Hydrodynamic reactions on a small body with surface undergoing deformation in an ideal incompressible fluid when the flow is three dimensional and irrotational or two dimensional with uniform vorticity

1980 ◽  
Vol 15 (2) ◽  
pp. 210-216
Author(s):  
S. D. Vil'khovchenko ◽  
Yu. L. Yakimov
Keyword(s):  
Incompressible Fluid ◽  
Small Body ◽  
Three Dimensional ◽  
Ideal Incompressible Fluid ◽  
Two Dimensional

INCOMPRESSIBLE FLUIDS

2005 ◽  
Vol 20 (27) ◽  
pp. 6122-6132 ◽  
Author(s):  
S. G. RAJEEV
Keyword(s):  
Fluid Flow ◽  
Incompressible Fluid ◽  
Quantum Groups ◽  
Three Dimensional ◽  
Incompressible Fluids ◽  
Two Dimensional ◽  
Incompressible Fluid Flow ◽  
Fluid System ◽  
Random Forces ◽  
Turbulent Incompressible Fluid

We propose a model for random forces in a turbulent incompressible fluid by balancing the energy gain from fluctuations against dissipation by viscosity. This leads to a more singular covariance distribution for the random forces than is ordinarily allowed. We then propose regularization of the fluid system by matrix models. A formula for entropy of a two dimensional fluid is derived and then a vorticity profile of a hurricane that maximizes entropy. A regularization of three dimensional incompressible fluid flow using quantum groups is also proposed.

Vortex ring eigen-oscillations as a source of sound

1997 ◽  
Vol 341 ◽  
pp. 19-57 ◽  
Author(s):  
V. F. KOPIEV ◽  
S. A. CHERNYSHEV
Keyword(s):  
Incompressible Fluid ◽  
Vortex Ring ◽  
Compressible Fluid ◽  
Acoustic Radiation ◽  
Three Dimensional ◽  
Sound Radiation ◽  
Complex Form ◽  
Ideal Incompressible Fluid ◽  
Dimensionless Frequency ◽  
Weakly Compressible

Two coupled problems are investigated: a complete description of long-wave vortex ring oscillations in an ideal incompressible fluid, and an examination of sound radiation by these oscillations in a weakly compressible fluid.The first part of the paper relates to the problem of eigen-oscillations of a thin vortex ring (μ[Lt ]1) in an ideal incompressible fluid. The solution of the problem is obtained in the form of an asymptotic expansion in the small parameter μ. The complete set of three-dimensional eigen-oscillations and axisymmetric modes (two-dimensional oscillations) is obtained. It is shown that, unlike the vortex column oscillations which have the form of simple angular harmonics, the majority of eigen-oscillations of a thin vortex ring have a more complex form which is a combination of two harmonics in the leading approximation. This leads to dramatic changes in the efficiency of sound radiation produced by modes of the vortex ring in comparison with the corresponding modes of the vortex column.In the second part of the paper the solution obtained is used to investigate the process of sound radiation by vortex perturbations in a weakly compressible fluid. The vortex ring eigen-oscillations are classified according to their sound radiation efficiency. It is shown that the modes with the dimensionless frequency ω≈1/2 radiate sound most efficiently. They are two isolated modes, two infinite families of Bessel modes and a set of axisymmetric modes. The frequencies of these modes are in the interval Δω=O(μ).The results obtained are compared with known experimental data on acoustic radiation of a turbulent vortex ring. Within the limits of the theory derived an explanation of the main characteristics of sound radiation is presented.

Experimental studies on the motion of a flexible hydrofoil

1964 ◽  
Vol 19 (1) ◽  
pp. 30-48 ◽  
Author(s):  
H. R. Kelly ◽  
A. W. Rentz ◽  
J. Siekmann
Keyword(s):  
Error Analysis ◽  
Incompressible Fluid ◽  
Experimental Verification ◽  
Experimental Studies ◽  
Ideal Incompressible Fluid ◽  
Two Dimensional ◽  
Typical Data

A thin, flexible hydrofoil has been used as a model to simulate the swimming of a two-dimensional fish in an ideal, incompressible fluid, as treated in recent theoretical papers. The apparatus is described in some detail and typical data are compared with the predictions of theory. An error analysis is given, showing that, within the expected errors and limits of validity of theory, experimental verification of theory is very good.

Mapping a Duck: Geological Features and Region Definitions on Comet 67P/Churyumov-Gerasimenko

2021 ◽  
Author(s):  
Björn Grieger ◽  
Mireia Leon-Dasi ◽  
Sebastien Besse ◽  
Michael Küppers
Keyword(s):  
Small Body ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Map Projection ◽  
Complete Surface ◽  
Narrow Angle ◽  
Mapping Tool ◽  
Geological Features ◽  
Comet 67P

<p>The data from the Rosetta mission enabled the reconstruction of the shape of comet 67P/Churyumov-Gerasimenko (hereafter 67P) and the identification of the terrains and features forming its surface. The highly irregular  shape of the comet poses a challenge for the depiction of these geological features on two-dimensional maps. Standard global map projections cannot display the complete surface of 67P because different points on the surface can have the same longitude and latitude.  As a consequence, the geological maps published to date are  created on top of comet images, making them dependent on the viewing angle and image coverage and resolution.</p><p>Here, we make use of the recently published Quincuncial Adaptive Closed Kohonen (QuACK) map. It projects the complete surface of 67P unambiguously onto a square. The QuACK map is topologically equivalent to the Peirce quincuncial projection of the world, which makes it  possible to define generalized longitudes and latitudes. These can be used within any global map projection in order to obtain an  unambiguous QuACK version.</p><p>The mapping of geological features is carried out in three dimensions employing the Small Body Mapping Tool (SBMT). We use images from  the OSIRIS Narrow Angle Camera aboard Rosetta which have been projected onto the shape model of the SBMT. The three-dimensional coordinates are then projected onto two-dimensional maps, either in the QuACK map projection or in the QuACK version of  the equidistant cylindrical projection. We present individual maps for 17 of the 26 regions of 67P, mostly located in the northern  hemisphere. The new maps combine features published in previous studies with newly identified features.</p><p>We discuss the distribution of geological features and the characteristics of the regions. In order to align region boundaries with geological features, we propose two modifications of region definitions.</p>

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