Objective Liutex from Flow Data Measured in a Non-Inertial Frame

Objectivity is a fundamental requirement for vortex identification, ensuring that vortex structures observed remain invariant under changes in the reference frame. However, although most conventional vortex identification methods, including Liutex, are Galilean invariant, they are not objective. Since the accelerated motion of the observer does not affect the velocity gradient tensor at an instant of time, the rotational motion is only considered for the non-inertial frame. This paper proposes a method to recover the angular velocity of a rotating observer directly from flow field data measured in the rotating frame. The approach exploits the observation that, in an inertial frame, zero-vorticity points tend to dominate the region with an almost identical nonzero vorticity in the observer’s non-inertial coordinate system. By identifying the most frequently occurring vorticity within the domain, the observer’s angular velocity can be uniquely determined, enabling reconstruction of the objective velocity gradient tensor and, consequently, the objective Liutex. The key issue is to find a reference point (RP). The RP should have zero vorticity in the inertial coordinate system, and then the RP has the same angular speed as the observer. The RP can be found by comparing the vorticity of all points in the computational domain and the RP will correspond to the vorticity vector with the highest percentage in the non-inertial coordinate system. The proposed method is validated using DNS data of the boundary layer transition over a flat plate with an artificially imposed angular velocity. The recovered angular velocity agrees closely with the true value within an acceptable margin of error. Furthermore, the objective Liutex reconstructed from the rotating frame data is visually indistinguishable from the original inertial frame Liutex. These results demonstrate that the method provides a simple and accurate way to restore objectivity for Liutex and other vortex identification techniques. The objective Liutex will be equal to the original Liutex in an inertial coordinate system when the observer does not have rotational motion.