Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 11 of 11
Full-Text Articles in Physical Sciences and Mathematics
Thermal And Viscous Boundary Layers In Turbulent Rayleigh–Bénard Convection, Janet Scheel, E. Kim, K. White
Thermal And Viscous Boundary Layers In Turbulent Rayleigh–Bénard Convection, Janet Scheel, E. Kim, K. White
Janet D. Scheel
We present the results from numerical simulations of turbulent Rayleigh–Bénard convection for an aspect ratio (diameter/height) of 1.0, Prandtl numbers of 0.4 and 0.7, and Rayleigh numbers from $1\ensuremath{\times} 1{0}^{5} $ to $1\ensuremath{\times} 1{0}^{9} $. Detailed measurements of the thermal and viscous boundary layer profiles are made and compared to experimental and theoretical (Prandtl–Blasius) results. We find that the thermal boundary layer profiles disagree by more than 10 % when scaled with the similarity variable (boundary layer thickness) and likewise disagree with the Prandtl–Blasius results. In contrast, the viscous boundary profiles collapse well and do agree (within 10 %) with …
Patterns In Rotating Rayleigh–Bénard Convection At High Rotation Rates, Janet Scheel, P. Mutyaba, T. Kimmel
Patterns In Rotating Rayleigh–Bénard Convection At High Rotation Rates, Janet Scheel, P. Mutyaba, T. Kimmel
Janet D. Scheel
We present the results from numerical and theoretical investigations of rotating Rayleigh–Bénard convection for relatively large dimensionless rotation rates, 170 < Ω < 274, and a Prandtl number of 6.4. Unexpected square patterns were found experimentally by Bajaj et al. (Phys. Rev. Lett., vol. 81, 1998, p. 806) in this parameter regime and near threshold for instability in the bulk. These square patterns have not yet been understood theoretically. Sánchez-Álvarez et al. (Phys. Rev. E, vol. 72, 2005, p. 036307) have found square patterns in numerical simulations for similar parameters when only the Coriolis force is included. We performed detailed numerical studies …
Onset Of Rayleigh-Bénard Convection In Cylindrical Containers, Janet Scheel, Francois Herbert, Ryan Hufschmid, Guenter Ahlers
Onset Of Rayleigh-Bénard Convection In Cylindrical Containers, Janet Scheel, Francois Herbert, Ryan Hufschmid, Guenter Ahlers
Janet D. Scheel
We determined the critical Rayleigh numbers Rac for the onset of convection in cylindrical containers with aspect ratios 1≲Γ≡D/L≲9 (D is the diameter and L the height) and the patterns that form just above Rac, both from experiment and by direct numerical simulation (DNS). Results for Rac agree well with the linear stability analysis by Buell and Catton for containers with finite sidewall conductivity. For Γ≤1.58±0.10, we found that the patterns correspond to an azimuthal Fourier mode with mode number m=1, corresponding to a single convection roll. For 1.58≲Γ≲3.26±0.02, the pattern was a concentric roll, corresponding to m=0. For 3.26≤Γ≲4, …
The Amplitude Equation For Rotating Rayleigh–Bénard Convection, Janet Scheel
The Amplitude Equation For Rotating Rayleigh–Bénard Convection, Janet Scheel
Janet D. Scheel
The amplitude equation for rotating Rayleigh–Bénard convection is derived from the Boussinesq equations with the Coriolis force included. The vertical boundary conditions are no-slip, and the lateral boundary conditions are either periodic or rigid. In order to keep track of the mean flow, the full system of equations is considered, instead of a potential formulation. A multiple scales perturbation expansion in the control parameter ϵ is performed, and appropriate solvability conditions are imposed. This leads to the usual amplitude equation at order ϵ3/2, but a new rotation term enters at order ϵ7/4. This rotation term will cause a change of …
Lyapunov Exponents For Small Aspect Ratio Rayleigh-Benard Convection, Janet Scheel, M. Cross
Lyapunov Exponents For Small Aspect Ratio Rayleigh-Benard Convection, Janet Scheel, M. Cross
Janet D. Scheel
Leading order Lyapunov exponents and their corresponding eigenvectors have been computed numerically for small aspect ratio, three-dimensional Rayleigh-Benard convection cells with no-slip boundary conditions. The parameters are the same as those used by Ahlers and Behringer [Phys. Rev. Lett. 40, 712 (1978)] and Gollub and Benson [J. Fluid Mech. 100, 449 (1980)] in their work on a periodic time dependence in Rayleigh-Benard convection cells. Our work confirms that the dynamics in these cells truly are chaotic as defined by a positive Lyapunov exponent. The time evolution of the leading order Lyapunov eigenvector in the chaotic regime will also be discussed. …
Characterization Of The Domain Chaos Convection State By The Largest Lyapunov Exponent, Janet Scheel, A. Jayaraman, H. Greenside, P. Fischer
Characterization Of The Domain Chaos Convection State By The Largest Lyapunov Exponent, Janet Scheel, A. Jayaraman, H. Greenside, P. Fischer
Janet D. Scheel
Using numerical integrations of the Boussinesq equations in rotating cylindrical domains with realistic boundary conditions, we have computed the value of the largest Lyapunov exponent λ1 for a variety of aspect ratios and driving strengths. We study in particular the domain chaos state, which bifurcates supercritically from the conducting fluid state and involves extended propagating fronts as well as point defects. We compare our results with those from Egolf et al., [Nature 404, 733 (2000)], who suggested that the value of λ1 for the spiral defect chaos state of a convecting fluid was determined primarily by bursts of instability arising …
Effect Of The Centrifugal Force On Domain Chaos In Rayleigh-Bénard Convection, Janet Scheel, N. Becker, M. Cross, G. Ahlers
Effect Of The Centrifugal Force On Domain Chaos In Rayleigh-Bénard Convection, Janet Scheel, N. Becker, M. Cross, G. Ahlers
Janet D. Scheel
Experiments and simulations from a variety of sample sizes indicated that the centrifugal force significantly affects the domain-chaos state observed in rotating Rayleigh-Bénard convection-patterns. In a large-aspect-ratio sample, we observed a hybrid state consisting of domain chaos close to the sample center, surrounded by an annulus of nearly stationary nearly radial rolls populated by occasional defects reminiscent of undulation chaos. Although the Coriolis force is responsible for domain chaos, by comparing experiment and simulation we show that the centrifugal force is responsible for the radial rolls. Furthermore, simulations of the Boussinesq equations for smaller aspect ratios neglecting the centrifugal force …
Scaling Laws For Rotating Rayleigh-Bénard Convection, Janet Scheel, M. Cross
Scaling Laws For Rotating Rayleigh-Bénard Convection, Janet Scheel, M. Cross
Janet D. Scheel
Numerical simulations of large aspect ratio, three-dimensional rotating Rayleigh-Bénard convection for no-slip boundary conditions have been performed in both cylinders and periodic boxes. We have focused near the threshold for the supercritical bifurcation from the conducting state to a convecting state exhibiting domain chaos. A detailed analysis of these simulations has been carried out and is compared with experimental results, as well as predictions from multiple scale perturbation theory. We find that the time scaling law agrees with the theoretical prediction, which is in contradiction to experimental results. We also have looked at the scaling of defect lengths and defect …
Traveling Waves In Rotating Rayleigh-Bénard Convection: Analysis Of Modes And Mean Flow, Janet Scheel, M. Paul, P. Fishcer
Traveling Waves In Rotating Rayleigh-Bénard Convection: Analysis Of Modes And Mean Flow, Janet Scheel, M. Paul, P. Fishcer
Janet D. Scheel
Numerical simulations of the Boussinesq equations with rotation for realistic no-slip boundary conditions and a finite annular domain are presented. These simulations reproduce traveling waves observed experimentally. Traveling waves are studied near threshhold by using the complex Ginzburg-Landau equation (CGLE): a mode analysis enables the CGLE coefficients to be determined. The CGLE coefficients are compared with previous experimental and theoretical results. Mean flows are also computed and found to be more significant as the Prandtl number decreases (from σ=6.4 to σ=1). In addition, the mean flow around the outer radius of the annulus appears to be correlated with the mean …
Analytical Mechanics, Janet Scheel, Louis Hand
Using An E-Mail Tutorial And Student Seminars To Improve An Intermediate-Level Undergraduate Physics Course, Janet Scheel
Using An E-Mail Tutorial And Student Seminars To Improve An Intermediate-Level Undergraduate Physics Course, Janet Scheel
Janet D. Scheel
The authors revised the junior-level classical mechanics course at Cornell University to incorporate asynchronous, autonomous, and group learning. We created an E-mail tutorial and a student seminar. We will first discuss the theoretical background for these changes and then describe the results of their implementation over a period of three years.