Heat fluctuations for harmonic oscillators

Heat fluctuations of a harmonic oscillator in contact with a thermostat and driven out of equilibrium by an external deterministic force are studied experimentally and theoretically within the context of Fluctuation Theorems. We consider the case of a periodic forcing of the oscillator, and we calculate the analytic probability density function of heat fluctuations. The limit of large time is discussed and we show that heat fluctuations satisfy the conventional fluctuation theorem, even if a different fluctuation relation exists for this quantity. Experimental results are also given for a transient state.Comment: Submitted to Europhysics Letter

Experimental study of parametric subharmonic instability for internal waves

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

Experimental observation of a strong mean flow induced by internal gravity waves

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

Breaking of internal waves parametrically excited by ageostrophic anticyclonic instability

A gradient-wind balanced flow with an elliptic streamline parametrically excites internal inertia-gravity waves through ageostrophic anticyclonic instability (AAI). This study numerically investigates the breaking of internal waves and the following turbulence generation resulting from the AAI. In our simulation, we periodically distort the calculation domain following the streamlines of an elliptic vortex and integrate the equations of motion using a Fourier spectral method. This technique enables us to exclude the overall structure of the large-scale vortex from the computation and concentrate on resolving the small-scale waves and turbulence. From a series of experiments, we identify two different scenarios of wave breaking conditioned on the magnitude of the instability growth rate scaled by the buoyancy frequency, $\lambda/N$. First, when $\lambda/N\gtrsim0.008$, the primary wave amplitude excited by AAI quickly goes far beyond the overturning threshold and directly breaks. The resulting state is thus strongly nonlinear turbulence. Second, if $\lambda/N\lesssim0.008$, weak wave-wave interactions begin to redistribute energy across frequency space before the primary wave reaches a breaking limit. Then, after a sufficiently long time, the system approaches a Garrett-Munk-like stationary spectrum, in which wave breaking occurs at finer vertical scales. Throughout the experimental conditions, the growth and decay time scales of the primary wave energy are well correlated. However, since the primary wave amplitude reaches a prescribed limit in one scenario but not in the other, the energy dissipation rates exhibit two types of scaling properties. This scaling classification has similarities and differences with D'Asaro and Lien's (2000) wave-turbulence transition model.Comment: 53 pages, 18 figures. This Work has been submitted to Journal of Physical Oceanography. Copyright in this Work may be transferred without further notic

Internal wave-vorticity coupling for an oscillating disk

International audienceIn a density-stratified fluid, viscosity couples internal waves with vertical vorticity. So far this coupling used to be neglected in analytical studies and only the viscous attenuation and spreading of the waves was taken into account, except in a very recent study of the oscillations of a horizontal circular disk (Davis & Llewellyn Smith, JFM 2010). We investigate the relations between the previous analytical approaches of the disk, considering either inviscid or viscous propagation of the waves and either free- or no-slip conditions at the disk, and compare their output with an original approach based on the boundary integral method. In particular, the role of the Stokes number is clarified. The analytical predictions are compared with contact measurements for vertical oscillations (Bardakov, Vasil'ev & Chashechkin, Fluid Dynamics 2007) and with original PIV measurements and visualizations for both vertical and horizontal oscillations

Fluctuations in out of equilibrium systems: from theory to experiment

Submitted to JSTATInternational audienceWe introduce from an experimental point of view the main concepts of fluctuation theorems for work, heat and entropy production in out of equilibrium systems. We will discuss the important difference between the applications of these concepts to stochastic systems and to a second class of systems (chaotic systems) where the fluctuations are induced either by chaotic flows or by fluctuating driving forces. We will mainly analyze the stochastic systems using the measurements performed in two experiments : a) a harmonic oscillator driven out of equilibrium by an external force b) a colloidal particle trapped in a time dependent double well potential. We will rapidly describe some consequences of fluctuation theorems and some useful applications to the analysis of experimental data. As an example the case of a molecular motor will be analyzed in some details. Finally we will discuss the problems related to the applications of fluctuation theorems to chaotic systems

Internal waves and boundary layer for an oscillating disc in a stratified fluid

International audienceInternal or baroclinic tides, namely internal waves generated in the ocean by the oscillation of the barotropic tide over bottom topography, exhibit a complex pattern of primary wave beams and secondary beams resulting from the interaction of the primary beams with themselves and with the boundary layer at the topography. In this context, the problem of an oscillating horizontal disc, however remote it may be from oceanic configurations, recently gained visibility as the only problem for which a full analytical solution may be found including both waves and the boundary layer (Davis & Llewellyn Smith 2010). To date, all available approaches used an approximate free-slip condition at the topography instead of the actual no-slip condition, thus eliminating the boundary layer. In this communication, we examine the relation between those approaches and compare them with original high-resolution experimental measurements. Specifically, we consider the vertical heaving oscillations of a horizontal circular disc and compare fully inviscid investigations where both the generation and propagation of the waves are inviscid – using either orthogonal curvilinear coordinates (Sarma & Krishna 1972), boundary integrals (Gabov & Pletner 1988) or eigenfunction expansions (Martin & Llewellyn Smith 2011, 2012) – with fully viscous investigations where both generation and propagation are viscous – using either the actual disc oscillating in free space (Davis & Llewellyn Smith 2010) or a fictitious baffled disc oscillating through an aperture in a horizontal plane (Chashechkin, Vasil'ev & Bardakov 2004; Bardakov, Vasil'ev & Chashechkin 2007). We discuss the relevance of an intermediate model where propagation is viscous but generation inviscid (as used recently for a sphere by Voisin, Ermanyuk & Flór 2011), as a function of the Reynolds-Stokes number. At all but very high values of this number (of order $10^5$ or more say), it appears that the presence of the boundary layer must be taken into account for accurate prediction of the waves

Internal waves and boundary layers in a density-stratified fluid

International audienceThe topic of internal gravity wave generation by oscillating bodies in density-stratified fluids has recently gained prominence owing to the importance of oceanic internal tides, generated by the oscillation of the barotropic tide over bottom topography, in the dynamics of the Earth-Moon system. To assess the role of the boundary condition at the body (in the ocean at the topography), we consider the only problem for which a full viscous solution is known: the oscillating circular disk. The inviscid theory, the full viscous theory (i.e. with viscous effects on both wave propagation and generation) and the partial viscous theory (i.e. with viscous effects on propagation alone) are compared with low-resolution conductimetric measurements from the literature and with new and original high-resolution PIV measurements. Viscous effects on propagation are required for prediction of the wave profiles; generation becomes free-slip at Stokes number over a million, and remains no-slip otherwise

Entropy production and time asymmetry in nonequilibrium fluctuations

The time-reversal symmetry of nonequilibrium fluctuations is experimentally investigated in two out-of-equilibrium systems namely, a Brownian particle in a trap moving at constant speed and an electric circuit with an imposed mean current. The dynamical randomness of their nonequilibrium fluctuations is characterized in terms of the standard and time-reversed entropies per unit time of dynamical systems theory. We present experimental results showing that their difference equals the thermodynamic entropy production in units of Boltzmann's constant

Energy cascade in internal wave attractors

One of the pivotal questions in the dynamics of the oceans is related to the cascade of mechanical energy in the abyss and its contribution to mixing. Here, we propose internal wave attractors in the large amplitude regime as a unique self-consistent experimental and numerical setup that models a cascade of triadic interactions transferring energy from large-scale monochro-matic input to multi-scale internal wave motion. We also provide signatures of a discrete wave turbulence framework for internal waves. Finally, we show how beyond this regime, we have a clear transition to a regime of small-scale high-vorticity events which induce mixing. Introduction