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Recently, a vector called Rortex was proposed and successfully applied to identify the local fluid rotation with both the rotation axis and strength. The first implementation relies on the real Schur decomposition of the velocity gradient tensor, resulting in a relatively long computational time. Subsequently, a mathematically equivalent eigenvector-based definition of Rortex was introduced with an improved implementation. Unfortunately, this definition still tends to be an algorithmic description rather than an explicit one and involves two successive cumbersome coordinate rotations. In this paper, a simple and explicit expression for the calculation of the Rortex vector, which is based on a special (transposed) Schur form of the velocity gradient tensor, is presented. The explicit expression is consistent with the previous definition but avoids the explicit calculation of the coordinate rotation, and thus can significantly simplify the implementation. According to the explicit expression, a new implementation is proposed and validated by a large eddy simulation of the flow transition around a NACA0012 airfoil and a direct numerical simulation of the boundary layer transition on a flat plate.

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