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Register a new userDispersion free control of hydroelastic waves down to sub-wavelength scale
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Hydroelastic surface waves propagate at the surface of water covered by a thin elastic sheet and can be directly measured with accurate space and time resolution. We present an experimental approach using hydroelastic waves that allows us to control waves down to the sub-wavelength scale. We tune the wave dispersion relation by varying locally the properties of the elastic cover and we introduce a local index contrast. This index contrast is independent of the frequency leading to a dispersion-free Snell-Descartes law for hydroelastic waves. We then show experimental evidence of broadband focusing, reflection and refraction of the waves. We also investigate the limits of diffraction through the example of a macroscopic analog to optical nanojets, revealing that any sub-wavelength configuration gives access to new features for surface waves.
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An approximate dispersion relation is derived and presented for linear surface waves atop a shear current whose magnitude and direction can vary arbitrarily with depth. The approximation, derived to first order of deviation from potential flow, is shown to produce good approximations at all wavelengths for a wide range of naturally occuring shear flows as well as widely used model flows. The relation reduces in many cases to a 3D generalization of the much used approximation by Skop [1987], developed further by Kirby & Chen [1989], but is shown to be more robust, succeeding in situations where the Kirby & Chen model fails. The two approximations incur the same numerical cost and difficulty. While the Kirby & Chen approximation is excellent for a wide range of currents, the exact criteria for its applicability have not been known. We explain the apparently serendipitous success of the latter and derive proper conditions of applicability for both approximate dispersion relations. Our new model has a greater range of applicability. A second order approximation is also derived. It greatly improves accuracy, which is shown to be important in difficult cases. It has an advantage over the corresponding 2nd order expression proposed by Kirby & Chen that its criterion of accuracy is explicitly known, which is not currently the case for the latter to our knowledge. Our 2nd order term is also arguably significantly simpler to implement, and more physically transparent, than its sibling due to Kirby & Chen.
A new method for the localization of the regions where small scale turbulent fluctuations are present in hypersonic flows is applied to the large-eddy simulation (LES) of a compressible turbulent jet with an initial Mach number equal to 5. The localization method used is called selective LES and is based on the exploitation of a scalar probe function $f$ which represents the magnitude of the stretching-tilting term of the vorticity equation normalized with the enstrophy (Tordella et al. 2007). For a fully developed turbulent field of fluctuations, statistical analysis shows that the probability that $f$ is larger than 2 is almost zero, and, for any given threshold, it is larger if the flow is under-resolved. By computing the spatial field of $f$ in each instantaneous realization of the simulation it is possible to locate the regions where the magnitude of the normalized vortical stretching-tilting is anomalously high. The sub-grid model is then introduced into the governing equations in such regions only. The results of the selective LES simulation are compared with those of a standard LES, where the sub-grid terms are used in the whole domain, and with those of a standard Euler simulation with the same resolution. The comparison is carried out by assuming as reference field a higher resolution Euler simulation of the same jet. It is shown that the selective LES modifies the dynamic properties of the flow to a lesser extent with respect to the classical LES. In particular, the prediction of the enstrophy, mean velocity and density distributions and of the energy and density spectra are substantially improved.
In fully-developed pressure-driven flow, the spreading of a dissolved solute is enhanced in the flow direction due to transverse velocity variations in a phenomenon now commonly referred to as Taylor-Aris dispersion. It is well understood that the characteristics of the dispersion are sensitive to the channels cross-sectional geometry. Here we demonstrate a method for manipulation of dispersion in a single rectangular microchannel via controlled deformation of its upper wall. Using a rapidly prototyped multi-layer microchip, the channel wall is deformed by a controlled pressure source allowing us to characterize the dependence of the dispersion on the deflection of the channel wall and overall channel aspect ratio. For a given channel aspect ratio, an optimal deformation to minimize dispersion is found, consistent with prior numerical and theoretical predictions. Our experimental measurements are also compared directly to numerical predictions using an idealized geometry.
Based on the concept of sub-wavelength imaging through compensated bilayer of anisotropic metamaterials (AMMs), which is an expansion of the perfect lens configuration, we propose two dimensional prism pair structures of compensated AMMs that are capable of manipulating two dimensional sub-wavelength images. We demonstrate that through properly designed symmetric and asymmetric compensated prism pair structures planar image rotation with arbitrary angle, lateral image shift, as well as image magnification could be achieved with sub-wavelength resolution. Both theoretical analysis and full wave electromagnetic simulations have been employed to verify the properties of the proposed prism structures. Utilizing the proposed AMM prisms, flat optical image of objects with sub-wavelength features can be projected and magnified to wavelength scale allowing for further optical processing of the image by conventional optics.
We report the observation of gravity-capillary waves on a torus of fluid. By means of an original technique, a stable torus is achieved by depositing water on a superhydrophobic groove with a shallow wedge-shaped channel running along its perimeter. Using a spatio-temporal optical measurement, we report the full dispersion relation of azimuthal waves propagating along the inner and outer torus borders, highlighting several branches modeled as varicose, sinuous and sloshing modes. Standing azimuthal waves are also studied leading to polygon-like patterns arising on the two torus borders with a number of sides different when a tunable decoupling of the two interfaces occurs. The quantized nature of the dispersion relation is also evidenced.
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