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We present an investigation of the resonance conditions of axisymmetric internal wave sub-harmonics in confined and unconfined domains. In both cases, sub-harmonics can be spontaneously generated from a primary wave field if they satisfy at least a resonance condition on their frequencies, of the form $\omega_0 = \pm \omega_1 \pm \omega_2$. We demonstrate that, in an unconfined domain, the sub-harmonics follow three dimensional spatial resonance conditions similar to the ones of Triadic Resonance Instability (TRI) for Cartesian plane waves. In a confined domain, however, the spatial structure of the sub-harmonics is fully determined by the boundary conditions and we observed that these conditions prevail upon the resonance conditions. In both configurations, these findings are supported by experimental data showing good agreement with analytical and numerical derivations.

In this paper, we present an experimental study of weakly non-linear interaction of axisymmetric internal gravity waves in a resonant cavity, supported by theoretical considerations. Contrary to plane waves in Cartesian coordinates, for which self-interacting terms are null in a linear stratifiation, the non-linear self-interaction of an internal wave mode in axisymmetric geometry is found to be efficient at producing super-harmonics, i.e. waves whose frequencies are integer multiples of the excitation frequency. Due to the range of frequencies tested in our experiments, the first harmonic frequency is below the cut-off imposed by the stratification so the lowest harmonic created can always propagate. The study shows that the super-harmonic wave field is a sum of standing waves satisfying both the dispersion relation for internal waves and the boundary conditions imposed by the cavity walls, while conserving the axisymmetry.

The shear resulting from internal wave reflections can play a crucial role in the transport and resuspension of sediments in oceanic conditions. In particular, when these waves undergo a \textit{critical reflection} phenomenon, the reflected wave can produce a very large shear. Separating the reflected wave from the incident wave is a technical challenge since the two waves share the same temporal frequency. In our study, we present a series of experimental measurements of internal waves in \textit{critical reflection} configuration and we analyze them using the 2D-VMD-prox decomposition method. This decomposition method was adapted to specifically decompose waves in an internal wave critical reflection, showing an improvement in its performance with respect to preexisting internal wave decomposition methods. Being able to confidently isolate the reflected wave allowed us to compare our results to a viscous and non-linear model for critical reflection, that correctly describes the dependence of the shear rate produced in the boundary as a function of the experimental parameters., Comment: 14 pages, 20 figures

We present an experimental study of the saturated non-linear dynamics of an inertial wave attractor in an axisymmetric geometrical setting. The experiments are carried out in a rotating ring-shaped fluid domain delimited by two vertical coaxial cylinders, a conical bottom, and a horizontal deformable upper lid as wave generator: the meridional cross-section of the fluid volume is a trapezium, while the horizontal cross-section is a ring. First, the fluid is set into a rigid-body rotation. Thereafter, forcing is introduced into the system via axisymmetric low-amplitude volume-conserving oscillatory motion of the upper lid. After a short transient of about 10 forcing periods, a quasi-linear regime is established, with an axisymmetric inertial wave attractor. The attractor is prone to instability: at long time-scale (order 100 forcing periods) a saturated fully non-linear regime develops as a consequence of an energy cascade draining energy towards a slow two-dimensional manifold represented by a regular polygonal system of axially-oriented cyclonic vortices that are slowly precessing around the inner cylinder. We show that this slow two-dimensional manifold manifests a persistent slow prograde motion and a strong cyclonic-anticyclonic asymmetry quantified by the time-evolution of the probability density function of the vertical vorticity.

To date, the influence of non-linear stratifications and two layer stratifications on internal wave propagation has been studied for two-dimensional wave fields in a cartesian geometry. Here, we use a novel wave generator configuration to investigate transmission in non-linear stratifications of axisymmetric internal wave. Two configurations are studied, both theoretically and experimentally. In the case of a free incident wave, a transmission maximum is found in the vicinity of evanescent frequencies. In the case of a confined incident wave, resonant effects lead to enhanced transmission rates from an upper layer to layer below. We consider the oceanographic relevance of these results by applying them to an example oceanic stratification, finding that there can be real-world implications., Comment: 21 pages, 15 figures

To date, axisymmetric internal wave fields, which have relevance to atmospheric internal wave fields generated by storm cells and oceanic near-inertial wave fields generated by surface storms, have been experimentally realized using an oscillating sphere or torus as the source. Here, we use a novel wave generator configuration capable of exciting axisymmetric internal wave fields of arbitrary radial form to generate axisymmetric internal wave modes. After establishing the theoretical background for axisymmetric mode propagation, taking into account lateral and vertical confinement, and also accounting for the effects of weak viscosity, we experimentally generate and study modes of different order. We characterize the efficiency of the wave generator through careful measurement of the wave amplitude based upon group velocity arguments. This established, we investigate the ability of vertical confinement to induce resonance, identifying a series of experimental resonant peaks that agree well with theoretical predictions. In the vicinity of resonance, the wave fields undergo a transition to non-linear behaviour that is initiated on the central axis of the domain and proceeds to erode the wave field throughout the domain., Comment: 15 pages, 9 figures

The energy pathways from propagating internal waves to the scales of irreversible mixing in the ocean are not fully described. In the ocean interior, the triadic resonant instability is an intrinsic destabilization process that may enhance the energy cascade away from topographies. The present study focuses on the integrated impact of mixing processes induced by a propagative normal mode-1 over long term experiments in an idealised setup. The internal wave dynamics and the evolution of the density profile are followed using the light attenuation technique. Diagnostics of the turbulent diffusivity $K_{T}$ and background potential energy $BPE$ are provided. Mixing effects result in a partially mixed layer colocated with the region of maximum shear induced by the forcing normal mode. The maximum measured turbulent diffusivity is 250 times larger than the molecular value, showing that diapycnal mixing is largely enhanced by small scale turbulent processes. Intermittency and reversible energy transfers are discussed to bridge the gap between the present diagnostic and the larger values measured in Dossmann et al, Experiments in Fluids, 57(8), 132 (2016). The mixing efficiency $\eta$ is assessed by relating the $BPE$ growth to the linearized $KE$ input. One finds a value of $\Gamma=12-19\%$ larger than the mixing efficiency in the case of breaking interfacial wave. After several hours of forcing, the development of staircases in the density profile is observed. This mechanism has been previously observed in experiments with weak homogeneous turbulence and explained by argument. The present experiments suggest that internal wave forcing could also induce the formation of density interfaces in the ocean.

Internal gravity waves play a primary role in geophysical fluids: they contribute significantly to mixing in the ocean and they redistribute energy and momentum in the middle atmosphere. Until recently, most studies were focused on plane wave solutions. However, these solutions are not a satisfactory description of most geophysical manifestations of internal gravity waves, and it is now recognized that internal wave beams with a confined profile are ubiquitous in the geophysical context. We will discuss the reason for the ubiquity of wave beams in stratified fluids, related to the fact that they are solutions of the nonlinear governing equations. We will focus more specifically on situations with a constant buoyancy frequency. Moreover, in light of recent experimental and analytical studies of internal gravity beams, it is timely to discuss the two main mechanisms of instability for those beams. i) The Triadic Resonant Instability generating two secondary wave beams. ii) The streaming instability corresponding to the spontaneous generation of a mean flow.

The parametric subharmonic instability in stratified fluids depends on the frequency and the amplitude of the primary plane wave. In this paper, we present experimental and numerical results emphasizing that the finite width of the beam also plays an important role on this triadic instability. A new theoretical approach based on a simple energy balance is developed and compared to numerical and experimental results. Because of the finite width of the primary wave beam, the secondary pair of waves can leave the interaction zone which affects the transfer of energy. Experimental and numerical results are in good agreement with the prediction of this theory, which brings new insights on energy transfers in the ocean where internal waves with finite-width beams are dominant.

We apply a new threshold detection method based on the extreme value theory to the von K\'arm\'an sodium (VKS) experiment data. The VKS experiment is a successful attempt to get a dynamo magnetic field in a laboratory liquid-metal experiment. We first show that the dynamo threshold is associated to a change of the probability density function of the extreme values of the magnetic field. This method does not require the measurement of response functions from applied external perturbations, and thus provides a simple threshold estimate. We apply our method to different configurations in the VKS experiment showing that it yields a robust indication of the dynamo threshold as well as evidence of hysteretic behaviors. Moreover, for the experimental configurations in which a dynamo transition is not observed, the method provides a way to extrapolate an interval of possible threshold values., Comment: 10 pages, 7 figures

We analyze time series stemming from experiments and direct numerical simulations of hydrodynamic and magnetohydrodynamic turbulence. Simulations are done in periodic boxes, but with a volumetric forcing chosen to mimic the geometry of the flow in the experiments, the von K\'arm\'an swirling flow between two counter-rotating impellers. Parameters in the simulations are chosen to (within computational limitations) allow comparisons between the experiments and the numerical results. Conducting fluids are considered in all cases. Two different configurations are considered: a case with a weak externally imposed magnetic field, and a case with self-sustained magnetic fields. Evidence of long-term memory and $1/f$ noise is observed in experiments and simulations, in the case with weak magnetic field associated with the hydrodynamic behavior of the shear layer in the von K\'arm\'an flow, and in the dynamo case associated with slow magnetohydrodynamic behavior of the large scale magnetic field., Comment: 10 pages, 9 figures

We present experimental measurements of a wall-bounded gravity current, motivated by characterizing natural gravity currents such as oceanic overflows. We use particle image velocimetry and planar laser-induced fluorescence to simultaneously measure the velocity and density fields as they evolve downstream of the initial injection from a turbulent channel flow onto a plane inclined at 10$^\circ$ with respect to horizontal. The turbulence level of the input flow is controlled by injecting velocity fluctuations upstream of the output nozzle. The initial Reynolds number based on Taylor microscale of the flow, R$_\lambda$, is varied between 40 and 120, and the effects of the initial turbulence level are assessed. The bulk Richardson number $Ri$ for the flow is about 0.3 whereas the gradient Richardson number $Ri_g$ varies between 0.04 and 0.25, indicating that shear dominates the stabilizing effect of stratification. Kelvin-Helmholtz instability results in vigorous vertical transport of mass and momentum. We present baseline characterization of standard turbulence quantities and calculate, in several different ways, the fluid entrainment coefficient $E$, a quantity of considerable interest in mixing parameterization for ocean circulation models. We also determine properties of mixing as represented by the flux Richardson number $Ri_f$ as a function of $Ri_g$ and diapycnal mixing parameter $K_\rho$ versus buoyancy Reynolds number $Re_b$. We find reasonable agreement with results from natural flows., Comment: 36 pages, 21 figures, submitted to JFM

Internal waves are believed to be of primary importance as they affect ocean mixing and energy transport. Several processes can lead to the breaking of internal waves and they usually involve non linear interactions between waves. In this work, we study experimentally the parametric subharmonic instability (PSI), which provides an efficient mechanism to transfer energy from large to smaller scales. It corresponds to the destabilization of a primary plane wave and the spontaneous emission of two secondary waves, of lower frequencies and different wave vectors. Using a time-frequency analysis, we observe the time evolution of the secondary waves, thus measuring the growth rate of the instability. In addition, a Hilbert transform method allows the measurement of the different wave vectors. We compare these measurements with theoretical predictions, and study the dependence of the instability with primary wave frequency and amplitude, revealing a possible effect of the confinement due to the finite size of the beam, on the selection of the unstable mode.

Internal gravity waves contribute to fluid mixing and energy transport, not only in oceans but also in the atmosphere and in astrophysical bodies. We provide here the first experimental measurement of the growth rate of a resonant triad instability (also called parametric subharmonic instability) transferring energy to smaller scales where it is dissipated. We make careful and quantitative comparisons with theoretical predictions for propagating vertical modes in laboratory experiments.

We report the experimental observation of a robust horizontal mean flow induced by internal gravity waves. A wave beam is forced at the lateral boundary of a tank filled with a linearly stratified fluid initially at rest. After a transient regime, a strong jet appears in the wave beam, with horizontal recirculations outside the wave beam. We present a simple physical mechanism predicting the growth rate of the mean flow and its initial spatial structure. We find good agreement with experimental results.

Ni-Mn-Ga films in the austenite and the martensite structures at room temperature have been obtained using the DC magnetron sputtering technique. Two elaboration processes were studied. A first batch of samples was deposited using a resist sacrificial layer in order to release the film from the substrate before vacuum annealing. This process leads to polycrystalline films with a strong (022) fiber texture. The martensitic phase transformation of such polycrystalline freestanding films has been studied by optical and scanning electron microscopy. A second batch of samples was grown epitaxially on (100)MgO substrates using different deposition temperatures. The texture has been analyzed with four-circle X-ray diffraction. Epitaxial films crystallized both in the austenite and the martensite structures at room temperature have been studied.

In order to obtain modulated-martensite in our epitaxial Ni-Mn-Ga films, we have tuned the composition by using a co-sputtering process. Here we present how the composition affects the variant distribution of the 14-modulated martensite at room temperature. The nature of such modulated-martensites is still strongly debated for magnetic shape memory alloys. It has been very recently demonstrated that the modulated-martensites in Ni-Mn-Ga are adaptive phases. The results presented here corroborate this theory for the first time, for three different compositions. Moreover, we demonstrate with the help of the adaptive modulations theory that b-variants of the 14-modulated martensite form close to the free-surface of the film to release the stress induced by branching of macro-twinned domains during the martensitic transformation on a rigid substrate. At room temperature, the content of such b-variants is found to strongly decrease when the macro-twinned domain sizes increase.

La2Zr2O7 (LZO) formation of bulk powders and of films by Chemical Solution Deposition (CSD) process have been studied using propionates. The treatment involved a one step cycle in the reducing forming gas (Ar-5%H2) to be compatible with Ni-5at%W RABITS. Large amount of residual carbon was found in LZO powders formed in these conditions (10 wt %). The volume fraction of the cube texture in LZO films on Ni-5at%w RABITS was found to be a function of the speed of the gas flown above sample. This phenomenon is discussed in considering the C deposited from the carbon-containing gases emitted during the pyrolysis of the precursor. Using proper conditions (950 ^\circC and the speed of gas of 6.8\times10^{-2} m/s), LZO films with good surface crystallinity could be obtained on Ni-5at%W RABITS as demonstrated by X-ray diffraction, electron backscattered diffraction and RHEED. The existence of residual carbon in oxide films is a common question to films deposited by CSD processes under reducing condition.

We study magnetohydrodynamics in a von K\'arm\'an flow driven by the rotation of impellers made of material with varying electrical conductivity and magnetic permeability. Gallium is the working fluid and magnetic Reynolds numbers of order unity are achieved. We find that specific induction effects arise when the impeller's electric and magnetic characteristics differ from that of the fluid. Implications in regards to the VKS dynamo are discussed., Comment: 14 pages, 7 figures

Shear-induced vertical mixing in a stratified flow is a key ingredient of thermohaline circulation. We experimentally determine the vertical flux of momentum and density of a forced gravity current using high-resolution velocity and density measurements. A constant eddy viscosity model provides a poor description of the physics of mixing, but a Prandtl mixing length model relating momentum and density fluxes to mean velocity and density gradients works well. For $ \approx 0.08$ and $Re_\lambda \approx 100$, the mixing lengths are fairly constant, about the same magnitude, comparable to the turbulent shear length., Comment: 4 pages, 4 figures, accepted in PRL, February 2009

Studies of magnetic induction in von K\'arm\'an swirling flows have so far linked the time-averaged induced magnetic field to the structure of the mean flow. They have evidenced the Omega and Parker mechanism generated respectively by the flow differential rotation and helicity, which underly the Duddley and James \cite{DuddleyJames} dynamos. Using an array of Hall probes we study here the dynamical regime. In the experimental flow, turbulence is fully developed and large fluctuations are observed in the magnetic induction processes. We find that the large scale turbulent fluctuations have different characteristics when induction results from the differential rotation or from the dynamics of the stagnation point in the mid plane of the von K\'arm\'an flow. Symmetry considerations indicate that the dynamical flow spends half of its time away from the time-averaged structure. The consequences of these observations for dynamo experiments are discussed., Comment: 26 pages, 14 figures