We report experiments on buoyant-thermocapillary instabilities in differentially heated liquid layers. The results are obtained for a fluid of Prandtl number 10 in a rectangular geometry with different aspect ratios. Depending on the height of liquid and on the aspect ratios, the two-dimensional basic flow destabilizes into oblique traveling waves or longitudinal stationary rolls, respectively, for small and large fluid heights. Temperature measurements and space-time recordings reveal the waves to correspond to the hydrothermal waves predicted by the linear stability analysis of Smith and Davis ͓J. Fluid Mech. 132, 119 ͑1983͔͒. Moreover, the transition between traveling and stationary modes agrees with the work by Mercier and Normand ͓Phys. Fluids 8, 1433 ͑1996͔͒ even if the exact characteristics of longitudinal rolls differ from theoretical predictions. A discussion about the relevant nondimensional parameters is included. In the stability domain of the waves, two types of sources have been evidenced. For larger heights, the source is a line and generally evolves towards one end of the container leaving a single wave whereas for smaller heights, the source looks like a point and emits a circular wave which becomes almost planar farther from the source in both directions.

International audienceWe study the nonlinear dynamics of hydrothermal waves produced by a surface-tension-driven convective flow in a long and thin annular channel heated from the side. Above onset, the supercritical traveling wave pattern undergoes a secondary instability: a supercritical Eckhaus instability. This leads to a small-wave-number phase-modulated nonlinear mode, and shows the first experimental evidence of a nonlinearly saturated phase instability mode for traveling wave patterns. At higher forcing level, this secondary pattern is subject to a tertiary instability. This mode is an amplitude mode characterized by traveling hole patterns, i.e., space-time defects that change the wave numbe

We present and analyze experimental results on the dynamics of hydrothermal waves occuring in a laterally-heated fluid layer. We argue that the large-scale modulations of the waves are governed by a one-dimensional complex Ginzburg-Landau equation (CGLE). We determine quantitatively all the coefficients of this amplitude equation using the localized amplitude holes observed in the experiment, which we show to be well described as Bekki-Nozaki hole solutions of the CGLE.Comment: 4 pages, uses RevTeX, 9 EPS figure

Waves appear in a liquid layer with a free surface if a sufficiently high horizontal temperature gradient is imposed. These waves have been compared to the hydrothermal waves predicted by a linear stability analysis of a parallel flow. However, depending on the experimental configurations, significant differences with theory are found. We show that there exists another kind of wave that cannot be explained by previous analysis. Our aim is to investigate which is the mechanism leading to this instability. Differential interferometry is used to obtain quantitative information on the temperature field. Experimental evidence is presented suggesting that these waves are the result of a boundary layer instability: the roll near the hot wall begins to oscillate, and the perturbations are dragged and amplified downflow. This mechanism could explain discrepancies between theory and some experimental observations.

We present experimental results for wave numbers q s selected in a thin horizontal fluid layer heated from below. The cylindrical sample had an interior section of uniform spacing d d 0 for radii r , r 0 (G 0 ϵ r 0 ͞d 0 43) and a ramp d͑r͒ for r . r 0 . For Rayleigh numbers R 0 . R c 1708 in the interior, straight or slightly curved rolls with an average ͗q s ͘ q c 1 ae 0 ͑e 0 ϵ R 0 ͞R c 2 1͒ and q c , q c 3.117 were selected, and q s varied on two length scales approximately equal to G 0 and to four roll wavelengths. For e & 0.03 and e * 0.18 the pattern repeatedly formed defects.

We present experimental results for pattern formation in a thin horizontal fluid layer heated from below. The fluid was SF 6 at a pressure of 20.0 bar with a Prandtl number of 0.87. The cylindrical sample had an interior section of uniform spacing d = d 0 for radii r < r 0 and a ramp d(r) for r > r 0 . For Rayleigh numbers R 0 > R c in the interior, straight or slightly curved rolls with an average wavenumber k s = kc + k 1 ε 0 (ε 0 ≡ R 0 /R c − 1) with k 1 0.8 were selected. The critical wavenumber kc depended sensitively on the cell spacing. For the largest kc the patterns were skewed-varicose unstable and dislocation pairs were generated repeatedly in the interior and for all ε. For slightly smaller kc time-independent rolls were stable for ε 0.15, but for larger ε the skewedvaricose instability was encountered near the sample centre and dislocation pairs were formed repeatedly for all samples. When stationary rolls were stable, their slight curvature and the width of their wavenumber distribution slowly increased with ε. This led to a complicated shape and overall broadening of the structure factor S(k). For ε 0.05 the inverse width ξ 2 of S(k) was roughly constant and presumably limited by the finite sample size, but for larger ε we found ξ 2 ∝ ε −0.5 .

is an 11th and 12th grade Physics Teacher at Saint Ursula Academy. She earned a PhD in Physics from the University of Paris XI and her teaching license through the Alternative Education License program from the University of Cincinnati. Her experiences include 4 years as a Post doctoral fellow (University of California, Santa Barbara and University of Cincinnati) and 7 years as a High school teacher. Michelle Beach, Midpark High School Michelle Beach is an 11th and 12th grade Physics/Chemistry Teacher in Cleveland Ohio. She earned her bachelors in Civil Environmental Engineering (2004) and her Masters in Secondary Education (2006) from the University of Cincinnati. Her experiences include 3 years as a National Science Foundation STEP Fellow were she taught in several Cincinnati Public Schools and 3 years as a high school science teacher in Cleveland. Jaswinder Dhillon, Withrow High School Jaswinder Dhillon teaches Mathematics at Withrow University High School in Cincinnati, OH. He has taught classes including Pre-Calculus, Algebra 2 and Algebra 1 to 9th-12th graders. This is his third year teaching at Withrow as well as his third year teaching overall. Jaswinder received a Bachelor's degree in Economics with a minor in Mathematics from University of California at Davis, along with a Master's in Sociology and Teaching Credentials from California State University of Hayward. He initially worked for six years as a Project Manager for multiple large online marketing firms in New York prior to becoming a teacher.