<p>Energy Gradient Theory has been developed in recent years for a better understanding of the flow instability and transition from laminar to turbulence in the fluid flow. In this work, we reconstruct the energy gradient theory to establish a relation between the point of inflection and Taylor-Görtler-Like (TGL) vortices in the three-dimensional (3D) rectangular lid-driven cavity flow and find out the exact location from where the TGL vortices start to be formed. Point of inflection declares whether a flow is stable or not, whereas TGL vortices are formed due to the instability or disturbances of the flow. To build the relation among them, we utilize the notion of inflectional instability for the formation of TGL vortices in the lid-driven cavity. Further, we investigate the reason for the formation of Tollmien-Schlichting or T-S waves in the cavity and how this wave plays an important role in the development of the TGL vortices. In the process, we also find the region of maximum kinetic energy, which is the birthplace of TGL vortices in the cavity. The formation of TGL vortices and their consistent relation with mushroom-shaped vortices are also discussed.</p>

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On the formation and exact location of Taylor-Görtler-Like vortices in a rectangular lid-driven cavity

  • Rathindra Nath Basak,
  • Sougata Biswas

摘要

Energy Gradient Theory has been developed in recent years for a better understanding of the flow instability and transition from laminar to turbulence in the fluid flow. In this work, we reconstruct the energy gradient theory to establish a relation between the point of inflection and Taylor-Görtler-Like (TGL) vortices in the three-dimensional (3D) rectangular lid-driven cavity flow and find out the exact location from where the TGL vortices start to be formed. Point of inflection declares whether a flow is stable or not, whereas TGL vortices are formed due to the instability or disturbances of the flow. To build the relation among them, we utilize the notion of inflectional instability for the formation of TGL vortices in the lid-driven cavity. Further, we investigate the reason for the formation of Tollmien-Schlichting or T-S waves in the cavity and how this wave plays an important role in the development of the TGL vortices. In the process, we also find the region of maximum kinetic energy, which is the birthplace of TGL vortices in the cavity. The formation of TGL vortices and their consistent relation with mushroom-shaped vortices are also discussed.