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48-412: A zigzag is a pattern made up of small corners at variable angles, though constant within the zigzag, tracing a path between two parallel lines ; it can be described as both jagged and fairly regular. In geometry , this pattern is described as a skew apeirogon . From the point of view of symmetry , a regular zigzag can be generated from a simple motif like a line segment by repeated application of

96-424: A Kármán vortex street (or a von Kármán vortex street ) is a repeating pattern of swirling vortices , caused by a process known as vortex shedding , which is responsible for the unsteady separation of flow of a fluid around blunt bodies. It is named after the engineer and fluid dynamicist Theodore von Kármán , and is responsible for such phenomena as the " singing " of suspended telephone or power lines and

144-404: A bicomplex variable . A vortex street forms only at a certain range of flow velocities, specified by a range of Reynolds numbers ( Re ), typically above a limiting Re value of about 90. The ( global ) Reynolds number for a flow is a measure of the ratio of inertial to viscous forces in the flow of a fluid around a body or in a channel, and may be defined as a nondimensional parameter of

192-864: A glide reflection . Although the origin of the word is unclear, its first printed appearances were in French-language books and ephemera of the late 17th century. Pattern Any of the senses may directly observe patterns. Conversely, abstract patterns in science , mathematics , or language may be observable only by analysis. Direct observation in practice means seeing visual patterns, which are widespread in nature and in art. Visual patterns in nature are often chaotic , rarely exactly repeating, and often involve fractals . Natural patterns include spirals , meanders , waves , foams , tilings , cracks , and those created by symmetries of rotation and reflection . Patterns have an underlying mathematical structure; indeed, mathematics can be seen as

240-538: A chosen effect on the viewer. Nature provides examples of many kinds of pattern, including symmetries , trees and other structures with a fractal dimension, spirals , meanders , waves , foams , tilings , cracks and stripes. Symmetry is widespread in living things. Animals that move usually have bilateral or mirror symmetry as this favours movement. Plants often have radial or rotational symmetry , as do many flowers, as well as animals which are largely static as adults, such as sea anemones . Fivefold symmetry

288-491: A cloud layer is present at the relevant altitude, the streets become visible. Such cloud layer vortex streets have been photographed from satellites. The vortex street can reach over 400 km (250 mi) from the obstacle and the diameter of the vortices are normally 20–40 km (12–25 mi). In low turbulence, tall buildings can produce a Kármán street, so long as the structure is uniform along its height. In urban areas where there are many other tall structures nearby,

336-428: A doctoral candidate, Karl Hiemenz, to whom he gave the task of constructing a water channel in which he could observe the separation of the flow behind a cylinder. The object was to check experimentally the separation point calculated by means of the boundary-layer theory. For this purpose, it was first necessary to know the pressure distribution around the cylinder in a steady flow. Much to his surprise, Hiemenz found that

384-415: A generic non-circular cylinder or a bluff body or a revolution body like a fuselage or a submarine, it is usually the profile chord or the profile thickness, or some other given widths that are in fact stable design inputs; for flow channels usually the hydraulic diameter about which the fluid is flowing. For an aerodynamic profile the reference length depends on the analysis. In fact, the profile chord

432-510: A medium – air or water, making it oscillate as they pass by. Wind waves are surface waves that create the chaotic patterns of the sea. As they pass over sand, such waves create patterns of ripples; similarly, as the wind passes over sand, it creates patterns of dunes . Foams obey Plateau's laws , which require films to be smooth and continuous, and to have a constant average curvature . Foam and bubble patterns occur widely in nature, for example in radiolarians , sponge spicules , and

480-411: A roughly pyramidal form, where elements of the pattern repeat in a fractal -like way at different sizes. Mathematics is sometimes called the "Science of Pattern", in the sense of rules that can be applied wherever needed. For example, any sequence of numbers that may be modeled by a mathematical function can be considered a pattern. Mathematics can be taught as a collection of patterns. Gravity

528-587: A ‘global fractal forest.’ The local ‘tree-seed’ patterns, global configuration of tree-seed locations, and overall resulting ‘global-forest’ patterns have fractal qualities. These designs span multiple mediums yet are all intended to lower occupant stress without detracting from the function and overall design of the space. In this series of studies, we first establish divergent relationships between various visual attributes, with pattern complexity, preference, and engagement ratings increasing with fractal complexity compared to ratings of refreshment and relaxation which stay

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576-473: Is a source of ubiquitous scientific patterns or patterns of observation. The sun rising and falling pattern each day results from the rotation of the earth while in orbit around the sun. Likewise, the moon's path through the sky is due to its orbit of the earth. These examples, while perhaps trivial, are examples of the "unreasonable effectiveness of mathematics" which obtain due to the differential equations whose application within physics function to describe

624-467: Is driven by a balance between increased arousal (desire for engagement and complexity) and decreased tension (desire for relaxation or refreshment). Installations of these composite mid-high complexity ‘global-forest’ patterns consisting of ‘tree-seed’ components balance these contrasting needs, and can serve as a practical implementation of biophilic patterns in human-made environments to promote occupant wellbeing. Vortex street In fluid dynamics ,

672-494: Is found in the echinoderms , including starfish , sea urchins , and sea lilies . Among non-living things, snowflakes have striking sixfold symmetry : each flake is unique, its structure recording the varying conditions during its crystallisation similarly on each of its six arms. Crystals have a highly specific set of possible crystal symmetries ; they can be cubic or octahedral , but cannot have fivefold symmetry (unlike quasicrystals ). Spiral patterns are found in

720-522: Is known as the Strouhal number and is named after the Czech physicist, Vincenc Strouhal (1850–1922) who first investigated the steady humming or singing of telegraph wires in 1878. Although named after Theodore von Kármán , he acknowledged that the vortex street had been studied earlier by Arnulph Mallock and Henri Bénard . Kármán tells the story in his book Aerodynamics : [...] Prandtl had

768-417: Is specifically designed and tuned to counteract the vibrations induced by vortex shedding. When a tuned mass damper is installed on a cylindrical structure, such as a tall chimney or mast, it helps to reduce the vibration amplitudes caused by vortex shedding. The tuned mass damper consists of a mass that is attached to the structure through springs or dampers. In many cases, the spring is replaced by suspending

816-400: Is usually chosen as the reference length also for aerodynamic coefficient for wing sections and thin profiles in which the primary target is to maximize the lift coefficient or the lift/drag ratio (i.e. as usual in thin airfoil theory, one would employ the chord Reynolds as the flow speed parameter for comparing different profiles). On the other hand, for fairings and struts the given parameter

864-400: Is usually the dimension of internal structure to be streamlined (let us think for simplicity it is a beam with circular section), and the main target is to minimize the drag coefficient or the drag/lift ratio. The main design parameter which becomes naturally also a reference length is therefore the profile thickness (the profile dimension or area perpendicular to the flow direction), rather than

912-460: The animals' appearance changing imperceptibly as Turing predicted. In visual art, pattern consists in regularity which in some way "organizes surfaces or structures in a consistent, regular manner." At its simplest, a pattern in art may be a geometric or other repeating shape in a painting , drawing , tapestry , ceramic tiling or carpet , but a pattern need not necessarily repeat exactly as long as it provides some form or organizing "skeleton" in

960-603: The artwork. In mathematics, a tessellation is the tiling of a plane using one or more geometric shapes (which mathematicians call tiles), with no overlaps and no gaps. In architecture, motifs are repeated in various ways to form patterns. Most simply, structures such as windows can be repeated horizontally and vertically (see leading picture). Architects can use and repeat decorative and structural elements such as columns , pediments , and lintels . Repetitions need not be identical; for example, temples in South India have

1008-491: The body in question, causing it to vibrate. If the vortex shedding frequency is similar to the natural frequency of a body or structure, it causes resonance . It is this forced vibration that, at the correct frequency, causes suspended telephone or power lines to "sing" and the antenna on a car to vibrate more strongly at certain speeds. The flow of atmospheric air over obstacles such as islands or isolated mountains sometimes gives birth to von Kármán vortex streets. When

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1056-576: The body plans of animals including molluscs such as the nautilus , and in the phyllotaxis of many plants, both of leaves spiralling around stems, and in the multiple spirals found in flowerheads such as the sunflower and fruit structures like the pineapple . Chaos theory predicts that while the laws of physics are deterministic , there are events and patterns in nature that never exactly repeat because extremely small differences in starting conditions can lead to widely differing outcomes. The patterns in nature tend to be static due to dissipation on

1104-466: The circle boundary, forming rows of vortices in its wake. The alternation leads to the core of a vortex in one row being opposite the point midway between two vortex cores in the other row, giving rise to the distinctive pattern shown in the picture. Ultimately, the energy of the vortices is consumed by viscosity as they move further down stream, and the regular pattern disappears. Above the Re value of 188.5,

1152-414: The efficient measurements of von Kármán streets can be performed using smart sensing algorithms such as compressive sensing. Even more serious instability can be created in concrete cooling towers , especially when built together in clusters. Vortex shedding caused the collapse of three towers at Ferrybridge Power Station C in 1965 during high winds. The failure of the original Tacoma Narrows Bridge

1200-412: The emergence process, but when there is interplay between injection of energy and dissipation there can arise a complex dynamic. Many natural patterns are shaped by this complexity, including vortex streets , other effects of turbulent flow such as meanders in rivers. or nonlinear interaction of the system Waves are disturbances that carry energy as they move. Mechanical waves propagate through

1248-419: The flow becomes three-dimensional, with periodic variation along the cylinder. Above Re on the order of 10 at the drag crisis , vortex shedding becomes irregular and turbulence sets in. When a single vortex is shed, an asymmetrical flow pattern forms around the body and changes the pressure distribution. This means that the alternate shedding of vortices can create periodic lateral (sideways) forces on

1296-404: The flow in his channel oscillated violently. When he reported this to Prandtl, the latter told him: 'Obviously your cylinder is not circular.' However, even after very careful machining of the cylinder, the flow continued to oscillate. Then Hiemenz was told that possibly the channel was not symmetric, and he started to adjust it. I was not concerned with this problem, but every morning when I came in

1344-476: The global Reynolds numbers should be referred to the same reference length. This is actually the reason for which the most precise sources for airfoil and channel flow data specify the reference length at the Reynolds number. The reference length can vary depending on the analysis to be performed: for a body with circle sections such as circular cylinders or spheres, one usually chooses the diameter; for an airfoil,

1392-482: The global speed of the whole fluid flow: R e L = U L ν 0 {\displaystyle \mathrm {Re} _{L}={\frac {UL}{\nu _{0}}}} where: ν 0 = μ 0 ρ 0 {\displaystyle \nu _{0}={\frac {\mu _{0}}{\rho _{0}}}} between: For common flows (the ones which can usually be considered as incompressible or isothermal),

1440-435: The impact of other visual judgments. Here we examine the aesthetic and perceptual experience of fractal ‘global-forest’ designs already installed in humanmade spaces and demonstrate how fractal pattern components are associated with positive psychological experiences that can be utilized to promote occupant wellbeing. These designs are composite fractal patterns consisting of individual fractal ‘tree-seeds’ which combine to create

1488-452: The kinematic viscosity is everywhere uniform over all the flow field and constant in time, so there is no choice on the viscosity parameter, which becomes naturally the kinematic viscosity of the fluid being considered at the temperature being considered. On the other hand, the reference length is always an arbitrary parameter, so particular attention should be put when comparing flows around different obstacles or in channels of different shapes:

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1536-412: The laboratory I asked him, 'Herr Hiemenz, is the flow steady now?' He answered very sadly, 'It always oscillates.' In his autobiography, von Kármán described how his discovery was inspired by an Italian painting of St Christopher carrying the child Jesus whilst wading through water. Vortices could be seen in the water, and von Kármán noted that "The problem for historians may have been why Christopher

1584-430: The mass on cables such that it forms a pendulum system with the same resonance frequency. The mass is carefully tuned to have a natural frequency that matches the dominant frequency of the vortex shedding. As the structure is subjected to vortex shedding-induced vibrations, the tuned mass damper oscillates in an out-of-phase motion with the structure. This counteracts the vibrations, reducing their amplitudes and minimizing

1632-426: The mathematical biologist James D. Murray and other scientists, described a mechanism that spontaneously creates spotted or striped patterns, for example in the skin of mammals or the plumage of birds: a reaction–diffusion system involving two counter-acting chemical mechanisms, one that activates and one that inhibits a development, such as of dark pigment in the skin. These spatiotemporal patterns slowly drift,

1680-443: The most general empirical patterns of the universe . Daniel Dennett 's notion of real patterns , discussed in his 1991 paper of the same name, provides an ontological framework aiming to discern the reality of patterns beyond mere human interpretation, by examining their predictive utility and the efficiency they provide in compressing information. For example, centre of gravity is a real pattern because it allows us to predict

1728-450: The movements of a bodies such as the earth around the sun, and it compresses all the information about all the particles in the sun and the earth that allows us to make those predictions. Some mathematical rule-patterns can be visualised, and among these are those that explain patterns in nature including the mathematics of symmetry, waves, meanders, and fractals. Fractals are mathematical patterns that are scale invariant. This means that

1776-401: The potential for resonance and structural damage. The effectiveness of a tuned mass damper in mitigating vortex shedding-induced vibrations depends on factors such as the mass of the damper, its placement on the structure, and the tuning of the system. Engineers carefully analyze the structural dynamics and characteristics of the vortex shedding phenomenon to determine the optimal parameters for

1824-408: The profile chord. The range of Re values varies with the size and shape of the body from which the eddies are shed , as well as with the kinematic viscosity of the fluid. For the wake of a circular cylinder, for which the reference length is conventionally the diameter d of the circular cylinder, the lower limit of this range is Re ≈ 47. Eddies are shed continuously from each side of

1872-407: The same or decrease with complexity. Subsequently, we determine that the local constituent fractal (‘tree-seed’) patterns contribute to the perception of the overall fractal design, and address how to balance aesthetic and psychological effects (such as individual experiences of perceived engagement and relaxation) in fractal design installations. This set of studies demonstrates that fractal preference

1920-483: The search for regularities, and the output of any function is a mathematical pattern. Similarly in the sciences, theories explain and predict regularities in the world. In many areas of the decorative arts , from ceramics and textiles to wallpaper , "pattern" is used for an ornamental design that is manufactured, perhaps for many different shapes of object. In art and architecture, decorations or visual motifs may be combined and repeated to form patterns designed to have

1968-519: The shape of the pattern does not depend on how closely you look at it. Self-similarity is found in fractals. Examples of natural fractals are coast lines and tree shapes, which repeat their shape regardless of what magnification you view at. While self-similar patterns can appear indefinitely complex, the rules needed to describe or produce their formation can be simple (e.g. Lindenmayer systems describing tree shapes). In pattern theory , devised by Ulf Grenander , mathematicians attempt to describe

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2016-425: The skeletons of silicoflagellates and sea urchins . Cracks form in materials to relieve stress: with 120 degree joints in elastic materials, but at 90 degrees in inelastic materials. Thus the pattern of cracks indicates whether the material is elastic or not. Cracking patterns are widespread in nature, for example in rocks, mud, tree bark and the glazes of old paintings and ceramics. Alan Turing , and later

2064-800: The top, which effectively create asymmetric three-dimensional flow, thereby discouraging the alternate shedding of vortices; this is also found in some car antennas. Another countermeasure with tall buildings is using variation in the diameter with height, such as tapering - that prevents the entire building from being driven at the same frequency. This formula generally holds true for the range 250 < Re d < 200000: St = 0.198 ( 1 − 19.7 Re d )   {\displaystyle {\text{St}}=0.198\left(1-{\frac {19.7}{{\text{Re}}_{d}}}\right)\ } where: St = f d U {\displaystyle {\text{St}}={\frac {fd}{U}}} This dimensionless parameter St

2112-493: The tuned mass damper. Another solution to prevent the unwanted vibration of such cylindrical bodies is a longitudinal fin that can be fitted on the downstream side, which, provided it is longer than the diameter of the cylinder, prevents the eddies from interacting, and consequently they remain attached. Obviously, for a tall building or mast, the relative wind could come from any direction. For this reason, helical projections resembling large screw threads are sometimes placed at

2160-505: The turbulence produced by these can prevent the formation of coherent vortices. Periodic crosswind forces set up by vortices along object's sides can be highly undesirable, due to the vortex-induced vibrations caused, which can damage the structure, hence it is important for engineers to account for the possible effects of vortex shedding when designing a wide range of structures, from submarine periscopes to industrial chimneys and skyscrapers . For monitoring such engineering structures,

2208-475: The vibration of a car antenna at certain speeds. Mathematical modeling of von Kármán vortex street can be performed using different techniques including but not limited to solving the full Navier-Stokes equations with k-epsilon, SST, k-omega and Reynolds stress, and large eddy simulation (LES) turbulence models, by numerically solving some dynamic equations such as the Ginzburg–Landau equation , or by use of

2256-729: The world in terms of patterns. The goal is to lay out the world in a more computationally friendly manner. In the broadest sense, any regularity that can be explained by a scientific theory is a pattern. As in mathematics, science can be taught as a set of patterns. A recent study from Aesthetics and Psychological Effects of Fractal Based Design suggested that fractal patterns possess self-similar components that repeat at varying size scales. The perceptual experience of human-made environments can be impacted with inclusion of these natural patterns. Previous work has demonstrated consistent trends in preference for and complexity estimates of fractal patterns. However, limited information has been gathered on

2304-403: Was originally attributed to excessive vibration due to vortex shedding, but was actually caused by aeroelastic flutter . Kármán turbulence is also a problem for airplanes, especially when landing. To prevent vortex shedding and mitigate the unwanted vibration of cylindrical bodies is the use of a tuned mass damper (TMD). A tuned mass damper is a device consisting of a mass-spring system that

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