A letter for objective Liutex

Vortex structures, detected by the existing popular vortex identification methods, of the same case are generally different if the results are measured by different observers, who are moving with different coordinate systems. These coordinate systems can be inertial or non-inertial. Galilean invariance can solve the moving observer problems in different inertial coordinate systems. A variable is invariant under Galilean transformation is called Galilean invariant. Galilean invariant vortex identification methods can provide invariant vortex structures based on different inertial observers. However, for some situations, the observers are non-inertial, e.g., the observer is sitting on an aircraft which is accelerating or rotating. In such a situation, it requires to use an objective method. Objectivity represents a property that one variable is not observer-dependent (the observer’s motion can be either inertial or non-inertial). A strategy based on a zero-vorticity (measured in inertial frame) reference point is proposed in this letter to find the objective vortex structure. Liutex is chosen as the vortex indicator and two numerical examples are used to test the proposed strategy. The results show that the strategy is effective.