Instabilities in internal gravity waves
Internal gravity waves are propagating disturbances in stably stratified fluids, and can transport momentum and energy over large spatial extents. From a fundamental viewpoint, internal waves are interesting due to the nature of their dispersion relation, and their linear dynamics are reasonably wel...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-03-01
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| Series: | Mathematics in Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.2023016?viewType=HTML |
| _version_ | 1797825572367237120 |
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| author | Dheeraj Varma Manikandan Mathur Thierry Dauxois |
| author_facet | Dheeraj Varma Manikandan Mathur Thierry Dauxois |
| author_sort | Dheeraj Varma |
| collection | DOAJ |
| description | Internal gravity waves are propagating disturbances in stably stratified fluids, and can transport momentum and energy over large spatial extents. From a fundamental viewpoint, internal waves are interesting due to the nature of their dispersion relation, and their linear dynamics are reasonably well-understood. From an oceanographic viewpoint, a qualitative and quantitative understanding of significant internal wave generation in the ocean is emerging, while their dissipation mechanisms are being debated. This paper reviews the current knowledge on instabilities in internal gravity waves, primarily focusing on the growth of small-amplitude disturbances. Historically, wave-wave interactions based on weakly nonlinear expansions have driven progress in this field, to investigate spontaneous energy transfer to various temporal and spatial scales. Recent advances in numerical/experimental modeling and field observations have further revealed noticeable differences between various internal wave spatial forms in terms of their instability characteristics; this in turn has motivated theoretical calculations on appropriately chosen internal wave fields in various settings. After a brief introduction, we present a pedagogical discussion on linear internal waves and their different two-dimensional spatial forms. The general ideas concerning triadic resonance in internal waves are then introduced, before proceeding towards instability characteristics of plane waves, wave beams and modes. Results from various theoretical, experimental and numerical studies are summarized to provide an overall picture of the gaps in our understanding. An ocean perspective is then given, both in terms of the relevant outstanding questions and the various additional factors at play. While the applications in this review are focused on the ocean, several ideas are relevant to atmospheric and astrophysical systems too. |
| first_indexed | 2024-03-13T10:55:55Z |
| format | Article |
| id | doaj.art-045cf0aebeb94c2a8b19b8beaac7c0bd |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-03-13T10:55:55Z |
| publishDate | 2023-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-045cf0aebeb94c2a8b19b8beaac7c0bd2023-05-17T01:32:06ZengAIMS PressMathematics in Engineering2640-35012023-03-015113410.3934/mine.2023016Instabilities in internal gravity wavesDheeraj Varma0Manikandan Mathur 1Thierry Dauxois 21. ENS de Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, France2. Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai-600036, India 3. Geophysical Flows Lab, Indian Institute of Technology Madras, Chennai-600036, India1. ENS de Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, France 2. Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai-600036, IndiaInternal gravity waves are propagating disturbances in stably stratified fluids, and can transport momentum and energy over large spatial extents. From a fundamental viewpoint, internal waves are interesting due to the nature of their dispersion relation, and their linear dynamics are reasonably well-understood. From an oceanographic viewpoint, a qualitative and quantitative understanding of significant internal wave generation in the ocean is emerging, while their dissipation mechanisms are being debated. This paper reviews the current knowledge on instabilities in internal gravity waves, primarily focusing on the growth of small-amplitude disturbances. Historically, wave-wave interactions based on weakly nonlinear expansions have driven progress in this field, to investigate spontaneous energy transfer to various temporal and spatial scales. Recent advances in numerical/experimental modeling and field observations have further revealed noticeable differences between various internal wave spatial forms in terms of their instability characteristics; this in turn has motivated theoretical calculations on appropriately chosen internal wave fields in various settings. After a brief introduction, we present a pedagogical discussion on linear internal waves and their different two-dimensional spatial forms. The general ideas concerning triadic resonance in internal waves are then introduced, before proceeding towards instability characteristics of plane waves, wave beams and modes. Results from various theoretical, experimental and numerical studies are summarized to provide an overall picture of the gaps in our understanding. An ocean perspective is then given, both in terms of the relevant outstanding questions and the various additional factors at play. While the applications in this review are focused on the ocean, several ideas are relevant to atmospheric and astrophysical systems too.https://www.aimspress.com/article/doi/10.3934/mine.2023016?viewType=HTMLtriadic resonancesubharmonicsuperharmonicplane wavewave beammode |
| spellingShingle | Dheeraj Varma Manikandan Mathur Thierry Dauxois Instabilities in internal gravity waves Mathematics in Engineering triadic resonance subharmonic superharmonic plane wave wave beam mode |
| title | Instabilities in internal gravity waves |
| title_full | Instabilities in internal gravity waves |
| title_fullStr | Instabilities in internal gravity waves |
| title_full_unstemmed | Instabilities in internal gravity waves |
| title_short | Instabilities in internal gravity waves |
| title_sort | instabilities in internal gravity waves |
| topic | triadic resonance subharmonic superharmonic plane wave wave beam mode |
| url | https://www.aimspress.com/article/doi/10.3934/mine.2023016?viewType=HTML |
| work_keys_str_mv | AT dheerajvarma instabilitiesininternalgravitywaves AT manikandanmathur instabilitiesininternalgravitywaves AT thierrydauxois instabilitiesininternalgravitywaves |