Numerical and experimental study of inertia-gravity waves in the differentially heated rotating annulus

International audienceThe occurrence and source mechanism of inertia-gravity waves (IGWs) are studied in the differentially heated rotating annulus via laboratory experiments (BTU) and numerical simulations (GUF). Two differentially heated rotating annulus experiments are used for this purpose at the BTU laboratories. The first is a modified version of the classical baroclinic experiment in which a juxtaposition of convective and motionless stratified layers can be created by introducing a vertical salt stratification. The thermal convective motions are suppressed in a central region at mid depth of the rotating tank, therefore baroclinic waves can only build up in thin layers located at the top and bottom, where the salt stratification is weakest. This new experimental setup, coined "barostrat instabil-ity", allows to study the exchange of momentum and energy between the layers, especially by the propagation of IGWs. Moreover, in contrast to the classical tank without salt stratification we have layers with N/f > 1. A ratio larger than unity implies that the IGW propagation in the experiment is expected to be qualitatively similar to the atmospheric case. Interestingly, we found local IGW packets along the jets in the surface and bottom layers where the local Rossby number is larger than 1, suggesting spontaneous imbalance as generating mechanism [1], and not boundary layer instability [2]. Theoretical considerations and numerical simulations have led to the identification of an annulus configuration, much wider and shallower, with a much larger temperature difference between the inner and outer cylinder walls, which is more atmosphere-like since it shows an N / f >1 even without the vertical salt stratification. Flow regime stability has been tested for this new differentially heated rotating annulus and compared with findings from the small tank. In view of the different geometries of the two experimental systems, their correspondence was excellent with respect to the large-scale. Moreover, direct numerical simulations were performed (GUF) for this atmosphere-like configuration of the experiment and possible regions of IGW activity were characterised by a Hilbert-transform algorithm. The simulations show a clear baroclinic wave structure exhibiting a realistic jet-front system superimposed by small-scale structures which are associated with IGWs occurring in wave packets [3]. The comparison of observations from a corresponding big tank experiment with numerical simulation shows that for both cases (as we already observed in the barostrat experiment), small scale wave packets are clearly correlated with an increased local Rossby number

The linear instability of the stratified plane Poiseuille flow

International audienceIn the non stratified case, plane Poiseuille flow is known to be linearly unstable for Reynolds numbers larger than 5572. Above this value, two dimensional waves-known as Tollmien-Schlichting waves-are viscously unstable and can propagate in the flow.We present here the stability analysis of a plane Poiseuille flow which is stably stratified in density along the vertical direction, i.e. orthogonal to the horizontal shear. Density stratification is ubiquitous in nature and we may think here to water flows in submarine canyons, to winds in valleys or to laminar flows in rivers or canals where stratification can be due to temperature or salinity gradients. Our study is based on laboratory experiments, on a linear stability analysis and on direct numerical simulations. This study follows recent investigations of instabilities in stratified rotating or non rotating shear flows: the stratorotational instability [1,2], the stratified boundary layer instability [3] or the stratified Plane Couette flow instability [4] where it is shown that these instabilities belong to a class of instabilities caused by the resonant interaction of Doppler shifted internal gravity waves. A particularity of the present case is that for the Poiseuille flow, Tollmien-Schlichting waves can also interact and possibly resonate with non viscous gravity waves. The experiments are realized in an annular channel having an inner diameter of 1.4 m and a rectangular vertical section of 85 x 200 mm 2. This channel is filled up to a level of 130 mm (position of the free surface) with salt stratified water using the classical double bucket technique. The free surface fluid is then entrained by the side and bottom walls of the canal when this one is set into slow rotation. However, a barrier, placed radially inside the channel, blocks the fluid, prohibiting solid body rotation and resulting in a nearly parabolic horizontal velocity profile. Visualizations and PIV measurements show the appearance of a stationary (versus the laboratory frame) braided pattern of waves above a given threshold that depends on the Reynolds and Froude numbers (Re c ∼ 2000, F r c ∼ 0.5). The comparison with the theoretical threshold and the critical wavenumbers calculated by linear analysis is excellent. Finally, direct numerical simulations permit to complete the description of this instability that can be interpreted as a resonant interaction of boundary trapped waves

ARTÍLES VIAT, Mª DEL CARMEN [Material gráfico]

Copia digital. Madrid : Ministerio de Educación, Cultura y Deporte, 201

IMA10: interfacial fluid dynamics and processes

IMA10–special issue presents recent advances on interfacial fluid dynamics with applications in microfluidics, biology, engineering and geophysics

Surface instability on thin fluid layers of a binary mixture

A long-wave model for thin layers consisting of two miscible fluids is presented. The model is a development of a simplified 2D model variant which considers the temperature and the concentration fields as linear functions on the vertical coordinate and neglect the convective terms from the corresponding equations. Now, the 2D thin film equation is coupled to complete 3D energy and mass conservations equation. We discuss the extended system in the linear approximation and in the initial nonlinear stage

Phys. Rev. Fluids

Based on the conservative phase field model developed by Lowengrub and Truskinovsky [Proc. R. Soc. London A 454, 2617 (1998)] for almost incompressible liquid binary mixtures, we propose an extended scheme for studying immiscible/miscible liquids. Below a critical temperature Tc, the liquids are immiscible with separating interfaces. Above Tc, the interfacial effects vanish, and the liquids become perfectly miscible. The free-energy density of the system depends not only on the phase field variable ϕ (which describes the system composition), but also on the reduced temperature r=(Tc−T)/Tc which measures the distance to the critical point described by Tc. The free energy suffers transformations through Tc in a way to permit a two-phase system in the subcritical (immiscible) regime and a monophase in the supercritical (miscible) regime. Numerical simulations in two spatial dimensions have been performed for isothermal problems (with r as control parameter) as well as for nonisothermal problems with the energy equation describing the temperature distribution. These simulations reveal the behavior of liquid mixtures and droplet coalescence placed in temperature gradients with temperatures continuously varying from TTc, problems that could be of large interest in phase transitions in micro- and nanofluidics

Dancing drops over vibrating substrates

We study the motion of a liquid drop on a solid plate simultaneously submitted to horizontal and vertical harmonic vibrations. The investigation is done via a phase field model earlier developed for describing static and dynamic contact angles. The density field is nearly constant in every bulk region (ρ = 1 in the liquid phase, ρ ≈ 0 in the vapor phase) and varies continuously from one phase to the other with a rapid but smooth variation across the interfaces. Complicated explicit boundary conditions along the interface are avoided and captured implicitly by gradient terms of ρ in the hydrodynamic basic equations. The contact angle θ is controlled through the density at the solid substrate ρS, a free parameter varying between 0 and 1 [R. Borcia, I.D. Borcia, M. Bestehorn, Phys. Rev. E 78, 066307 (2008)]. We emphasize the swaying and the spreading modes, earlier theoretically identified by Benilov and Billingham via a shallow-water model for drops climbing uphill along an inclined plane oscillating vertically [E.S. Benilov, J. Billingham, J. Fluid Mech. 674, 93 (2011)]. The numerical phase field simulations will be completed by experiments. Some ways to prevent the release of the dancing drops along a hydrophobic surface into the gas atmosphere are also discussed in this paper

Wetting properties of LIPSS structured silicon surfaces

The controlled dynamics of liquid drops via generation of specific wetting states on a solid surface is of great interests both in the fundamental and applied sciences. Considering that the wettability is strongly dependent on the surface topography and surface roughness, we investigate – through experiments and theory – the effect of laser-induced periodic surface structures (LIPSS) generated on silicon (100) targets as a control parameter of wetting properties. To obtain structured silicon surfaces with different morphological features, we patterned the surface by irradiation with femtosecond pulses from an amplified Ti:Sapphire laser system (790 nm/100 fs/1 kHz) at a fluence in the range of 0.4–1.2 J/cm2 on a spot with a diameter about of 100 μm. Variation of the applied irradiation dose results in surface modifications with the roughness about of a few tens of nanometers are ranging from regular LIPSS patterns with the lateral period of about 500–700 nm to complex agglomerations of 3-D microstructures with several-μm feature size. The theoretical study on the correlation of wetting properties with the surface topography has been performed within a phase field model. We found an excellent agreement of numerical results with experiments