Abstract
We present a novel characterization of mixing events associated with the propagation and overturning of internal waves studied, thanks to the simultaneous use of particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) techniques. This combination of techniques had been developed earlier to provide an access to simultaneous velocity and density fields in two-layer stratified flows with interfacial gravity waves. Here, for the first time, we show how it is possible to implement it quantitatively in the case of a continuously stratified fluid where internal waves propagate in the bulk. We explain in details how the calibration of the PLIF data is performed by an iterative procedure, and we describe the precise spatial and temporal synchronizations of the PIV and PLIF measurements. We then validate the whole procedure by characterizing the triadic resonance instability (TRI) of an internal wave mode. Very interestingly, the combined technique is then applied to a precise measurement of the turbulent diffusivity K t associated with mixing events induced by an internal wave mode. Values up to K t = 15 mm2 s−1 are reached when TRI is present (well above the noise of our measurement, typically 1 mm2 s−1), unambiguously confirming that TRI is a potential pathway to turbulent mixing in stratified flows. This work therefore provides a step on the path to new measurements for internal waves.
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Notes
Experimentally, this term is computed by taking an image with the lens cap on, leaving only the camera noise as signal.
In order to take into account the presence of ethanol in the fluid, in addition to the salt, the conductivity probe must be calibrated with the mixture of salt and ethanol in the same proportions, using a density meter Anton Paar DMA35.
Note that the more commonly used acronym parametric subharmonic instability (PSI) actually corresponds to a particular case of TRI in the case where viscosity is negligible; both unstable secondary waves then have a frequency equal to half of the forcing frequency. We prefer to use TRI to keep the generality.
The field of view does not have enough vertical extension to allow for a measurement of the vertical component of \(\mathbf {k_0}\). However, from the design of the wave generator, we know that this component is equal to \(\pi /H\), where H is the generator height.
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This work has been partially supported by the ONLITUR grant (ANR-2011-BS04-006-01) and achieved thanks to the resources of PSMN from ENS de Lyon.
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Dossmann, Y., Bourget, B., Brouzet, C. et al. Mixing by internal waves quantified using combined PIV/PLIF technique. Exp Fluids 57, 132 (2016). https://doi.org/10.1007/s00348-016-2212-y
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DOI: https://doi.org/10.1007/s00348-016-2212-y