Laboratory and numerical experiments on the near wake of a sphere in a stably stratified ambient

2021 ◽  
Vol 933 ◽  
Author(s):  
T.J. Madison ◽  
X. Xiang ◽  
G.R. Spedding
Keyword(s):  
Density Gradient ◽  
Model Problem ◽  
The Body ◽  
Near Wake ◽  
Subsequent Evolution ◽  
Universal Scaling ◽  
Background Density ◽  
Lee Waves ◽  
Distinguishing Features ◽  
Internal Froude Number

The flow around and behind a sphere in a linear density gradient has served as a model problem for both body-generated wakes in atmospheres and oceans, and as a means of generating a patch of turbulence that then decays in a stratified ambient. Here, experiments and numerical simulations are conducted for 20 values of Reynolds number, $Re$ , and internal Froude number, $Fr$ , where each is varied independently. In all cases, the early wake is affected by the background density gradient, notably in the form of the body-generated lee waves. Mean and fluctuating quantities do not reach similar states, and their subsequent evolution would not be collapsible under any universal scaling. There are five distinguishable flow regimes, which mostly overlap with previous literature based on qualitative visualisations and, in this parameter space, they maintain their distinguishing features up to and including buoyancy times of 20. The possible relation of the low $\{Re, Fr\}$ flows to their higher $\{Re, Fr\}$ counterparts is discussed.

The evolution of initially turbulent bluff-body wakes at high internal Froude number

1997 ◽  
Vol 337 ◽  
pp. 283-301 ◽  
Author(s):  
G. R. SPEDDING
Keyword(s):  
Kinetic Energy ◽  
Froude Number ◽  
Bluff Body ◽  
Decay Rates ◽  
The Body ◽  
Buoyancy Frequency ◽  
Universal Curve ◽  
Wake Structure ◽  
Background Density ◽  
Internal Froude Number

Coherent vortex structures are formed in the late wakes of towed spheres for all values of the internal Froude number, F≡2U/ND∈ [10, 240] (U is the body speed, D its diameter, and N is the buoyancy frequency). The eventual emergence of the long-lived and stable pattern of alternating-signed patches of vertical vorticity is characteristic of all towed-sphere wakes, from those dominated by internal lee waves at F=1, to initially fully turbulent early wakes at F[ges ]4. At late times, the local Froude number is always low, and a characteristic stratified wake structure and dynamics result. These wakes have high mean wake defect velocities compared with non-stratified wakes, but the decay rates of energy and enstrophy are similar. Experimental evidence is presented for the existence of an intermediate non-equilibrium (NEQ) regime with very low decay rates of kinetic energy, that precedes the late wake. The NEQ regime is the period when the initial turbulence reorganizes under the increasingly (relative to the decaying turbulent kinetic energy) powerful influence of the background density gradient, accompanied by conversion of potential to kinetic energy as the wake turbulence collapses. The stable long-lived late-wake structure that eventually emerges has a high degree of order and coherence that reflects the initial wake instability. A universal curve for the energy decay of all stratified drag wakes at high Froude and Reynolds numbers is proposed.

scholarly journals Proton acceleration in a laser-induced relativistic electron vortex

2019 ◽  
Vol 85 (4) ◽  
Author(s):  
L. Q. Yi ◽  
I. Pusztai ◽  
A. Pukhov ◽  
B. F. Shen ◽  
T. Fülöp
Keyword(s):  
Laser Pulse ◽  
Relativistic Electron ◽  
Density Gradient ◽  
Incidence Angle ◽  
Grazing Angle ◽  
Critical Density ◽  
Intense Laser ◽  
Plasma Parameters ◽  
Analytical Estimate ◽  
Background Density

We show that when a solid plasma foil with a density gradient on the front surface is irradiated by an intense laser pulse at a grazing angle, ${\sim}80^{\circ }$ , a relativistic electron vortex is excited in the near-critical-density layer after the laser pulse depletion. The vortex structure and dynamics are studied using particle-in-cell simulations. Due to the asymmetry introduced by non-uniform background density, the vortex drifts at a constant velocity, typically $0.2{-}0.3$ times the speed of light. The strong magnetic field inside the vortex leads to significant charge separation; in the corresponding electric field initially stationary protons can be captured and accelerated to twice the velocity of the vortex (100–200 MeV). A representative scenario – with laser intensity of $10^{21}~\text{W}~\text{cm}^{-2}$ – is discussed: two-dimensional simulations suggest that a quasi-monoenergetic proton beam can be obtained with a mean energy 140 MeV and an energy spread of ${\sim}10\,\%$ . We derive an analytical estimate for the vortex velocity in terms of laser and plasma parameters, demonstrating that the maximum proton energy can be controlled by the incidence angle of the laser and the plasma density gradient.

The turbulent wake of a towed grid in a stratified fluid

2015 ◽  
Vol 775 ◽  
pp. 149-177 ◽  
Author(s):  
X. Xiang ◽  
T. J. Madison ◽  
P. Sellappan ◽  
G. R. Spedding
Keyword(s):  
Density Gradient ◽  
Turbulent Flows ◽  
Initial Conditions ◽  
Local Density ◽  
Vertical Plane ◽  
Stratified Fluid ◽  
Vertical Shear ◽  
Gradient Field ◽  
Stratified Turbulence ◽  
Background Density

In a stable background density gradient, initially turbulent flows eventually evolve into a state dominated by low-Froude-number dynamics and frequently also contain persistent pattern information. Much empirical evidence has been gathered on these latter stages, but less on how they first got that way, and how information on the turbulence generator may potentially be encoded into the flow in a robust and long-lasting fashion. Here an experiment is described that examines the initial stages of evolution in the vertical plane of a turbulent grid-generated wake in a stratified ambient. Refractive-index-matched fluids allow optically based measurement of early ($Nt<2$) stages of the flow, even when there are strong variations in the local density gradient field. Suitably averaged flow measures show the interplay between internal wave motions and Kelvin–Helmholtz-generated vortical modes. The vertical shear is dominant at the wake edge, and the decay of horizontal vorticity is observed to be independent of $\mathit{Fr}$. Stratified turbulence, originating from Kelvin–Helmholtz instabilities, develops up to non-dimensional time $Nt\approx 10$, and the scale separation between Ozmidov and Kolmogorov scales is independent of $\mathit{Fr}$ at higher $Nt$. The detailed measurements in the near wake, with independent variation of both Reynolds and Froude numbers, while limited to one particular case, are sufficient to show that the initial turbulence in a stratified fluid is neither three-dimensional nor universal. The search for appropriately generalizable initial conditions may be more involved than hoped for.

Chromium, Nickel and Iron as clues to the formation histories of exoplanetary bodies

2021 ◽  
Author(s):  
Andrew Buchan ◽  
Amy Bonsor ◽  
Oliver Shorttle ◽  
Jon Wade ◽  
John Harrison
Keyword(s):  
White Dwarfs ◽  
The Body ◽  
Subsequent Evolution ◽  
Geological Process ◽  
The Core ◽  
Novel Approach ◽  
Geological Constraints ◽  
Insight Into ◽  
Key Parameter

&lt;p&gt;We are now entering an era of rocky exoplanet detection. To determine whether an exoplanet is &amp;#8216;Earth-like&amp;#8217;, we must estimate not only its mass, radius and insolation, but also its geological composition. These geological constraints have wide ranging implications, not least for a planet&amp;#8217;s subsequent evolution and habitability.&lt;/p&gt;&lt;p&gt;Polluted white dwarfs which have accreted fragments of planetary material provide a unique opportunity to probe exoplanetary interiors. We can also learn about their formation histories, including the geological process of core-mantle differentiation.&lt;/p&gt;&lt;p&gt;Cr, Ni and Fe behave differently during differentiation, depending on the conditions under which it occurs. This alters the Cr/Fe and Ni/Fe ratios in the core and mantle of differentiated bodies. The pressure inside the body is a key parameter, and depends on the body&amp;#8217;s size.&lt;/p&gt;&lt;p&gt;In our work, we present a novel approach for modelling this behaviour and use it to gain crucial insight into the sizes of exoplanetary bodies which pollute white dwarfs.&lt;/p&gt;

Flow Interaction Near the Tail of a Body of Revolution—Part 1: Flow Exterior to Boundary Layer and Wake

1976 ◽  
Vol 98 (3) ◽  
pp. 531-537 ◽  
Author(s):  
A. Nakayama ◽  
V. C. Patel ◽  
L. Landweber
Keyword(s):  
Boundary Layer ◽  
Integral Equation ◽  
Potential Flow ◽  
Present Method ◽  
Iterative Procedure ◽  
The Body ◽  
Body Of Revolution ◽  
Near Wake ◽  
Momentum Integral ◽  
Good Agreement

An iterative procedure for the calculation of the thick attached turbulent boundary layer near the tail of a body of revolution is presented. The procedure consists of the potential-flow calculation by a method of integral equation of the first kind and the calculation of the development of the boundary layer and the wake using an integral method with the condition that the velocity remains continuous across the edge of the boundary layer and the wake. The additional terms that appear in the momentum integral equation for the thick boundary layer and the near wake are taken into account and the pressure difference between the body surface and the edge of the boundary layer and the wake can be determined. The results obtained by the present method are in good agreement with the experimental data. Part 1 of this paper deals with the potential flow, while Part 2 [1] describes the boundary layer and wake calculations, and the overall iterative procedure and results.

scholarly journals A limitation on Long's model in stratified fluid flows

1971 ◽  
Vol 48 (1) ◽  
pp. 161-179 ◽  
Author(s):  
Harvey Segur
Keyword(s):  
Froude Number ◽  
Barrier Height ◽  
Density Gradient ◽  
Dynamic Pressure ◽  
Fluid Flows ◽  
Critical Value ◽  
Stratified Fluid ◽  
Lee Wave ◽  
Finite Barrier ◽  
Internal Froude Number

The flow of a continuously stratified fluid into a contraction is examined, under the assumptions that the dynamic pressure and the density gradient are constant upstream (Long's model). It is shown that a solution to the equations exists if and only if the strength of the contraction does not exceed a certain critical value which depends on the internal Froude number. For the flow of a stratified fluid over a finite barrier in a channel, it is further shown that, if the barrier height exceeds this same critical value, lee-wave amplitudes increase without bound as the length of the barrier increases. The breakdown of the model, as implied by these arbitrarily large amplitudes, is discussed. The criterion is compared with available experimental results for both geometries.

The wakes of cylindrical bluff bodies at low Reynolds number

1978 ◽  
Vol 288 (1354) ◽  
pp. 351-382 ◽  
Keyword(s):  
Reynolds Number ◽  
Low Reynolds Number ◽  
The Body ◽  
Circular Cylinders ◽  
Bluff Bodies ◽  
Near Wake ◽  
Cross Sectional ◽  
Molecular Diffusivity ◽  
Splitter Plates ◽  
Low Reynolds

Experiments on the near wake of a cylinder will be discribed in an attempt to present a coherent picture of the events encountered as the Reynolds number increases from small values up to values of a few thousand. Much work on this subject has already been done, but there are gaps in our description of these flows as well as more fundamental deficiencies in our understanding of them. The subject has been reviewed several times and most recently by Berger & Wille (1972) whose paper covers much of the ground that will be discussed again here. The present work may be regarded as built upon this latest review. I remember with gratitude many helpful discussions with the late Rudolph Wille who contributed so much to this subject. The investigation has concentrated on circular cylinders, but the wakes of bluff cylinders of different cross sectional shapes have also been observed. Bluff cylinders in general are considered in §§4 and 5, together with the effect of splitter plates on circular cylinders in §9. The experiments concern, almost exclusively, flow visualization of the wakes by means of dye washed from the bodies. The patterns of dye observed are, therefore, filament line representations of the flow leaving the separation lines on the body. It must be stressed that the dye does not make visible the vorticity bearing fluid because at low Reynolds number, vorticity diffuses considerably more rapidly than does dye. The ratio of the molecular diffusivity of momentum to that of mass of dye is of the order of 100.

Effect of Base Slant on Flow in the Near Wake of an Axisymmetric Cylinder

1980 ◽  
Vol 31 (2) ◽  
pp. 132-147 ◽  
Author(s):  
Thomas Morel
Keyword(s):  
Drag Coefficient ◽  
Three Dimensional ◽  
Local Maximum ◽  
The Body ◽  
Wake Flow ◽  
Force Measurements ◽  
Near Wake ◽  
Slant Angle ◽  
Cylinder Length ◽  
Axisymmetric Bodies

SummaryThe effects of slanting the base of a slender axisymmetric cylinder (length/diameter ratio of 9), aligned with the flow, was studied experimentally. The body was equipped with interchangeable rear ends covering a range of slant angles between 0° (vertical) and 70°. It was found that the base slant has a very dramatic effect on body drag, particularly in a relatively narrow range of slant angles where the drag coefficient exhibits a large local maximum (over-shoot). Detailed study of the flow showed that the drag overshoot is related to the existence of two very different Separation patterns on the slanted base. One pattern is similar to that found behind axisymmetric bodies with no base slant, and its main feature is the presence of a closed Separation region adjacent to the base. The other pattern is highly three-dimensional with two streamwise vortices forming along the sides of the slanted base. This pattern sets in very abruptly at a “critical” slant angle α ∼ 47°. Drag force measurements showed that, at first, the drag coefficient slowly increases with the slant angle, but then jumps suddenly upwards to more than double its baseline value (from CD = 0.24 to CD = 0.625) at the critical angle. At angles higher than that CD decreases again, and at 70° it is about equal to the baseline value. Further effects of the slant angle are the generation of a large side force and a significant increase in near-wake flow periodicity.

Linearly stratified flow past a horizontal circular cylinder

1989 ◽  
Vol 328 (1601) ◽  
pp. 501-528 ◽  
Keyword(s):  
Circular Cylinder ◽  
Parameter Space ◽  
Scaling Analysis ◽  
Maximum Width ◽  
Wide Range ◽  
Lee Waves ◽  
Streamwise Distance ◽  
Horizontal Circular Cylinder ◽  
Good Agreement ◽  
Internal Froude Number

The flow of a linearly stratified fluid past a long circular cylinder in a channel is considered experimentally. The characteristics of the flow depend on the internal Froude number F i the Reynolds number Re and the cylinder diameter to fluid depth ratio, d/H . A wide range of characteristic flow fields are observed in the parameter space investigated; i.e. 0.02 ⩽ F i ⩽ 13 , 5 ⩽ Re ⩽ 4000 and 0.03 ⩽ d / H ⩽ 0.20 . A flow regime diagram of F i against Re for these characteristic flows is developed. Some of the lower F i Re experiments are compared with numerical experiments. A theory is advanced which indicates that the dimensionless length, x b ∗ = x b / d of the blocked region ahead of the cylinder should scale as x b ∗ ≈ ( δ / d ) 5 R e F i − 2 , where δ is the thickness of the shear layer between the external flow and the approximately stagnant blocked region; the results of an experimental programme that support this scaling are presented. Measurements are made which indicate that for the range of parameter space in which lee waves occur, the lee wavelengths are predicted to a good approximation by linear theory. A scaling analysis is carried out which suggests that the height of the rotors above the streamwise centreline, Z r ∗ = Z r / d , scales with F i experiments aire in good agreement with this prediction. For conditions under which the wake of the cylinder is turbulent, scaling arguments suggest that the dimensionless maximum width of the wake, γ m ∗ = γ m / d , and the dimensionless streamwise distance at which this maximum occurs, β m ∗ = β m / d , scale as F i 1 2 Experiments are presented which support this scaling.

scholarly journals MORPHOLOGICAL CHARACTERISTICS AND NOMENCLATURE OF LEPTOSPIRA (SPIROCHÆTA) ICTEROHÆMORRHAGIÆ (INADA AND IDO)

1918 ◽  
Vol 27 (5) ◽  
pp. 575-592 ◽  
Author(s):  
Hideyo Noguchi
Keyword(s):  
Comparative Study ◽  
Causative Agent ◽  
New Genus ◽  
Morphological Characteristics ◽  
Systematic Position ◽  
The Body ◽  
Morphological Description ◽  
Caudal Portion ◽  
Destructive Action ◽  
Distinguishing Features

The present study deals with the morphology and systematic position of the causative agent of infectious jaundice. There are several features which are not found in any of the hitherto known genera of Spirochætoidea which led me to give this organism an independent generic name, Leptospira, denoting the peculiar minute elementary spirals running throughout the body. The absence of a definite terminal flagellum or any flagella, and the remarkable flexibility of the terminal or caudal portion of the organism are other distinguishing features. Unlike all other so called spirochetes the present organism resists the destructive action of 10 per cent saponin. A detailed comparative study of related genera, including Spirochæta, Saprospira, Cristispira, Spironema, and Treponema, has been given with the view of bringing out more strongly the contrast between them and the new genus. A study has been made to discover whether any differential features exist among the strains of Leptospira icterohæmorrhagiæ derived from the American, Japanese, and European sources, but none has been found. It is hoped that the creation of a new genus may facilitate a more exact morphological description than has hitherto been possible, due to the vague use of the term Spirochæta which indiscriminately covered at least six large genera of spiral organisms.

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