Gravity wave instability in a turbulent free-surface Taylor–Couette flow: experiments and comparison with an amplitude equation with additive noise
We present an experimental and theoretical study on the gravity-wave instability developing in a highly turbulent free-surface Taylor–Couette flow, for which only the inner cylinder rotates. Above a critical rotation speed, from an axisymmetric turbulent base state a non-axisymmetric fluctuating gra...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2015-01-01
|
| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/17/1/013039 |
| _version_ | 1797751218664112128 |
|---|---|
| author | J Martínez-Mercado Cristóbal Arratia Claudio Falcón Nicolás Mujica |
| author_facet | J Martínez-Mercado Cristóbal Arratia Claudio Falcón Nicolás Mujica |
| author_sort | J Martínez-Mercado |
| collection | DOAJ |
| description | We present an experimental and theoretical study on the gravity-wave instability developing in a highly turbulent free-surface Taylor–Couette flow, for which only the inner cylinder rotates. Above a critical rotation speed, from an axisymmetric turbulent base state a non-axisymmetric fluctuating gravity-wave state develops, with an m = 1 azimuthal wave number. The bifurcation is discontinuous and presents hysteresis. In contrast to previously reported work (Mujica N and Lathrop D 2006 J. Fluid Mech. http://dx\buildrel{\rm{d}}\over{.}oi.org/10.1017/S0022112005007901 51 http://dx\buildrel{\rm{d}}\over{.}oi.org/10.1017/S0022112005007901 ), here we compare our experimental results with a universal model based on a quintic subcritical amplitude equation with additive noise. In general, the model describes correctly the mean free-surface oscillation amplitude and its fluctuations, although differences exist in the bistability region width and the free-surface fluctuations in the gravity wave state. These differences are due to the finite time measurements and non-linear effects, respectively. Indeed, we show that longer measurement times allow the system to transit in either direction (from or to the base state), which results in the shrinking of the bistability region. For very long measurement times, and in a very narrow range of rotation rates, the system presents a series of random reversals between both states. Finally, by removing the mean wave and flow oscillations in the measured free-surface and bulk pressure signals, we demonstrate that their dynamic fluctuations depend on the system state. |
| first_indexed | 2024-03-12T16:45:22Z |
| format | Article |
| id | doaj.art-38c67898b70646fc9b29eace9b57f13e |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:45:22Z |
| publishDate | 2015-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-38c67898b70646fc9b29eace9b57f13e2023-08-08T14:16:06ZengIOP PublishingNew Journal of Physics1367-26302015-01-0117101303910.1088/1367-2630/17/1/013039Gravity wave instability in a turbulent free-surface Taylor–Couette flow: experiments and comparison with an amplitude equation with additive noiseJ Martínez-Mercado0Cristóbal Arratia1Claudio Falcón2Nicolás Mujica3Departamento de Física, Facultad de Ciencias Físicas y Matemáticas , Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile .Departamento de Física, Facultad de Ciencias Físicas y Matemáticas , Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile .Departamento de Física, Facultad de Ciencias Físicas y Matemáticas , Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile .Departamento de Física, Facultad de Ciencias Físicas y Matemáticas , Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile .We present an experimental and theoretical study on the gravity-wave instability developing in a highly turbulent free-surface Taylor–Couette flow, for which only the inner cylinder rotates. Above a critical rotation speed, from an axisymmetric turbulent base state a non-axisymmetric fluctuating gravity-wave state develops, with an m = 1 azimuthal wave number. The bifurcation is discontinuous and presents hysteresis. In contrast to previously reported work (Mujica N and Lathrop D 2006 J. Fluid Mech. http://dx\buildrel{\rm{d}}\over{.}oi.org/10.1017/S0022112005007901 51 http://dx\buildrel{\rm{d}}\over{.}oi.org/10.1017/S0022112005007901 ), here we compare our experimental results with a universal model based on a quintic subcritical amplitude equation with additive noise. In general, the model describes correctly the mean free-surface oscillation amplitude and its fluctuations, although differences exist in the bistability region width and the free-surface fluctuations in the gravity wave state. These differences are due to the finite time measurements and non-linear effects, respectively. Indeed, we show that longer measurement times allow the system to transit in either direction (from or to the base state), which results in the shrinking of the bistability region. For very long measurement times, and in a very narrow range of rotation rates, the system presents a series of random reversals between both states. Finally, by removing the mean wave and flow oscillations in the measured free-surface and bulk pressure signals, we demonstrate that their dynamic fluctuations depend on the system state.https://doi.org/10.1088/1367-2630/17/1/013039Taylor–Couette flowpattern forming systemamplitude equationsturbulent fluctuationssurface waves47.20.QR |
| spellingShingle | J Martínez-Mercado Cristóbal Arratia Claudio Falcón Nicolás Mujica Gravity wave instability in a turbulent free-surface Taylor–Couette flow: experiments and comparison with an amplitude equation with additive noise New Journal of Physics Taylor–Couette flow pattern forming system amplitude equations turbulent fluctuations surface waves 47.20.QR |
| title | Gravity wave instability in a turbulent free-surface Taylor–Couette flow: experiments and comparison with an amplitude equation with additive noise |
| title_full | Gravity wave instability in a turbulent free-surface Taylor–Couette flow: experiments and comparison with an amplitude equation with additive noise |
| title_fullStr | Gravity wave instability in a turbulent free-surface Taylor–Couette flow: experiments and comparison with an amplitude equation with additive noise |
| title_full_unstemmed | Gravity wave instability in a turbulent free-surface Taylor–Couette flow: experiments and comparison with an amplitude equation with additive noise |
| title_short | Gravity wave instability in a turbulent free-surface Taylor–Couette flow: experiments and comparison with an amplitude equation with additive noise |
| title_sort | gravity wave instability in a turbulent free surface taylor couette flow experiments and comparison with an amplitude equation with additive noise |
| topic | Taylor–Couette flow pattern forming system amplitude equations turbulent fluctuations surface waves 47.20.QR |
| url | https://doi.org/10.1088/1367-2630/17/1/013039 |
| work_keys_str_mv | AT jmartinezmercado gravitywaveinstabilityinaturbulentfreesurfacetaylorcouetteflowexperimentsandcomparisonwithanamplitudeequationwithadditivenoise AT cristobalarratia gravitywaveinstabilityinaturbulentfreesurfacetaylorcouetteflowexperimentsandcomparisonwithanamplitudeequationwithadditivenoise AT claudiofalcon gravitywaveinstabilityinaturbulentfreesurfacetaylorcouetteflowexperimentsandcomparisonwithanamplitudeequationwithadditivenoise AT nicolasmujica gravitywaveinstabilityinaturbulentfreesurfacetaylorcouetteflowexperimentsandcomparisonwithanamplitudeequationwithadditivenoise |