Rayleigh-Taylor Unstable Flames: the Effect of Two-Mode Coupling
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909425634115584 |
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| author | Liu, Mingxuan Hicks, Elizabeth P. |
| author_facet | Liu, Mingxuan Hicks, Elizabeth P. |
| contents | In the classical Rayleigh-Taylor (RT) instability, initial conditions are forgotten and the growth of the mixing layer becomes self-similar when short wavelength modes couple to generate longer wavelength modes. In this paper, we explore how adding a reaction at the unstable interface affects this inverse cascade in wavenumber ("inverse k-cascade"). We simulate a 2D, Boussinesq, premixed model flame perturbed by a large amplitude primary mode ($k_1$) and a smaller amplitude secondary mode ($k_2$). Early on, the modes are uncoupled and the flame propagates as a metastable traveling wave. Once the secondary mode has grown large enough, the modes couple. The traveling wave is destabilized and the flame front bubbles rapidly grow. This inverse k-cascade, driven by two-mode coupling, ultimately generates a long wavelength mode with wavenumber GCD$(k_1,k_2)$, where GCD is the greatest common divisor. We identify five distinct flame growth solution types, and show that the flame may stall, develop coherent pulsations, or even become a metastable traveling wave again depending on GCD$(k_1,k_2)$. Finally, we compare our results with two-mode coupling in ablative and classical RT and show that all three systems may follow the same mode coupling dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_15046 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rayleigh-Taylor Unstable Flames: the Effect of Two-Mode Coupling Liu, Mingxuan Hicks, Elizabeth P. Fluid Dynamics In the classical Rayleigh-Taylor (RT) instability, initial conditions are forgotten and the growth of the mixing layer becomes self-similar when short wavelength modes couple to generate longer wavelength modes. In this paper, we explore how adding a reaction at the unstable interface affects this inverse cascade in wavenumber ("inverse k-cascade"). We simulate a 2D, Boussinesq, premixed model flame perturbed by a large amplitude primary mode ($k_1$) and a smaller amplitude secondary mode ($k_2$). Early on, the modes are uncoupled and the flame propagates as a metastable traveling wave. Once the secondary mode has grown large enough, the modes couple. The traveling wave is destabilized and the flame front bubbles rapidly grow. This inverse k-cascade, driven by two-mode coupling, ultimately generates a long wavelength mode with wavenumber GCD$(k_1,k_2)$, where GCD is the greatest common divisor. We identify five distinct flame growth solution types, and show that the flame may stall, develop coherent pulsations, or even become a metastable traveling wave again depending on GCD$(k_1,k_2)$. Finally, we compare our results with two-mode coupling in ablative and classical RT and show that all three systems may follow the same mode coupling dynamics. |
| title | Rayleigh-Taylor Unstable Flames: the Effect of Two-Mode Coupling |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2309.15046 |