We propose here the use of the variational level set methodology to captureLagrangian vortex boundaries in 2D unsteady velocity fields. This methodreformulates earlier approaches that seek material vortex boundaries asextremum solutions of variational problems. We demonstrate the performance ofthis technique for two different variational formulations built upon differentnotions of coherence. The first formulation uses an energy functional thatpenalizes the deviation of a closed material line from piecewise uniformstretching [Haller and Beron-Vera, J. Fluid Mech. 731, R4 (2013)]. The secondenergy function is derived for a graph-based approach to vortex boundarydetection [Hadjighasem et al., Phys. Rev. E 93, 063107 (2016)]. Our level-setformulation captures an a priori unknown number of vortices simultaneously atrelatively low computational cost. We illustrate the approach by identifyingvortices from different coherence principles in several examples.
展开▼
机译：我们在这里建议使用变分水平集方法来捕获二维非定常速度场中的拉格朗日涡旋边界。该方法重新构造了寻求物质涡旋边界作为变分问题极值解的早期方法。我们证明了该技术对于基于不同连贯性概念的两种不同变体形式的性能。第一种配方使用能量函数，该函数可减小封闭材料线与分段均匀拉伸的偏差[Haller and Beron-Vera，J. Fluid Mech。 731，R4（2013）]。第二能函数是基于图的涡旋边界检测方法推导的[Hadjighasem等，Phys。 Rev 93，063107（2016）]。我们的水平集公式同时捕获了先验未知数量的旋涡，同时计算成本相对较低。我们通过在几个示例中确定来自不同相干原理的涡旋来说明该方法。
展开▼
