2017/06/14 by Divyanshu Bhardwaj, Bhardwaj, Divyanshu, Anirban Guha +1
Earth and Planetary Sciences · Engineering · #Computational Fluid Dynamics and Aerodynamics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Ocean Waves and Remote Sensing #Tropical and Extratropical Cyclones Research
paper · pdf · doi:10.48550/arxiv.1706.04343
openalex publication_date 2017/06/14 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28
Theoretical studies on linear shear instabilities often use simple velocity\nand density profiles (e.g. constant, piecewise) for obtaining good qualitative\nand quantitative predictions of the initial disturbances. Furthermore, such\nsimple profiles provide a minimal model for obtaining a mechanistic\nunderstanding of otherwise elusive shear instabilities. However, except a few\nspecific cases, the efficacy of simple profiles has remained limited to the\nlinear stability paradigm. In this work we have proposed a general framework\nthat can simulate the fully nonlinear evolution of a variety of stratified\nshear instabilities as well as wave-wave and wave-topography interaction\nproblems having simple profiles. To this effect, we have modified the classical\nvortex method by extending the Birkhoff-Rott equation to multiple interfaces,\nand furthermore, have incorporated background shear across a density interface.\nThe latter is more subtle, and originates from the understanding that\nBernoulli's equation is not just limited to irrotational flows, but can be\nmodified to make it applicable for piecewise velocity profiles. We have solved\ndiverse problems that can be essentially reduced to the multiple interacting\ninterfaces paradigm, e.g. spilling and plunging breakers, stratified shear\ninstabilities like Holmboe and Taylor-Caulfield, jet flows, and even\nwave-topography interaction problem like Bragg resonance. Free-slip boundary\nbeing a vortex sheet, its effect can also be effectively captured using vortex\nmethod. We found that the minimal models capture key nonlinear features, e.g.\nwave breaking features like cusp formation and roll-ups, which are observed in\nexperiments and/or extensive simulations with smooth, realistic profiles.\n