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A fluid flowing around an object exerts a force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the force parallel to the flow direction. Lift conventionally acts in an upward direction in order to counter the force of gravity, but it can act in any direction at right angles to the flow.
In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space. For instance, a vector field in the plane can be visualised as a collection of arrows with a given magnitude and direction, each attached to a point in the plane. Vector fields are often used to model, for example, the speed and direction of a moving fluid throughout space, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from one point to another point.
In continuum mechanics, vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point, as would be seen by an observer located at that point and traveling along with the flow. It is an important quantity in the dynamical theory of fluids and provides a convenient framework for understanding a variety of complex flow phenomena, such as the formation and motion of vortex rings.
Streamlines, streaklines and pathlines are field lines in a fluid flow. They differ only when the flow changes with time, that is, when the flow is not steady. Considering a velocity vector field in three-dimensional space in the framework of continuum mechanics, we have that:
In fluid dynamics, the drag coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment, such as air or water. It is used in the drag equation in which a lower drag coefficient indicates the object will have less aerodynamic or hydrodynamic drag. The drag coefficient is always associated with a particular surface area.
In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed.
Parasitic drag, also known as profile drag, is a type of aerodynamic drag that acts on any object when the object is moving through a fluid. Parasitic drag is a combination of form drag and skin friction drag. It affects all objects regardless of whether they are capable of generating lift.
Scientific visualization is an interdisciplinary branch of science concerned with the visualization of scientific phenomena. It is also considered a subset of computer graphics, a branch of computer science. The purpose of scientific visualization is to graphically illustrate scientific data to enable scientists to understand, illustrate, and glean insight from their data. Research into how people read and misread various types of visualizations is helping to determine what types and features of visualizations are most understandable and effective in conveying information.
A four-dimensional space (4D) is a mathematical extension of the concept of three-dimensional or 3D space. Three-dimensional space is the simplest possible abstraction of the observation that one only needs three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world. For example, the volume of a rectangular box is found by measuring and multiplying its length, width, and height.
In applied mathematics, in particular the context of nonlinear system analysis, a phase plane is a visual display of certain characteristics of certain kinds of differential equations; a coordinate plane with axes being the values of the two state variables, say, or etc.. It is a two-dimensional case of the general n-dimensional phase space.
In fluid dynamics, drag is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid. This can exist between two fluid layers or a fluid and a solid surface. Unlike other resistive forces, such as dry friction, which are nearly independent of velocity, drag force depends on velocity.
A triangulated irregular network (TIN) is a representation of a continuous surface consisting entirely of triangular facets, used mainly as Discrete Global Grid in primary elevation modeling.
Three-dimensional space is a geometric setting in which three values are required to determine the position of an element. This is the informal meaning of the term dimension.
A field line is a graphical visual aid for visualizing vector fields. It consists of a directed line which is tangent to the field vector at each point along its length. A diagram showing a representative set of neighboring field lines is a common way of depicting a vector field in scientific and mathematical literature; this is called a field line diagram. They are used to show electric fields, magnetic fields, and gravitational fields among many other types. In fluid mechanics field lines showing the velocity field of a fluid flow are called streamlines.
Flow visualization or flow visualisation in fluid dynamics is used to make the flow patterns visible, in order to get qualitative or quantitative information on them.
A flow map is a type of thematic map that uses linear symbols to represent movement. It may thus be considered a hybrid of a map and a flow diagram. The movement being mapped may be that of anything, including people, highway traffic, trade goods, water, ideas, or even telecommunications data. The wide variety of moving material, and the variety of geographic networks through they move, has led to many different design strategies. Some cartographers have expanded this term to any thematic map of a linear network, while others restrict its use to maps that specifically show movement of some kind.
In technical applications of 3D computer graphics (CAx) such as computer-aided design and computer-aided manufacturing, surfaces are one way of representing objects. The other ways are wireframe and solids. Point clouds are also sometimes used as temporary ways to represent an object, with the goal of using the points to create one or more of the three permanent representations.
In scientific visualization, line integral convolution (LIC) is a technique proposed by Brian Cabral and Leith Leedom to visualize a vector field, such as fluid motion. Compared to other integration-based techniques that compute field lines of the input vector field, LIC has the advantage that all structural features of the vector field are displayed, without the need to adapt the start and end points of field lines to the specific vector field. LIC is a method from the texture advection family.
In scientific visualization, texture advection is a family of methods to densely visualize vector fields or flows. Scientists can use the created images and animations to better understand these flows and reason about them. In comparison to techniques that visualise streamlines, streaklines, or timelines, methods of this family don't need any seed points and can produce a whole image at every step.
In scientific visualization a streamsurface is the 3D generalization of a streamline. It is the union of all streamlines seeded densely on a curve. Like a streamline, a streamsurface is used to visualize flows – three-dimensional flows in this case. Specifically, it is "the locus of an infinite set of such curves [streamlines], rooted at every point along a continuous originating line segment."
References
- 1 2 3 Jean Délery (2011), Separation in three-dimensional flow: critical points, separation lines and vortices (PDF)[ permanent dead link ]
Additional sources
- Chapman, G. T. Topological classification of flow separation on three-dimensional bodies AIAA, Aerospace Sciences Meeting, 24th, Reno, NV, Jan. 6–9, 1986. 22 p.
- Skin friction lines | CSA [ permanent dead link ]
- New developments and applications of skin-friction measuring techniques - Abstract - Measurement Science and Technology - IOPscience
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