Biswas, L and Shukla, P (2024) Resonant Three-Wave Interactions in a Shear Flow with Density Stratification. In: 9th International and 49th National Conference on Fluid Mechanics and Fluid Power, FMFP 2022, 14 December 2022 through 16 December 2022, Roorkee, India, pp. 263-274.
Full text not available from this repository.Abstract
This paper examines resonant three-wave interactions between internal gravity waves in a uniform shear flow with stable stratification confined between two oppositely moving horizontal plates. In particular, we present the existence of 1: 2: 3 resonance interactions among internal waves in a uniform shear flow with stable density stratification by varying the Richardson number. Such resonances occur when a fundamental wave (km, �m) interacts with its second harmonic (2km, 2�m) and produce the third harmonic (3km, 3�m), where km and �m, respectively, denote the wave number and frequency of the fundamental mode. In this study, we develop an algorithm to classify resonating modes and critical Richardson number at which 1:2:3 resonances occur by solving the linearized Boussinesq Navier�Stokes equation. Finally, the existence of 1: 2: 3 resonance and the spatial structures of resonating modes are graphically demonstrated for a particular critical Richardson number. © 2024, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
| Item Type: | Conference Paper |
|---|---|
| Publication: | Lecture Notes in Mechanical Engineering |
| Publisher: | Springer Science and Business Media Deutschland GmbH |
| Additional Information: | The copyright for this article belongs to Springer Science and Business Media Deutschland GmbH. |
| Keywords: | Gravity waves; Harmonic analysis; Navier Stokes equations, Critical Richardson number; Density stratification; Higher harmonic resonance; Horizontal plates; Internal gravity waves; Resonance interaction; Stable stratification; Stratified shear flow; Three-wave interactions; Uniform shear flow, Shear flow |
| Department/Centre: | Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering) |
| Date Deposited: | 16 Jul 2024 09:38 |
| Last Modified: | 16 Jul 2024 09:38 |
| URI: | http://eprints.iisc.ac.in/id/eprint/84437 |
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