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| Author | : Torsten Seelig |
| Publisher | : |
| Total Pages | : 111 |
| Release | : 2014-09-08 |
| Genre | : |
| ISBN | : 9783954047932 |
| Author | : Abouzar Ghasemi |
| Publisher | : Cuvillier Verlag |
| Total Pages | : 140 |
| Release | : 2017-03-15 |
| Genre | : Science |
| ISBN | : 3736983689 |
The current work aims to contribute to our understanding of mean flow generation mechanisms in rotating fluids. The focus is on the mean flow generation mechanisms by: 1) centrifugally unstable Görtler vortices and 2) resonant excitation of inertial waves in a stable regime. Direct numerical simulations (DNS) of the fluid flow in a rotating annular container with longitudinally librating walls are used to investigate the mechanisms. Longitudinal libration of the cylinder side walls of an annulus induces in a supercritical regime an unstable Stokes boundary layer which generates Görtler vortices in a portion of a libration cycle, as a discrete event. DNS results show that these vortices propagate into the fluid bulk and generate an azimuthal mean flow. Reynolds-averaged Navier–Stokes (RANS) equations are used as a diagnostic tool to investigate generation mechanism of the azimuthal mean flow in the bulk. First, we explain, phenomenologically, how absolute angular momentum of the bulk flow is mixed and changed due to propagation of the Görtler vortices, causing a new vortex of basin scale size. Then we investigate the RANS equations for an intermediate time scale of the development of the Görtler vortices, and for a long time scale of the order of several libration periods. The former exhibits sign selection of the azimuthal mean flow. Investigating the latter, we predict that the azimuthal mean flow is proportional to the libration amplitude squared and to the inverse square root of the Ekman number and libration frequency. We confirm this using the numerical data. Additionally, presence of an upscale cascade of energy is shown, using kinetic energy budget of fluctuating flow. In the second part of the current study, we investigate the mean flow generation mechanism by intrinsic nonlinearity of the inertial wave beams and normal modes in a rotating annular cavity with longitudinally librating top and bottom lids in a stable regime. We confirm the generation of progressive inertial waves as localized shear layer and normal modes as standing waves at and close to the resonance frequencies. We focus on the low order inertial normal modes. Using the DNS results, we show that when the low order normal modes are excited, a non-geostrophic azimuthal mean flow is generated in the bulk. Following Tilgner (2007) and using analytical and DNS solutions, we identify the source terms responsible for generation of the azimuthal mean flow. We show that helical property of the inertial waves and normal modes causes the source terms. Using the analytical solution, we separate the inertial wave beams from the DNS solution. We show that at and close to the resonance frequency, libration phase of the normal modes is always following that of the inertial wave beam, and their phase lag depends on the libration frequency. Analogy to classical mechanics is commented. Generation efficiency of the mean flow is discussed with respect to the phase lag. Additionally, we address wave-wave and wave-boundary layer interactions, and dependency of the mean flow on the dimensionless parameters. We show that the results obtained are valid for small inclination of the inner cylinder side wall.
| Author | : Sandy Dahley |
| Publisher | : Cuvillier Verlag |
| Total Pages | : 118 |
| Release | : 2016-02-01 |
| Genre | : Science |
| ISBN | : 3736981988 |
Geo- und astrophysikalisch motivierte Strömungen, wie sie in der Atmosphäre, in den Ozeanen oder im Inneren von Planeten auftreten, lassen sich in rotierenden Experimenten mit homogenen Fluiden untersuchen. In dieser Arbeit werden Untersuchungen zu Trägheitswellen und Wellenattraktoren in einer Kugelschale und einem rechteckigen Tank gezeigt. Viele geophysikalische Anwendungen mit planetaren Skalen motivieren den Einsatz von sphärischen Geometrien. Mit dem Kugelspaltexperiment, bestehend aus zwei rotierenden konzentrisch angeordneten Kugelschalen, werden die Anregung und Ausbildung verschiedener Wellenphänomene sowie der internen Grenzschichten untersucht. Durch eine Modulation der Rotationsgeschwindigkeit an der Innenkugel in Form einer Sinuskurve werden Wellen erzeugt, die an den gekrümmten Rändern des Modells mehrfach reflektiert werden und somit bestimmten Bahnen folgen. Für den Vergleich mit numerischen Untersuchungen werden unterschiedliche Visualisierungen und Messtechniken spezifiziert. Die numerische Simulation erlaubt dabei die Untersuchung in Parameterbereichen mit Instabilitäten, die für die experimentelle Untersuchung schwer zugänglich sind.
| Author | : Henk Schuttelaars |
| Publisher | : Springer Nature |
| Total Pages | : 324 |
| Release | : 2022-11-30 |
| Genre | : Mathematics |
| ISBN | : 3031095596 |
Over the past few decades, numerical simulation has become instrumental in understanding the dynamics of seas, coastal regions and estuaries. The decision makers rely more and more frequently on model results for the management of these regions. Some modellers are insufficiently aware of the theoretical underpinning of the simulation tools they are using. On the other hand, a number of applied mathematicians tend to view marine sciences as a domain in which they would like to use the tools they have a good command of. Bridging the gap between model users and applied mathematicians is the main objective of the present book. In this respect a vast number of issues in which mathematics plays a crucial role will be addressed.
| Author | : Michael Hoff |
| Publisher | : Cuvillier Verlag |
| Total Pages | : 238 |
| Release | : 2017-10-08 |
| Genre | : Science |
| ISBN | : 3736986440 |
Many planetary bodies in our solar system consist of a solid inner and a liquid outer core, surrounded by a solid mantle. Planetary cores do not rotate constantly but undergo certain variations in the angular speed due to gravitational couplings. Such rotational background systems have a significant influence on the fluid in the interior of planets and stars. It is worth to know the interaction between the core rotation and the interior of the fluid to understand tidal heating, fluid mixing, or the generation of magnetic fields. An opportunity to explore aspects of the dynamics in planetary cores is to do laboratory experiments. The present work focuses on experiments in a rapidly rotating fluid between two spherical shells. A common feature arising in such systems is the occurrence of inertial waves, which are Coriolis-restored propagating internal oscillations. In a system where the inner sphere oscillates around a mean angular speed, inertial waves appear as plane waves. Their excitation efficiency and reflection behavior at inclined walls as well as their tendency to form wave attractors is investigated. In a system where the spheres rotate differentially, so-called global inertial modes arise. Besides the investigation of mode excitation, structure and interaction, the present study reveals a new secondary instability of inertial modes characterized by a clear transition to small-scale turbulence. Finally, the formation of the Stewartson layer is investigated for both forcing systems. Especially the shear instability of the Stewartson layer leads to wave motions, so-called Rossby waves, whose very particular properties in the spherical gap are studied. It is found that these Rossby waves play a crucial role for mode selection in a rapidly rotating fluid between spherical shells.
| Author | : Andreas Keiling |
| Publisher | : John Wiley & Sons |
| Total Pages | : 325 |
| Release | : 2024-05-07 |
| Genre | : Science |
| ISBN | : 1394195958 |
An interdisciplinary review of recent advances in Alfvén wave research Alfvén waves are fundamental to the dynamics of space plasmas. Recent advances in our knowledge about Alfvén waves have come from several directions, including new space missions to unexplored heliospheric regions, sophisticated rocket campaigns in the auroral zone, enlarged magnetometer arrays and radar networks, and significant advances in computer modeling. Alfvén Waves Across Heliophysics: Progress, Challenges, and Opportunities is an interdisciplinary collaboration from different space science communities to review recent and current Alfvén wave research. Volume highlights include: Alfvén waves in the solar atmosphere Alfvén waves at the giant planets Alfvén waves at Mars Alfvén waves in moon-magnetosphere systems Alfvén waves in geospace Alfvén waves in the laboratory The American Geophysical Union promotes discovery in Earth and space science for the benefit of humanity. Its publications disseminate scientific knowledge and provide resources for researchers, students, and professionals.
| Author | : Dave Broutman |
| Publisher | : |
| Total Pages | : 166 |
| Release | : 1982 |
| Genre | : Internal waves |
| ISBN | : |
Two approaches are used to explore the effects of shear on short-wavelength internal waves. In the first, the Taylor-Goldstein equation is solved exactly. The solutions reveal the inaccuracy of WKB predictions when applied to a curved velocity profile with a minimum Richardson number of order unity. To investigate internal waves in an inertial current, ray calculations are made. This second approach reveals that the process of refractive convergence, which includes the critical-layer interaction as a special case, operates at virtually all phases of the inertial oscillation and affects short waves of nearly al frequencies. It is also found, in contrast to the results of steady shear analyses, that short waves with phase speeds less that the mean flow maximum can propagate for several inertial periods without becoming unstable, and conversely that waves with initial phase speeds of two or three times the mean flow maximum can quickly become focussed to unstably high amplitudes. The final section examines the mean flow induced by three-dimensional, low-frequency, internal wave packets. Rotation alters the character of the flow so that the mean momentum is not equal to E/c, where c is the horizontal phase speed of the short waves and E is the intrinsic energy density. The generation of inertial waves by the internal wave field as found by Hasselmann (1970) for a wave field that is statistically homogeneous in the horizontal, is not predicted by a calculation that incorporates horizontal variations.
| Author | : Keke Zhang |
| Publisher | : Cambridge University Press |
| Total Pages | : 541 |
| Release | : 2017-05-23 |
| Genre | : Science |
| ISBN | : 1108293468 |
A systematic account of the theory and modelling of rotating fluids that highlights the remarkable advances in the area and brings researchers and postgraduate students in atmospheres, oceanography, geophysics, astrophysics and engineering to the frontiers of research. Sufficient mathematical and numerical detail is provided in a variety of geometries such that the analysis and results can be readily reproduced, and many numerical tables are included to enable readers to compare or benchmark their own calculations. Traditionally, there are two disjointed topics in rotating fluids: convective fluid motion driven by buoyancy, discussed by Chandrasekhar (1961), and inertial waves and precession-driven flow, described by Greenspan (1968). Now, for the first time in book form, a unified theory is presented for three topics - thermal convection, inertial waves and precession-driven flow - to demonstrate that these seemingly complicated, and previously disconnected, problems become mathematically simple in the framework of an asymptotic approach that incorporates the essential characteristics of rotating fluids.
| Author | : |
| Publisher | : |
| Total Pages | : 864 |
| Release | : 1985 |
| Genre | : Mechanics, Applied |
| ISBN | : |
| Author | : |
| Publisher | : |
| Total Pages | : 316 |
| Release | : 1991 |
| Genre | : Aeronautics |
| ISBN | : |
