Nonlinear modeling of stratified shear instabilities, wave breaking, and wave-topography interactions using vortex method

Divyanshu Bhardwaj, Anirban Guha (Lead / Corresponding author)

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Article number014102
JournalPhysics of Fluids
Volume30
Issue number1
Early online date16 Jan 2018
DOIs
Publication statusPublished - Jan 2018

Fingerprint

topography
vortices
shear
profiles
interactions
velocity distribution
spilling
Bernoulli theorem
vortex sheets
circuit breakers
potential flow
jet flow
cusps
slip
disturbances
predictions
simulation

Cite this

@article{37b5f7bc822d4f29a81a94d5a0ed676f,
title = "Nonlinear modeling of stratified shear instabilities, wave breaking, and wave-topography interactions using vortex method",
abstract = "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.",
author = "Divyanshu Bhardwaj and Anirban Guha",
note = "The authors thank IITK/ME/2014338 for funding support.",
year = "2018",
month = "1",
doi = "10.1063/1.5006654",
language = "English",
volume = "30",
journal = "Physics of Fluids",
issn = "1070-6631",
publisher = "American Institute of Physics",
number = "1",

}

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

VL - 30

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 1

M1 - 014102

ER -