The theory of three-dimensional hetons and vortex-dominated spreading in localized turbulent convection in a fast rotating stratified fluid

2000 ◽  
Vol 423 ◽  
pp. 71-125 ◽  
Author(s):  
VLADIMIR M. GRYANIK ◽  
TATIANA N. DORONINA ◽  
DIRK J. OLBERS ◽  
TORSTEN H. WARNCKE
Keyword(s):  
Mixing Layer ◽  
Three Dimensional ◽  
Propagation Speed ◽  
Finite Depth ◽  
Spreading Rate ◽  
Lateral Spreading ◽  
Theoretical Explanation ◽  
Buoyancy Flux ◽  
Turbulent Convection ◽  
The Mean

The problem of lateral heat/buoyancy transport in localized turbulent convection dominated by rotation in continuously stratified fluids of finite depth is considered. We investigate the specific mechanism of the vortex-dominated lateral spreading of anomalous buoyancy created in localized convective regions owing to outward propagation of intense heton-like vortices (pairs of vortices of equal potential vorticity (PV) strength with opposite signs located at different depths), each carrying a portion of buoyancy anomaly. Assuming that the quasi-geostrophic form of the PV evolution equation can be used to analyse the spreading phenomenon at fast rotation, we develop an analytical theory for the dynamics of a population of three-dimensional hetons. We analyse in detail the structure and dynamics of a single three-dimensional heton, and the mutual interaction between two hetons and show that the vortices can be in confinement, splitting or reconnection regimes of motion depending on the initial distance between them and the ratio of the mixing-layer depth to the depth of fluid (local to bulk Rossby radii). Numerical experiments are made for ring-like populations of randomly distributed three-dimensional hetons. We found two basic types of evolution of the populations which are homogenizing confinement (all vortices are predominantly inside the localized region having highly correlated wavelike dynamics) and vortex-dominated spreading (vortices propagate out of the region of generation as individual hetons or heton clusters). For the vortex-dominated spreading, the mean radius of heton populations and its variance grow linearly with time. The law of spreading is quantified in terms of both internal (specific for vortex dynamics) and external (specific for convection) parameters. The spreading rate is proportional to the mean speed of propagation of individual hetons or heton clusters and therefore depends essentially on the strength of hetons and the ratio of local to bulk Rossby radii. A theoretical explanation for the spreading law is given in terms of the asymptotic dynamics of a single heton and within the frames of the kinetic equation derived for the distribution function of hetons in collisionless approximation. This spreading law gives an upper ‘advective’ bound for the superdiffusion of heat/buoyancy. A linear law of spreading implies that diffusion parameterizations of lateral buoyancy flux in non-eddy-resolving models are questionable, at least when the spreading is dominated by heton dynamics. We suggest a scaling for the ‘advective’ parameterization of the buoyancy flux, and quantify the exchange coefficient in terms of the mean propagation speed of hetons. Finally, we discuss the perspectives of the heton theories in other problems of geophysical fluid dynamics.

The three-dimensional evolution of a plane mixing layer: pairing and transition to turbulence

1993 ◽  
Vol 247 ◽  
pp. 275-320 ◽  
Author(s):  
Robert D. Moser ◽  
Michael M. Rogers
Keyword(s):  
Turbulent Flows ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Linear Stability Theory ◽  
Transition To Turbulence ◽  
Thin Sheets ◽  
Mean Velocity ◽  
Rapid Transition ◽  
The Mean ◽  
Simulated Flow

The evolution of three-dimensional temporally evolving plane mixing layers through as many as three pairings has been simulated numerically. All simulations were begun from a few low-wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity. Three-dimensional perturbations were used with amplitudes ranging from infinitesimal to large enough to trigger a rapid transition to turbulence. Pairing is found to inhibit the growth of infinitesimal three-dimensional disturbances, and to trigger the transition to turbulence in highly three-dimensional flows. The mechanisms responsible for the growth of three-dimensionality and onset of transition to turbulence are described. The transition to turbulence is accompanied by the formation of thin sheets of spanwise vorticity, which undergo secondary rollups. The post-transitional simulated flow fields exhibit many properties characteristic of turbulent flows.

Curved two-stream turbulent mixing layers: three-dimensional structure and streamwise evolution

1994 ◽  
Vol 270 ◽  
pp. 1-50 ◽  
Author(s):  
Michael W. Plesniak ◽  
Rabindra D. Mehta ◽  
James P. Johnston
Keyword(s):  
Boundary Layers ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Mixing Layers ◽  
Dimensional Structure ◽  
Far Field ◽  
Streamwise Vorticity ◽  
Unstable Case ◽  
The Mean

The three-dimensional structure and streamwise evolution of two-stream mixing layers at high Reynolds numbers (Reδ ∼ 2.7 × 104) were studied experimentally to determine the effects of mild streamwise curvature ($\delta/ \overline{R}$ < 3%). Mixing layers with velocity ratios of 0.6 and both laminar and turbulent initial boundary layers, were subjected to stabilizing and destabilizing longitudinal curvature (in the Taylor–Görtler sense). The mixing layer is affected by the angular momentum instability when the low-speed stream is on the outside of the curve, and it is stabilized when the streams are reversed so that the high-speed stream is on the outside. In both stable and unstable mixing layers, originating from laminar boundary layers, well-organized spatially stationary streamwise vorticity was generated, which produced significant spanwise variations in the mean velocity and Reynolds stress distributions. These vortical structures appear to result from the amplification of small incoming disturbances (as in the straight mixing layer), rather than through the Taylor–Görtler instability. Although the mean streamwise vorticity decayed with downstream distance in both cases, the rate of decay for the unstable case was lower. With the initial boundary layers on the splitter plate turbulent, spatially stationary streamwise vorticity was not generated in either the stable or unstable mixing layer. Linear growth was achieved for both initial conditions, but the rate of growth for the unstable case was higher than that of the stable case. Correspondingly, the far-field spanwise-averaged peak Reynolds stresses were significantly higher for the destabilized cases than for the stabilized cases, which exhibited levels comparable to, or slightly lower than, those for the straight case. A part of the Reynolds stress increase in the unstable layer is attributed to ‘extra’ production through terms in the transport equations which are activated by the angular momentum instability. Velocity spectra also indicated significant differences in the turbulence structure of the two cases, both in the near- and far-field regions.

Mach number effects on the global mixing modes induced by ramp injectors in supersonic flows

2014 ◽  
Vol 757 ◽  
pp. 403-431 ◽  
Author(s):  
Luca Massa
Keyword(s):  
Mach Number ◽  
Free Stream ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Base Flow ◽  
Recirculation Region ◽  
Mean Flow ◽  
Mixing Rate ◽  
Flow Distortion ◽  
The Mean

AbstractModern injectors for supersonic combustors (hypermixers) augment the fuel–air mixing rate by energizing the perturbation in the mixing layer. From an instability point of view, the increased perturbation growth is linked to the increased complexity of the equilibrium base flow when compared to the axisymmetric mixing layer. Common added features are streamwise vortex streaks, oblique recompression shocks and Prandtl–Meyer expansions. One of the main effects of such distortions of the mean flow is to transform the instability responsible for the creation of fine scales from a local amplified mode to a global self-sustained fluctuation. The focus of the present research is on the flow distortion induced by flushed ramps for free-stream Mach numbers in the range 2.5–3.5. The principal mean flow features are the recirculation region due to the recompression of the flow after the ramp, the shear layer over the recirculation region and the vortex streaks propagating from the ramp corners. A global three-dimensional stability analysis and three-dimensional direct numerical simulations of small perturbations of the mean flow are performed. The growth and energy distribution of the dominant and subdominant fluctuations supported by the three-dimensional steady laminar base flow are computed. The main results are the growth rates of the self-sustained varicose and sinuous modes and their correlation to the variation in the free-stream Mach number. The complex three-dimensional wavemaker is investigated by evaluating the three-dimensional eigenfunctions of the direct and adjoint modes, and the effects of the axial vorticity generated by the ramp corners are discussed.

The forced mixing layer between parallel streams

1982 ◽  
Vol 123 ◽  
pp. 91-130 ◽  
Author(s):  
D. Oster ◽  
I. Wygnanski
Keyword(s):  
Turbulent Mixing ◽  
Mixing Layer ◽  
Resonance Region ◽  
Spreading Rate ◽  
Initial Energy ◽  
Two Dimensional ◽  
Velocity Difference ◽  
Mean Velocity ◽  
Order Of Magnitude ◽  
The Mean

The effect of periodic two-dimensional excitation on the development of a turbulent mixing region was studied experimentally. Controlled oscillations of variable ampli- tude and frequency were applied at the initiation of mixing between two parallel air streams. The frequency of forcing was at least an order of magnitude lower than the initial instability frequency of the flow in order to test its effect far downstream. The effect of the velocity difference between the streams was also investigated in this experiment. A typical Reynolds number based on the velocity difference and the momentum thickness of the shear layer was l04.It was determined that the spreading rate of the mixing layer is sensitive to periodic surging even if the latter is so small that it does not contribute to the initial energy of the fluctuations. Oscillations at very small amplitudes tend to increase the spreading rate of the flow by enhancing the amalgamation of neighbouring eddies, but at higher amplitudes the flow resonates with the imposed oscillation. The resonance region can extend over a significant fraction of the test section depending on the Strouhal number and a dimensionless velocity-difference parameter. The flow in the resonance region consists of a single array of large, quasi-two-dimensional vortex lumps, which do not interact with one another. The exponential shape of the mean-velocity distribution is not affected in this region, but the spreading rate of the flow with increasing distance downstream is inhibited. The Reynolds stress in this region changes sign, indicating that energy is extracted from the turbulence to the mean motion; the intensity of the spanwise fluctuations is also reduced, suggesting that the flow tends to become more two-dimensional.Amalgamation of large coherent eddies is resumed beyond the resonance region, but the flow is not universally similar. There are many indications suggesting that the large eddies in the turbulent mixing layer at fairly large Re are governed by an inviscid instability.

Electron Holographic Nano-Characterization of Gold Catalyst at Interface

2002 ◽  
Vol 727 ◽  
Author(s):  
S. Ichikawa ◽  
T. Akita ◽  
M. Okumura ◽  
M. Haruta ◽  
K. Tanaka
Keyword(s):  
Contact Angle ◽  
Titanium Oxide ◽  
Gold Catalyst ◽  
Three Dimensional ◽  
High Resolution Electron Microscopy ◽  
Electron Holography ◽  
Gold Particles ◽  
Oxide Support ◽  
The Mean ◽  
A Charge

AbstractThe catalytic properties of nanostructured gold catalyst are known to depend on the size of the gold particles and to be activated when the size decreases to a few nanometers. We investigated the size dependence of the three-dimensional nanostructure on the mean inner potential of gold catalysts supported on titanium oxide using electron holography and high-resolution electron microscopy (HREM). The contact angle of the gold particles on the titanium oxide tended to be over 90° for gold particles with a size of over 5 nm, and below 90° for a size of below 2 nm. This decreasing change in the contact angle (morphology) acts to increase the perimeter and hence the area of the interface between the gold and titanium oxide support, which is considered to be an active site for CO oxidation. The mean inner potential of the gold particles also changed as their size decreased. The value of the inner potential of gold, which is approximately 25 V in bulk state, rose to over 40 V when the size of the gold particles was less than 2 nm. This phenomenon indicates the existence of a charge transfer at the interface between gold and titanium oxide. The 3-D structure change and the inner potential change should be attributed to the specific electronic structure at the interface, owing to both the “nano size effect” and the “hetero-interface effect.”

The Influence of Blade Wakes on the Performance of Interturbine Diffusers

1996 ◽  
Vol 118 (2) ◽  
pp. 347-352 ◽  
Author(s):  
R. G. Dominy ◽  
D. A. Kirkham
Keyword(s):  
Performance Modeling ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Two Dimensional ◽  
Correct Performance ◽  
Analysis Methods ◽  
Flow Factor ◽  
The Mean ◽  
Lp Turbine

Interturbine diffusers provide continuity between HP and LP turbines while diffusing the flow upstream of the LP turbine. Increasing the mean turbine diameter offers the potential advantage of reducing the flow factor in the following stages, leading to increased efficiency. The flows associated with these interturbine diffusers differ from those in simple annular diffusers both as a consequence of their high-curvature S-shaped geometry and of the presence of wakes created by the upstream turbine. It is shown that even the simplest two-dimensional wakes result in significantly modified flows through such ducts. These introduce strong secondary flows demonstrating that fully three-dimensional, viscous analysis methods are essential for correct performance modeling.

scholarly journals Proximity of the middle meningeal artery and maxillary artery to the mandibular head and mandibular neck as revealed by three-dimensional time-of-flight magnetic resonance angiography

2021 ◽  
Author(s):  
Daphne Schönegg ◽  
Raphael Ferrari ◽  
Julian Ebner ◽  
Michael Blumer ◽  
Martin Lanzer ◽  
...  
Keyword(s):  
Magnetic Resonance ◽  
Magnetic Resonance Angiography ◽  
Three Dimensional ◽  
Time Of Flight ◽  
Middle Meningeal Artery ◽  
Individual Variability ◽  
Maxillary Artery ◽  
Condylar Process ◽  
The Mean ◽  
Meningeal Artery

Abstract Purpose The close topographic relationship between vascular and osseous structures in the condylar and subcondylar region and marked variability in the arterial course has been revealed by both imaging and cadaveric studies. This study aimed to verify the previously published information in a large sample and to determine a safe surgical region. Methods We analyzed the three-dimensional time-of-flight magnetic resonance angiography images of 300 individuals. Results The mean distance between the middle meningeal artery and the apex of the condyle or the most medial point of the condyle was 18.8 mm (range: 11.2–25.9 mm) or 14.5 mm (range: 8.8–22.9 mm) respectively. The course of the maxillary artery relative to the lateral pterygoid muscle was medial in 45.7% of cases and lateral in 54.3%. An asymmetric course was evident in 66 patients (22%). The mean distance between the maxillary artery and condylar process at the deepest point of the mandibular notch was 6.2 mm in sides exhibiting a medial course (range: 3.7–9.8 mm) and 6.6 mm in sides exhibiting a lateral course (range: 3.9–10.4 mm). The distances were significantly influenced by age, gender, and the course of the maxillary artery. Conclusion Our study emphasizes the marked inter- and intra-individual variability of the maxillary and middle meningeal arterial courses. We confirmed the proximity of the arteries to the condylar process. Extensive surgical experience and thorough preparation for each individual case are essential to prevent iatrogenic vascular injury.

scholarly journals Interactions between Tandem Cylinders in an Open Channel: Impact on Mean and Turbulent Flow Characteristics

Water ◽  
2021 ◽  
Vol 13 (13) ◽  
pp. 1718
Author(s):  
Hasan Zobeyer ◽  
Abul B. M. Baki ◽  
Saika Nowshin Nowrin
Keyword(s):  
Turbulent Flow ◽  
Open Channel ◽  
Recirculation Zone ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Flow Recirculation ◽  
Tandem Cylinders ◽  
Flow Development ◽  
The Mean ◽  
Recirculation Length

The flow hydrodynamics around a single cylinder differ significantly from the flow fields around two cylinders in a tandem or side-by-side arrangement. In this study, the experimental results on the mean and turbulence characteristics of flow generated by a pair of cylinders placed in tandem in an open-channel flume are presented. An acoustic Doppler velocimeter (ADV) was used to measure the instantaneous three-dimensional velocity components. This study investigated the effect of cylinder spacing at 3D, 6D, and 9D (center to center) distances on the mean and turbulent flow profiles and the distribution of near-bed shear stress behind the tandem cylinders in the plane of symmetry, where D is the cylinder diameter. The results revealed that the downstream cylinder influenced the flow development between cylinders (i.e., midstream) with 3D, 6D, and 9D spacing. However, the downstream cylinder controlled the flow recirculation length midstream for the 3D distance and showed zero interruption in the 6D and 9D distances. The peak of the turbulent metrics generally occurred near the end of the recirculation zone in all scenarios.

scholarly journals Brain capillary structures of schizophrenia cases and controls show a correlation with their neuron structures

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Rino Saiga ◽  
Masayuki Uesugi ◽  
Akihisa Takeuchi ◽  
Kentaro Uesugi ◽  
Yoshio Suzuki ◽  
...  
Keyword(s):  
Blood Vessels ◽  
Structural Parameters ◽  
Three Dimensional ◽  
Superior Temporal Gyrus ◽  
Anterior Cingulate ◽  
Dimensional Structure ◽  
Constant Diameter ◽  
The Mean ◽  
Cartesian Coordinate ◽  
Micrometer Scale

AbstractBrain blood vessels constitute a micrometer-scale vascular network responsible for supply of oxygen and nutrition. In this study, we analyzed cerebral tissues of the anterior cingulate cortex and superior temporal gyrus of schizophrenia cases and age/gender-matched controls by using synchrotron radiation microtomography or micro-CT in order to examine the three-dimensional structure of cerebral vessels. Over 1 m of cerebral blood vessels was traced to build Cartesian-coordinate models, which were then used for calculating structural parameters including the diameter and curvature of the vessels. The distribution of vessel outer diameters showed a peak at 7–9 μm, corresponding to the diameter of the capillaries. Mean curvatures of the capillary vessels showed a significant correlation to the mean curvatures of neurites, while the mean capillary diameter was almost constant, independent of the cases. Our previous studies indicated that the neurites of schizophrenia cases are thin and tortuous compared to controls. The curved capillaries with a constant diameter should occupy a nearly constant volume, while neurons suffering from neurite thinning should have reduced volumes, resulting in a volumetric imbalance between the neurons and the vessels. We suggest that the observed structural correlation between neurons and blood vessels is related to neurovascular abnormalities in schizophrenia.

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