The seal structure, and a rotary machine

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A seal structure (2) for sealing a gap between a first structure body (10) and a second structure body (51). The seal structure includes : a peripheral surface formed on one of the first structure body and the second structure body; a plurality of seal fins (5) provided at intervals in the axial direction so as to form clearances (m) together with the peripheral surface and protrusions that form re-adhesion edges between pairs of axially adjacent seal fins; the re-adhesion edges being locations at which leak currents (SL) re-adhere that have passed through a clearance (mA) of an upstream seal fin; and the protrusions forming first cavities in which eddies (B1) are created that flow along the upstream seal fin toward the second structure body, and second cavities in which currents (B2) are created that cause a contraction current effect on a clearance (mB) of a downstream seal fin.