The vortex line in steady, incompressible Oseen flow

2005 ◽  
Vol 462 (2066) ◽  
pp. 391-401 ◽  
Author(s):  
Edmund Chadwick
Keyword(s):  
Velocity Field ◽  
Vortex Line ◽  
Horseshoe Vortex ◽  
Transverse Plane ◽  
Far Field ◽  
Two Dimensional ◽  
Streamwise Direction ◽  
Oseen Flow ◽  
Laminar Wake ◽  
Oseen Vortex

The horseshoe vortex is given in Oseen flow as a constant spanwise distribution of lift Oseenlets. From this, the vortex line is represented in steady, incompressible Oseen flow. The velocity near to the vortex line is determined, as well as near to and far from the far field wake. The velocity field in the transverse plane near to the vortex line is shown to approximate to the two-dimensional Lamb–Oseen vortex, and the velocity field in the streamwise direction is generated by the bound vortex line of the horseshoe vortex giving a streamwise decay much faster than that of the Batchelor vortex. The far field wake description is shown to be consistent with laminar wake theory.

Effects of Heating on Two-Dimensional Mixing Layers

1997 ◽  
Vol 119 (3) ◽  
pp. 180-183
Author(s):  
N. Butuk ◽  
S. R. Gollahalli
Keyword(s):  
Velocity Field ◽  
Shear Layer ◽  
Room Temperature ◽  
Shear Layers ◽  
Mixing Layers ◽  
Two Dimensional ◽  
Horizontal Shear ◽  
Streamwise Direction ◽  
The Mean

Transverse profiles of temperature and the mean velocities in the streamwise direction in a horizontal shear layer are presented. The variation of vorticity thickness along the streamwise coordinate is examined for the cases when both streams were at room temperature and when the top stream was heated to 360 K. The similarity of the velocity field is observed only near the plane of the interface of the two streams in both cases. The vorticity thickness-velocity ration correlation agrees well with the data available for the isothermal shear layers. The heating of one stream was not found to significantly influence the vorticity thickness, which is explained by the counteracting influences of viscosity and density changes.

scholarly journals Energy budget in internal wave attractor experiments

2019 ◽  
Vol 880 ◽  
pp. 743-763 ◽  
Author(s):  
Géraldine Davis ◽  
Thierry Dauxois ◽  
Timothée Jamin ◽  
Sylvain Joubaud
Keyword(s):  
Velocity Field ◽  
Internal Wave ◽  
Boundary Layers ◽  
Energy Budget ◽  
Dissipation Rate ◽  
Theoretical Expression ◽  
Two Dimensional ◽  
Energy Sink ◽  
Set Up ◽  
Different Sources

The current paper presents an experimental study of the energy budget of a two-dimensional internal wave attractor in a trapezoidal domain filled with uniformly stratified fluid. The injected energy flux and the dissipation rate are simultaneously measured from a two-dimensional, two-component, experimental velocity field. The pressure perturbation field needed to quantify the injected energy is determined from the linear inviscid theory. The dissipation rate in the bulk of the domain is directly computed from the measurements, while the energy sink occurring in the boundary layers is estimated using the theoretical expression for the velocity field in the boundary layers, derived recently by Beckebanze et al. (J. Fluid Mech., vol. 841, 2018, pp. 614–635). In the linear regime, we show that the energy budget is closed, in the steady state and also in the transient regime, by taking into account the bulk dissipation and, more importantly, the dissipation in the boundary layers, without any adjustable parameters. The dependence of the different sources on the thickness of the experimental set-up is also discussed. In the nonlinear regime, the analysis is extended by estimating the dissipation due to the secondary waves generated by triadic resonant instabilities, showing the importance of the energy transfer from large scales to small scales. The method tested here on internal wave attractors can be generalized straightforwardly to any quasi-two-dimensional stratified flow.

Restoration of the velocity field of the heart from two-dimensional echocardiograms

1989 ◽  
Vol 8 (2) ◽  
pp. 143-153 ◽  
Author(s):  
G.E. Mailloux ◽  
F. Langlois ◽  
P.Y. Simard ◽  
M. Bertrand
Keyword(s):  
Velocity Field ◽  
Two Dimensional

Oseen vortex as a maximum entropy state of a two dimensional fluid

2011 ◽  
Vol 23 (7) ◽  
pp. 075104 ◽  
Author(s):  
D. C. Montgomery ◽  
W. H. Matthaeus
Keyword(s):  
Maximum Entropy ◽  
Two Dimensional ◽  
Oseen Vortex

An Investigation of the Transverse Velocity Profile in the Case of Internal Viscous Aerodynamic Problems

1984 ◽  
Author(s):  
P. Kotidis ◽  
P. Chaviaropoulos ◽  
K. D. Papailiou
Keyword(s):  
Velocity Field ◽  
Flow Field ◽  
Velocity Profile ◽  
Shear Layer ◽  
Transverse Velocity ◽  
Transverse Plane ◽  
Zone Model ◽  
Viscous Shear ◽  
Rotational Part ◽  
Confined Flows

The development of transverse velocity profile is directly related to the development of secondary vorticity. In the internal aerodynamics case with potential external flow, although vorticity remains confined inside the viscous shear layer, secondary vorticity induced velocities exist outside of it. If the secondary vorticity field is known, the induced secondary velocity field is well approximated following Hawthorne’s classical analysis. In the present work, the above analysis is used to separate the velocity field in the transverse plane into a potential and a rotational part. In the case of confined flows, the rotational part is confined inside the viscous shear layer, while the potential part occupies the whole flow field. This last part is the consequence of the “displacement” effects of the shear layer in the transverse plane. Therefore, the present work allows a re-examination of the flow two-zone model (separation of the flow field in a viscous and an inviscid part) in confined flows. On the other hand, the limitations of Hawthorne’s theory are examined, while a parallel analysis is presented for the case where the secondary vorticity distribution varies not only along the blade height, but also circumferentially.

scholarly journals Two Dimensional Flow Analysis of a Laboratory Centrifugal Pump

1990 ◽  
Author(s):  
S. M. Miner ◽  
R. D. Flack ◽  
P. E. Allaire
Keyword(s):  
Velocity Field ◽  
Stagnation Point ◽  
Centrifugal Pump ◽  
Flow Rate ◽  
Flow Analysis ◽  
Tangential Component ◽  
Design Flow ◽  
Experimental Results ◽  
Two Dimensional ◽  
Flow Angle

Two dimensional potential flow was used to determine the velocity field within a laboratory centrifugal pump. In particular, the finite element technique was used to model the impeller and volute simultaneously. The rotation of the impeller within the volute was simulated by using steady state solutions with the impeller in 10 different angular orientations. This allowed the interaction between the impeller and the volute to develop naturally as a result of the solution. The results for the complete pump model showed that there are circumferential asymmetries in the velocity field, even at the design flow rate. Differences in the relative velocity components were as large as 0.12 m/sec for the radial component and 0.38 m/sec for the tangential component, at the impeller exit. The magnitude of these variations was roughly 25% of the magnitude of the average radial and tangential velocities at the impeller exit. These asymmetries were even more pronounced at off design flow rates. The velocity field was also used to determine the location of the tongue stagnation point and to calculate the slip within the impeller. The stagnation point moved from the discharge side of the tongue to the impeller side of the tongue, as the flow rate increased from below design flow to above design flow. At design flow, values of slip ranged from 0.96 to 0.71, from impeller inlet to impeller exit. For all three types of data (velocity profiles, stagnation point location, and slip factor) comparison was made to laser velocimeter data, taken for the same pump. At the design flow, the computational and experimental results agreed to within 17% for the velocity magnitude, and 2° for the flow angle. The stagnation point locations coincided for the computational and experimental results, and the values for slip agreed to within 10%.

scholarly journals Far-Field Focus and Dispersionless Anticrossing Bands in Two-Dimensional Photonic Crystals

2007 ◽  
Vol 2007 ◽  
pp. 1-8
Author(s):  
Xiaoshuang Chen ◽  
Renlong Zhou ◽  
Yong Zeng ◽  
Hongbo Chen ◽  
Wei Lu
Keyword(s):  
Photonic Crystal ◽  
Photonic Crystals ◽  
Negative Refraction ◽  
Far Field ◽  
Two Dimensional ◽  
Surface Polaritons ◽  
Concave Lens ◽  
Bloch Mode ◽  
Two Dimensional Photonic Crystal ◽  
Photonic Band

We review the simulation work for the far-field focus and dispersionless anticrossing bands in two-dimensional (2D) photonic crystals. In a two-dimensional photonic-crystal-based concave lens, the far-field focus of a plane wave is given by the distance between the focusing point and the lens. Strong and good-quality far-field focusing of a transmitted wave, explicitly following the well-known wave-beam negative refraction law, can be achieved. The spatial frequency information of the Bloch mode in multiple Brillouin zones (BZs) is investigated in order to indicate the wave propagation in two different regions. When considering the photonic transmission in a 2D photonic crystal composed of a negative phase-velocity medium (NPVM), it is shown that the dispersionless anticrossing bands are generated by the couplings among the localized surface polaritons of the NPVM rods. The photonic band structures of the NPVM photonic crystals are characterized by a topographical continuous dispersion relationship accompanied by many anticrossing bands.

scholarly journals NEGATIVE REFRACTION AND SUBWAVELENGTH FOCUSING USING PHOTONIC CRYSTALS

2004 ◽  
Vol 18 (25) ◽  
pp. 1275-1291 ◽  
Author(s):  
EKMEL OZBAY ◽  
KAAN GUVEN ◽  
ERTUGRUL CUBUKCU ◽  
KORAY AYDIN ◽  
B. KAMIL ALICI
Keyword(s):  
Optical Properties ◽  
Photonic Crystals ◽  
Negative Refraction ◽  
Numerical Study ◽  
Effective Index ◽  
Index Of Refraction ◽  
Far Field ◽  
Two Dimensional ◽  
Flat Lens ◽  
Effective Index Of Refraction

In this article, we present an experimental and numerical study of novel optical properties of two-dimensional dielectric photonic crystals (PCs) which exhibit negative refraction. We investigate two mechanisms which utilize the band structure of the PC to generate a negative effective index of refraction (n eff <0) and demonstrate the negative refraction experimentally. To the isotropic extend of n eff , different PC slab structures are employed to focus the radiation of a point source. It is shown experimentally that the PC can generate an image of the source with subwavelength resolution in the vicinity of the PC interface. Using a different PC, one can also obtain a far field focusing. In the latter case, we explicitly show the flat lens behavior of the structure. These examples indicate that PC-based lenses can surpass limitations of conventional lenses and lead to novel optics applications.

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