear regime, the stream lines (red) cross the field lines (black) in this construction. The magnetic field evolution implied by continuing island growth requires this cross-field flow in the regions outside the diffusion region. This cross-field flow will naturally cease when the linear phase ends and the island growth ends. Fully nonlinear treatments of the TM, in which island saturation occurs self-consistently, have found magnetic structures that are very similar to those produced by the linear modes with (Ofman et al. 1993 ; Chen et al. 1997 ; Li Ma 2010 ; Zhang et al. 2011 ; Doss et al. 2015 ). However, these treatments find a velocity field very different from the linear eigenmode. In particular, the velocity must align with the magnetic field outside the diffusion region, which is not the case with the unsaturated linear eigenmode, as seen in Figure 6 . Nonlinear studies of island saturation in the presence