Fundamentals of the Theory of Rotating Fluids

1963 ◽  
Vol 30 (4) ◽  
pp. 481-485 ◽  
Author(s):  
L. N. Howard
Keyword(s):  
Fluid Dynamics ◽  
Boundary Layer ◽  
Mathematical Models ◽  
Rotating Flows ◽  
Laboratory Studies ◽  
Geophysical Fluid Dynamics ◽  
Rotating Fluids ◽  
Ekman Boundary Layer ◽  
Physical Phenomena

This paper gives an expository survey of some of the principal mathematical models which have been used in the theory of rotating fluids, together with a discussion of several explicit examples. Some of these examples are related to geophysical fluid dynamics; others more directly to laboratory studies. In all cases the examples have been selected to illustrate some of the most important physical phenomena which are characteristic of rotating flows and distinguish them from other fluid motions. Physical concepts, such as the Taylor-Proudman effects, the Ekman boundary layer, and Rayleigh’s analogy, which have proved useful in obtaining a general understanding of rotating fluids, are presented and discussed.

Laboratory studies of equatorially trapped waves using ferrofluid

1997 ◽  
Vol 338 ◽  
pp. 35-58 ◽  
Author(s):  
DANIEL R. OHLSEN ◽  
PETER B. RHINES
Keyword(s):  
Fluid Dynamics ◽  
Rotation Rate ◽  
Large Scale ◽  
Rossby Waves ◽  
Low Frequency ◽  
Laboratory Studies ◽  
Geophysical Fluid Dynamics ◽  
Vertical Projection ◽  
Planetary Rotation ◽  
Oceanic Flows

We introduce a new technique to model spherical geophysical fluid dynamics in the terrestrial laboratory. The local vertical projection of planetary vorticity, f, varies with latitude on a rotating spherical planet and allows an important class of waves in large-scale atmospheric and oceanic flows. These Rossby waves have been extensively studied in the laboratory for middle and polar latitudes. At the equator f changes sign where gravity is perpendicular to the planetary rotation. This geometry has made laboratory studies of geophysical fluid dynamics near the equator very limited. We use ferrofluid and static magnetic fields to generate nearly spherical geopotentials in a rotating laboratory experiment. This system is the laboratory analogue of those large-scale atmospheric and oceanic flows whose horizontal motions are governed by the Laplace tidal equations. As the rotation rate in such a system increases, waves are trapped to latitudes near the equator and the dynamics can be formulated on the equatorial β-plane. This transition from planetary modes to equatorially trapped modes as the rotation rate increases is observed in the experiments. The equatorial β-plane solutions of non-dispersive Kelvin waves propagating eastward and non-dispersive Rossby waves propagating westward at low frequency are observed in the limit of rotation fast compared to gravity wave speed.

Interdisciplinary Research Programs in Geophysical Fluid Dynamics

2006 ◽  
Author(s):  
John A. Whitehead ◽  
Neil J. Balmforth ◽  
Philip J. Morrison
Keyword(s):  
Fluid Dynamics ◽  
Interdisciplinary Research ◽  
Geophysical Fluid Dynamics ◽  
Research Programs

Interdisciplinary Research Programs in Geophysical Fluid Dynamics

2008 ◽  
Author(s):  
John A. Whitehead ◽  
Neil J. Balmforth ◽  
Philip J. Morrison
Keyword(s):  
Fluid Dynamics ◽  
Interdisciplinary Research ◽  
Geophysical Fluid Dynamics ◽  
Research Programs

Analysis of an Airfoil Using a Transition and Turbulence Model

2016 ◽  
Vol 819 ◽  
pp. 356-360
Author(s):  
Mazharul Islam ◽  
Jiří Fürst ◽  
David Wood ◽  
Farid Nasir Ani
Keyword(s):  
Fluid Dynamics ◽  
Boundary Layer ◽  
Computational Fluid Dynamics ◽  
Kinetic Energy ◽  
Turbulence Model ◽  
Original Version ◽  
Transitional Region ◽  
Cfd Analysis ◽  
Computational Fluid Dynamics Cfd

In order to evaluate the performance of airfoils with computational fluid dynamics (CFD) tools, modelling of transitional region in the boundary layer is very critical. Currently, there are several classes of transition-based turbulence model which are based on different methods. Among these, the k-kL- ω, which is a three equation turbulence model, is one of the prominent ones which is based on the concept of laminar kinetic energy. This model is phenomenological and has several advantageous features. Over the years, different researchers have attempted to modify the original version which was proposed by Walter and Cokljat in 2008 to enrich the modelling capability. In this article, a modified form of k-kL-ω transitional turbulence model has been used with the help of OpenFOAM for an investigative CFD analysis of a NACA 4-digit airfoil at range of angles of attack.

scholarly journals Heat transfer in rotating Rayleigh–Bénard convection with rough plates

2017 ◽  
Vol 830 ◽  
Author(s):  
Pranav Joshi ◽  
Hadi Rajaei ◽  
Rudie P. J. Kunnen ◽  
Herman J. H. Clercx
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Ekman Layer ◽  
Ekman Pumping ◽  
Ekman Boundary Layer ◽  
Bénard Convection ◽  
Roughness Elements ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

This experimental study focuses on the effect of horizontal boundaries with pyramid-shaped roughness elements on the heat transfer in rotating Rayleigh–Bénard convection. It is shown that the Ekman pumping mechanism, which is responsible for the heat transfer enhancement under rotation in the case of smooth top and bottom surfaces, is unaffected by the roughness as long as the Ekman layer thickness $\unicode[STIX]{x1D6FF}_{E}$ is significantly larger than the roughness height $k$. As the rotation rate increases, and thus $\unicode[STIX]{x1D6FF}_{E}$ decreases, the roughness elements penetrate the radially inward flow in the interior of the Ekman boundary layer that feeds the columnar Ekman vortices. This perturbation generates additional thermal disturbances which are found to increase the heat transfer efficiency even further. However, when $\unicode[STIX]{x1D6FF}_{E}\approx k$, the Ekman boundary layer is strongly perturbed by the roughness elements and the Ekman pumping mechanism is suppressed. The results suggest that the Ekman pumping is re-established for $\unicode[STIX]{x1D6FF}_{E}\ll k$ as the faces of the pyramidal roughness elements then act locally as a sloping boundary on which an Ekman layer can be formed.

Sign in / Sign up

Export Citation Format

Share Document