TY - JOUR
T1 - Nonlinear modeling of stratified shear instabilities, wave breaking, and wave-topography interactions using vortex method
AU - Bhardwaj, Divyanshu
AU - Guha, Anirban
N1 - The authors thank IITK/ME/2014338 for funding support.
PY - 2018/1
Y1 - 2018/1
N2 - Theoretical studies on linear shear instabilities often use simple velocity and density profiles (e.g., constant, piecewise) for obtaining good qualitative and quantitative predictions of the initial disturbances. Furthermore, such simple profiles provide a minimal model for obtaining a mechanistic understanding of otherwise elusive shear instabilities. However, except a few specific cases, the efficacy of simple profiles has remained limited to the linear stability paradigm. In this work, we have proposed a general framework that can simulate the fully nonlinear evolution of a variety of stratified shear instabilities as well as wave-wave and wave-topography interaction problems having simple piecewise constant and/or linear profiles. To this effect, we have modified the classical vortex method by extending the Birkhoff-Rott equation to multiple interfaces and, furthermore, have incorporated background shear across a density interface. The latter is more subtle and originates from the understanding that Bernoulli's equation is not just limited to irrotational flows but can be modified to make it applicable for piecewise linear velocity profiles. We have solved diverse problems that can be essentially reduced to the multiple interacting interfaces paradigm, e.g., spilling and plunging breakers, stratified shear instabilities like Holmboe and Taylor-Caulfield, jet flows, and even wave-topography interaction problems like Bragg resonance. Free-slip boundary being a vortex sheet, its effect can also be effectively captured using vortex method. We found that the minimal models capture key nonlinear features, e.g., wave breaking features like cusp formation and roll-ups, which are observed in experiments and/or extensive simulations with smooth, realistic profiles.
AB - Theoretical studies on linear shear instabilities often use simple velocity and density profiles (e.g., constant, piecewise) for obtaining good qualitative and quantitative predictions of the initial disturbances. Furthermore, such simple profiles provide a minimal model for obtaining a mechanistic understanding of otherwise elusive shear instabilities. However, except a few specific cases, the efficacy of simple profiles has remained limited to the linear stability paradigm. In this work, we have proposed a general framework that can simulate the fully nonlinear evolution of a variety of stratified shear instabilities as well as wave-wave and wave-topography interaction problems having simple piecewise constant and/or linear profiles. To this effect, we have modified the classical vortex method by extending the Birkhoff-Rott equation to multiple interfaces and, furthermore, have incorporated background shear across a density interface. The latter is more subtle and originates from the understanding that Bernoulli's equation is not just limited to irrotational flows but can be modified to make it applicable for piecewise linear velocity profiles. We have solved diverse problems that can be essentially reduced to the multiple interacting interfaces paradigm, e.g., spilling and plunging breakers, stratified shear instabilities like Holmboe and Taylor-Caulfield, jet flows, and even wave-topography interaction problems like Bragg resonance. Free-slip boundary being a vortex sheet, its effect can also be effectively captured using vortex method. We found that the minimal models capture key nonlinear features, e.g., wave breaking features like cusp formation and roll-ups, which are observed in experiments and/or extensive simulations with smooth, realistic profiles.
UR - http://www.scopus.com/inward/record.url?scp=85040784359&partnerID=8YFLogxK
U2 - 10.1063/1.5006654
DO - 10.1063/1.5006654
M3 - Article
AN - SCOPUS:85040784359
SN - 1070-6631
VL - 30
JO - Physics of Fluids
JF - Physics of Fluids
IS - 1
M1 - 014102
ER -