Structure and dynamics of solitary waves in fluid media

PhD Thesis


Singh, Niharika. 2016. Structure and dynamics of solitary waves in fluid media. PhD Thesis Doctor of Philosophy. University of Southern Queensland.
Title

Structure and dynamics of solitary waves in fluid media

TypePhD Thesis
Authors
AuthorSingh, Niharika
SupervisorStepanyants, Professor Yury
Addie, Professor Ron
Institution of OriginUniversity of Southern Queensland
Qualification NameDoctor of Philosophy
Number of Pages135
Year2016
Abstract

This research deals with the study of nonlinear solitary waves in fluid media. The equations which model surface and internal waves in fluids have been studied and used in this research. The approach to study the structure and dynamics of internal solitary waves in near-critical situations is the traditional theoretical and numerical study of nonlinear wave processes based on the methods of dynamical systems. The synergetic approach has been exploited, which presumes a combination of theoretical and numerical methods. All numerical calculations were performed with the desktop personal computer. Traditional and novel methods of mathematical physics were actively used, including Fourier analysis technique, inverse scattering method, Hirota method, phase-plane analysis, analysis of integral invariants, finite-difference method, Petviashvili and Yang–Lakoba numerical iterative techniques for the numerical solution of Partial Differential Equation.

A new model equation, dubbed the Gardner–Kawahara equation, has been suggested to describe wave phenomena in the near-critical situations, when the nonlinear and dispersive coefficients become anomalously small. Such near-critical situations were not studied so far, therefore this study is very topical and innovative. Results obtained will shed a light on the structure of solitary waves in near-critical situation, which can occur in two-layer fluid with strong surface tension between the layers. A family of solitary waves was constructed numerically for the derived Gardner–Kawahara equation; their structure has been investigated analytically and numerically.

The problem of modulation stability of quasi-monochromatic wave-trains propagating in a media has also being studied. The Nonlinear Schrödinger equation (NLSE) has been derived from the unidirectional Gardner–Ostrovsky equation and a general Shrira equation which describes both surface and internal long waves in a rotating fluid. It was demonstrated that earlier obtained results (Grimshaw & Helfrich, 2008; 2012; Whitfield & Johnson, 2015a; 2015b) on modulational stability/instability are correct within the limited range of wavenumbers where the Ostrovsky equation is applicable. In the meantime, results obtained in this Thesis and published in the paper (Nikitenkova et al., 2015) are applicable in the wider range of wavenumbers up to k = 0. It was shown that surface and internal oceanic waves are stable with respect to selfmodulation at small wavenumbers when k → 0 in contrast to what was mistakenly obtained in (Shrira, 1981).

In Chapter 4 new exact solutions of the Kadomtsev-Petviashvili equation with a positive dispersion are obtained in the form of obliquely propagating skew lumps. Specific features of such lumps were studied in details. In particular, the integral characteristics of single lumps (mass, momentum components and energy) have been calculated and presented in terms of lump velocity. It was shown that exact stationary multi-lump solutions can be constructed for this equation. As the example, the exact bilump solution is presented in the explicit form and illustrated graphically. The relevance of skew lumps to the real physical systems is discussed.

ANZSRC Field of Research 2020401207. Fundamental and theoretical fluid dynamics
510301. Acoustics and acoustical devices; waves
Byline AffiliationsSchool of Agricultural, Computational and Environmental Sciences
Permalink -

https://research.usq.edu.au/item/q38q6/structure-and-dynamics-of-solitary-waves-in-fluid-media

Download files


Published Version
Thesis final copy-Niharika.pdf
File access level: Anyone

  • 1723
    total views
  • 292
    total downloads
  • 3
    views this month
  • 0
    downloads this month

Export as

Related outputs

True encounters with the fictional university: collectively rewriting the script of filmic dark academia from the academic margins
Hopkins, Susan, Balloo, Kieran, Ramos, Fabiane, Salmeron, Raquel, Singh, Niharika and Wilson, Victoria E.. 2024. "True encounters with the fictional university: collectively rewriting the script of filmic dark academia from the academic margins ." Culture and Organization. https://doi.org/10.1080/14759551.2024.2394461
Examining students’ behavioural engagement in lecture videos with and without embedded quizzes in an online course.
Singh, Niharika, Getenet, Seyum and Tualaulelei, Eseta. 2023. "Examining students’ behavioural engagement in lecture videos with and without embedded quizzes in an online course." 40th Annual Conference of the Australasian Society for Computers in Learning in Tertiary Education (ASCILITE 2023). Christchurch, New Zealand 03 - 06 Dec 2023 New Zealand. https://doi.org/10.14742/apubs.2023.571
Dynamics of Benjamin-Ono Solitons in a Two-Layer Ocean with a Shear Flow
Negi, Pawan, Sahoo, Trilochan, Singh, Niharika and Stepanyants, Yury. 2023. "Dynamics of Benjamin-Ono Solitons in a Two-Layer Ocean with a Shear Flow." Mathematics. 11 (15). https://doi.org/10.3390/math11153399
Exploring the identities of pathways educators through the lens of Third Space Theory
Balloo, Kieran, Ramos, Fabiane, Crank, Russell, Crane, Daniel, Hopkins, Susan, McGovern, Mary, Parkes, Frey, Penno, Julie, Singh, Niharika, Todd, Nicholas, Wilson, Victoria, Windsor, Angela and Worsley, Sue. 2024. "Exploring the identities of pathways educators through the lens of Third Space Theory." Pedagogy Culture and Society. 32 (5), pp. 1549-1571. https://doi.org/10.1080/14681366.2023.2230986
Mapping the values and identities of academics who teach into widening participation university preparation programs
Balloo, Kieran, Crane, Daniel, Crank, Russell, Hopkins, Susan, McGovern, Mary, Parkes, Geoffrey, Penno, Julie, Ramos, Fabiane, Singh, Niharika, Todd, Nicholas, Wilson, Victoria, Windsor, Angela and Worsley, Sue. 2022. "Mapping the values and identities of academics who teach into widening participation university preparation programs." Society for Research into Higher Education International Research (SRHE) Conference 2022. 05 - 09 Dec 2022 United Kingdom.
Students’ behavioural engagement with recorded lecture videos: Panopto video analytics
Getenet, Seyum, Singh, Niharika, Tualaulelei, Eseta, Pillay, Yosheen and Worsley, Sue. 2022. "Students’ behavioural engagement with recorded lecture videos: Panopto video analytics." EdMedia + Innovate Learning Conference 2022. United States 01 - 03 Nov 2022 United States.
Internal solitary waves in two-layer fluids at near-critical situation
Kurkina, O., Singh, N. and Stepanyants, Y.. 2014. "Internal solitary waves in two-layer fluids at near-critical situation." 19th Australasian Fluid Mechanics Conference (AFMC 2014). Melbourne, Australia 08 - 11 Dec 2014 Australia.
Obliquely propagating skew KP lumps
Singh, N. and Stepanyants, Y.. 2016. "Obliquely propagating skew KP lumps." Wave Motion. 64, pp. 92-102. https://doi.org/10.1016/j.wavemoti.2016.03.005
Modulational instability of wave trains in a rotating ocean
Nikitenkova, S. P., Singh, N. N. and Stepanyants, Y. A.. 2016. "Modulational instability of wave trains in a rotating ocean." 20th Australasian Fluid Mechanics Conference (AFMC 2016). Perth, Australia 05 - 08 Dec 2016 Australia.
Modulational stability of weakly nonlinear wave-trains in media with small- and large-scale dispersions
Nikitenkova, S., Singh, N. and Stepanyants, Y.. 2015. "Modulational stability of weakly nonlinear wave-trains in media with small- and large-scale dispersions." Chaos: an interdisciplinary journal of nonlinear science. 25 (12), pp. 123113-1. https://doi.org/10.1063/1.4937362
Structure of internal solitary waves in two-layer fluid at near-critical situation
Kurkina, O., Singh, N. and Stepanyants, Y.. 2015. "Structure of internal solitary waves in two-layer fluid at near-critical situation." Communications in Nonlinear Science and Numerical Simulation. 22 (1-3), pp. 1235-1242. https://doi.org/10.1016/j.cnsns.2014.09.018