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Type of fluid motion where all flow velocities are parallel to a fixed plane
In fluid mechanics, a two-dimensional flow is a form of fluid flow where the flow velocity at every point is parallel to a fixed plane. The velocity at
Two-dimensional_flow
Branch of fluid mechanics
solve for the flow conditions. Although one-dimensional flow can be directly analysed, it is merely a specialized case of two-dimensional flow. It follows
Compressible_flow
Function for incompressible divergence-free flows in two dimensions
(divergence-free), two-dimensional flows. The Stokes stream function, named after George Gabriel Stokes, is defined for incompressible, three-dimensional flows with
Stream_function
Pseudovector field describing the local rotation of a continuum near some point
vortices. This is true in the case of two-dimensional potential flow (i.e. two-dimensional zero viscosity flow), in which case the flowfield can be modeled
Vorticity
Force perpendicular to flow of surrounding fluid
ratio, such as a typical delta wing, two-dimensional theories may provide a poor model and three-dimensional flow effects can dominate. Even for wings
Lift_(force)
Velocity field as the gradient of a scalar function
Shock waves at the pointed leading edge of two-dimensional wedge or three-dimensional cone (Taylor–Maccoll flow) has constant intensity. 2) For weak shock
Potential_flow
Streamlined body for generating lift
Glauert and others in the 1920s. The theory idealizes the flow around an airfoil as two-dimensional flow around a thin airfoil. It can be imagined as addressing
Airfoil
Specific point in fluid flow dynamics
point flow refers to a fluid flow in the neighbourhood of a stagnation point (in two-dimensional flows) or a stagnation line (in three-dimensional flows) with
Stagnation_point_flow
Tendency of a fluid jet to stay attached to a surface of any form
number of 100. L. C. Woods also made the calculation of the inviscid two-dimensional flow of a free jet of width h, deflected round a circularly cylindrical
Coandă_effect
Concept in physics
from a spoon as a smooth unbroken stream. For a two-dimensional flow, the divergence of v has only two terms and quantifies the change in area rather than
Strain-rate_tensor
Equation describing the evolution of the vorticity of a fluid particle as it flows
\nabla ^{2}} is the Laplace operator. Under the further assumption of two-dimensional flow, the equation simplifies to: D ω D t = ν ∇ 2 ω {\displaystyle {\frac
Vorticity_equation
Partial differential equation
following three conditions: M is two-dimensional M is three-dimensional and g0 has positive Ricci curvature M has dimension greater than three and the product
Ricci_flow
Dimensionless quantity relating lift to fluid density and velocity over an area
the flow, its Reynolds number and its Mach number. The section lift coefficient cl refers to the dynamic lift characteristics of a two-dimensional foil
Lift_coefficient
Theorem in geometric topology
four-dimensional space). Originally conjectured by Henri Poincaré in 1904, the theorem concerns spaces that locally look like ordinary three-dimensional Euclidean
Poincaré_conjecture
Device to measure the pressure and velocity components of a moving fluid
for two-dimensional flow measurement, the latter two for three-dimensional flow measurement. In the three-hole kind of instrument, there are two yaw direction
Cobra_probe
Computer models of groundwater flow systems
of two-dimensional groundwater models. Three-dimensional models like Modflow require discretization of the entire flow domain. To that end the flow region
Groundwater_model
Dimensionless quantity; ratio of a fluid's buoyancy to viscosity
equations to follow apply both to rotational symmetric flow as well as two-dimensional planar flow. ∂ ∂ s ( ρ u r 0 n ) + ∂ ∂ y ( ρ v r 0 n ) = 0 {\displaystyle
Grashof_number
1828 essay by George Green
of potential. In physics, Green's theorem is mostly used to solve two-dimensional flow integrals, stating that the sum of fluid outflows at any point inside
An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism
An_Essay_on_the_Application_of_Mathematical_Analysis_to_the_Theories_of_Electricity_and_Magnetism
Theoretical construct in flow physics
compressible, inviscid flow. For two-dimensional flow, the linearized pressures in such a flow are equal to those found from incompressible flow theory multiplied
Prandtl–Glauert_singularity
Mathematical technique in aerodynamics
{1}{\beta ^{2}}}{\bar {C}}_{p}} which is known as Göthert's rule For two-dimensional flow, the net result is that C p {\displaystyle C_{p}} and also the lift
Prandtl–Glauert transformation
Prandtl–Glauert_transformation
measuring the loss of smoothness of flow, and resulting inefficiencies, becomes difficult, unlike two-dimensional losses where mathematical complexity
Three-dimensional losses and correlation in turbomachinery
Three-dimensional_losses_and_correlation_in_turbomachinery
Grassland areas in the western United States
their height ranges from 0.3–17 m (0.98–55.77 ft). They are all two-dimensional, flow transverse, sinuous, sedimentary bedforms. The wavelength and height
Camas_prairie
phenomena); or, b. the two-dimensional form of the problem is more tractable than the analogous mathematically more complex three-dimensional problem. While physicists
Two-dimensional_gas
Linear map that preserves areas
a flow with hyperbolic streamlines, see Potential flow § Power laws with n = 2. In 1989 Ottino described the "linear isochoric two-dimensional flow" as
Squeeze_mapping
system. Because this flow is incompressible (i.e., ∇ ⋅ v = 0 {\displaystyle \nabla \cdot \mathbf {v} =0} ) and two-dimensional, its velocity can be expressed
Elementary_flow
Line integral of the fluid velocity around a closed curve
fluid dynamics, the lift per unit span (L') acting on a body in a two-dimensional flow field is directly proportional to the circulation. Lift per unit
Circulation_(physics)
Distinguished surfaces of dynamic trajectories
geophysical flows (see Fig. 11b). In three-dimensional flows, tubular level surfaces of the LAVD define initial positions of two-dimensional eddy boundary
Lagrangian_coherent_structure
Rear edge of an aerodynamic surface
edge angle is zero it is described as a cusped trailing edge. In two-dimensional flow around a uniform wing of infinite span, the slope of the lift curve
Trailing_edge
American aeronautical engineer
(1941) A Graphical Method of Determining Pressure Distribution in Two-dimensional Flow with Robert T. Jones (1941) Theoretical Distribution of Load over
Doris_Cohen
Mathematical theory on dynamical systems
systems that exclude the existence of periodic orbits of two-dimensional flows. Here a flow can be visualized as the surface of a pond. If you drop a
Bendixson–Dulac_theorem
Analysis of the dimensions of different physical quantities
sides, a property known as dimensional homogeneity. Checking for dimensional homogeneity is a common application of dimensional analysis, serving as a plausibility
Dimensional_analysis
Two-dimensional laminar boundary layer that forms on a semi-infinite plate
the steady two-dimensional laminar boundary layer that forms on a semi-infinite plate which is held parallel to a constant unidirectional flow. Falkner
Blasius_boundary_layer
Set of quasilinear hyperbolic equations governing adiabatic and inviscid flow
where: u {\displaystyle \mathbf {u} } is the flow velocity vector field, with components in an N-dimensional space u 1 , u 2 , … , u N {\displaystyle u_{1}
Euler equations (fluid dynamics)
Euler_equations_(fluid_dynamics)
Type of data structure
support for multi-dimensional arrays, and so has C (1972). In C++ (1983), class templates exist for multi-dimensional arrays whose dimension is fixed at runtime
Array_(data_structure)
Hydrologic simulation software suite
excellent mass balances in the water flow calculations. While SWMII could simulate water flow in either two-dimensional vertical or horizontal planes, SWMS_2D
Hydrus_(software)
Gas chromatography technique
Comprehensive two-dimensional gas chromatography, or GC×GC, is a multidimensional gas chromatography technique that was originally described in 1984 by
Comprehensive two-dimensional gas chromatography
Comprehensive_two-dimensional_gas_chromatography
Conservation law for two-phase flow in porous media
in a one-dimensional or quasi-one-dimensional reservoir. This equation can be derived from the mass conservation equations of two-phase flow, under the
Buckley–Leverett_equation
American synthetic biologist
of misconceptions about the origin of fluid turbulence in simple two-dimensional flow situations. Within the Artificial Intelligence Laboratory, he led
Tom_Knight_(scientist)
Topics referred to by the same term
function Digamma function Polygamma functions Stream function, in two-dimensional flows Polar tangential angle of a curve Probability of ultimate ruin,
Psi
Signal processing algorithm
algorithm to any dimensional data we only use it for Two dimension applications. Because the computation time of higher dimensional data would be proportional
Multidimensional empirical mode decomposition
Multidimensional_empirical_mode_decomposition
Theorem in quantum field theory
information is lost as we flow from the former to the latter. Alexander Zamolodchikov proved in 1986 that two-dimensional quantum field theory always
C-theorem
Formula relating lift on an airfoil to fluid speed, density, and circulation
airfoil, the rotating flow may be regarded as induced by a line vortex (with the rotating line perpendicular to the two-dimensional plane). In the derivation
Kutta–Joukowski_theorem
Russian mathematician (1930–1992)
gas-dynamic flow during the movement of an axisymmetric shock wave. In this work, an original method of mathematical description of two-dimensional flow and a
Nikolai_Chentsov
French physicist and mathematician (1854–1948
fluid flow. He explored the formation of vortices. Brillouin proved in 1911 that the discontinuity surfaces must be infinite in a two-dimensional flow, otherwise
Marcel_Brillouin
flow corresponds to an exact solution of the Navier–Stokes equations and are interpreted to describe the flow behind a two-dimensional grid. The flow
Kovasznay_flow
American mathematician (1943–2024)
inequalities for the scalar curvature along a positively-curved Ricci flow on a two-dimensional closed manifold.[H88] With more effort, he was able to formulate
Richard_S._Hamilton
2006 indie game
PlayStation 4 and PlayStation Vita versions in 2013. In Flow, the player navigates a series of two-dimensional planes with an aquatic microorganism that grows
Flow_(video_game)
Tsiklauri, M. G. (1991). Ordered three-dimensional structures resulting from instability of two-dimensional flow in crossed channels. Fluid dynamics, 26(2)
Kerr–Dold_vortex
a flow is unstable or not, it suffices to look at two-dimensional perturbations. These are governed by the Orr–Sommerfeld equation for viscous flow, and
Squire's_theorem
Analysis and solving of problems that involve fluid flows
microchannel flows, in which case it can be supplanted by a locally fully developed assumption. One-dimensional Euler equations or one-dimensional gas-dynamic
Computational_fluid_dynamics
Russian mathematician (born 1966)
"Ricci flow with surgery" for four-dimensional spaces. As an application of his construction, Hamilton was able to settle a four-dimensional curvature-based
Grigori_Perelman
Type of two-dimensional corner flow
In fluid dynamics, Taylor scraping flow is a type of two-dimensional corner flow occurring when one of the wall is sliding over the other with constant
Taylor_scraping_flow
direction of energy flow during turbulence. Instead of the three-dimensional process involving the formation of smaller rotating eddies, in two-dimensions small
Two-dimensional quantum turbulence
Two-dimensional_quantum_turbulence
Study of sudden qualitative behavior changes caused by small parameter changes
Springer. ISBN 978-0-387-96775-2. Nonlinear dynamics Bifurcations and Two Dimensional Flows by Elmer G. Wiens Introduction to Bifurcation theory by John David
Bifurcation_theory
Type of graph
A flow net is a graphical representation of two-dimensional steady-state groundwater flow through aquifers. Construction of a flow net is often used for
Flow_net
Ultrasound imaging of the movement of tissues and body fluids using the Doppler effect
ultrasonography consists of two components: brightness mode (B-mode) showing anatomy of the organs, and Doppler mode (showing blood flow) superimposed on the
Doppler_ultrasonography
Gauss curvature flow is a geometric flow for oriented hypersurfaces of Riemannian manifolds. In the case of curves in a two-dimensional manifold, it is
Gauss_curvature_flow
Projection of data onto lower-dimensional manifolds
is a sample on a two-dimensional manifold in 1024-dimensional space (a Hamming space). The intrinsic dimensionality is two, because two variables (rotation
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
Geometric model of the physical space
rarely, tri-dimensional space. Most commonly, it means the three-dimensional Euclidean space, that is, the Euclidean space of dimension three, which
Three-dimensional_space
Three dimensional analogue of uniformization conjecture
associated with it. It is an analogue of the uniformization theorem for two-dimensional surfaces, which states that every simply connected Riemann surface
Geometrization_conjecture
Flow of fluids with zero viscosity (superfluids)
dynamics, inviscid flow is the flow of fluid that is not viscous. The principles of inviscid flow can also be applied to the flow of fluids of low viscosity
Inviscid_flow
Eigenvalue equation
linear two-dimensional modes of disturbance to a viscous parallel flow. The solution to the Navier–Stokes equations for a parallel, laminar flow can become
Orr–Sommerfeld_equation
Model of viscous fluid flow between two surfaces moving relative to each other
In fluid dynamics, Couette flow is the flow of a viscous fluid in the space between two surfaces, one of which is moving tangentially relative to the other
Couette_flow
irregular connectivity. It cannot easily be expressed as a two-dimensional or three-dimensional array in computer memory. This allows for any possible element
Types_of_mesh
Mathematical model of the time dependence of a point in space
action of the flow on an observable function, the finite-dimensional nonlinear problem involving Φ t gets mapped into an infinite-dimensional linear problem
Dynamical_system
American fluid dynamicist (born 1956)
of Electrostatic Forces on the distribution of Drops in a Channel Flow—Two-Dimensional Oblate Drops“ Phys. Fluids 17 (2005), 093302 A. Esmaeeli and G. Tryggvason
Gretar_Tryggvason
Canadian engineer
focusing on the numerical analysis of solid blocking effects for two-dimensional flow past an airfoil in a wind tunnel. He then pursued a Ph.D. under the
Ugo_Piomelli
variables, which can be one-dimensional, two-dimensional or multidimensional. In most cases, the variable of one-dimensional analog signals are time. After
Two-dimensional_filter
image-based flow visualization (or visualisation) is a computer modelling technique developed by Jarke van Wijk to visualize two dimensional flows of liquids
Image-based flow visualization
Image-based_flow_visualization
arrangement, three-dimensional illumination of an observation volume, recording of the time sequence of stereoscopic images of optical targets (flow tracers illuminated
Particle_tracking_velocimetry
Full immersion in an activity
of flow itself, and utilising a language accessible to all scientific disciplines, Norsworthy et al.'s three dimensional conceptualsiation of flow offers
Flow_(psychology)
Multi-scale chaotic motions
extent of the flow structure. In other words, underlying the three-dimensional chaotic vorticity expressions typical of turbulent flows, there is an organized
Coherent_turbulent_structure
Metalworking process
balanced to avoid extreme difference in metal flow. Full advantage is taken of fiber flow lines. Dimensional tolerances are not closer than necessary. Barrelling
Forging
Flow of electric charge
An electric current is a flow of charged particles, such as electrons or ions, through an electrical conductor or space. It is defined as the net rate
Electric_current
Mathematical Model
particular inviscid and steady dipolar vortex flow. It is a non-trivial solution to the two-dimensional Euler equations. The model is named after Horace
Lamb–Chaplygin_dipole
Equations of motion for viscous fluids
} Two examples of periodic fully-three-dimensional viscous solutions are described in. These solutions are defined on a three-dimensional torus T
Navier–Stokes_equations
Software for simulating water flow within rivers
designed to model flow in open channels in one dimension. The first version of HEC-RAS was released in July of 1995. Though one-dimensional HEC-RAS solves
HEC-RAS
Parabolic partial differential equation
curvature flow is an example of a geometric flow of hypersurfaces in a Riemannian manifold (for example, smooth surfaces in 3-dimensional Euclidean space)
Mean_curvature_flow
Graph used in fluid dynamics
in non-dimensional form that relates the Darcy–Weisbach friction factor fD, Reynolds number Re, and surface roughness for fully developed flow in a circular
Moody_chart
in two-dimensional scatter plots (gating), to use dimensionality reduction to aid gating, and to find populations automatically in higher-dimensional space
Flow_cytometry_bioinformatics
Mathematical model of the physical space
{\displaystyle n} -dimensional analogues of regular polygons and Platonic solids. He found there are six regular convex polytopes in dimension four, and three
Euclidean_geometry
one-dimensional curve-shortening flow (for which every embedded closed curve converges to a circle as it shrinks to a point), the two-dimensional mean-curvature
Angenent_torus
analysis known as dynamical systems theory, a linear flow on the torus is a flow on the n-dimensional torus T n = S 1 × S 1 × ⋯ × S 1 ⏟ n , {\displaystyle
Linear_flow_on_the_torus
Vector function in optics
every point in a three-dimensional space. The mathematical space of all possible light rays is given by the five-dimensional plenoptic function (with
Light_field
Method to measure velocities in fluid
between PIV and those techniques is that PIV produces two-dimensional or even three-dimensional vector fields, while the other techniques measure the
Particle_image_velocimetry
Mathematical relationship describing the flow of groundwater through an aquifer
these coordinates the general Laplacian operator becomes (for three-dimensional flow) specifically ∂ h ∂ t = α [ ∂ 2 h ∂ x 2 + ∂ 2 h ∂ y 2 + ∂ 2 h ∂ z 2
Groundwater_flow_equation
Predicting and managing water resources
v={k \over n}R^{2/3}S^{1/2}} Darcy's law describes steady, one-dimensional groundwater flow using the hydraulic conductivity and the hydraulic gradient:
Hydrological_model
Motion of a curve based on its curvature
curvature. The curve-shortening flow is an example of a geometric flow, and is the one-dimensional case of the mean curvature flow. Other names for the same
Curve-shortening_flow
Work by James Clerk Maxwell (1881)
Richardson, for example, developed a trial and error method of solving two-dimensional flow nets, using a comment in Chapter VI: Maxwell in §92 of his Elementary
An Elementary Treatise on Electricity
An_Elementary_Treatise_on_Electricity
2-dimensional esoteric programming language
two-dimensional grid. "Arrow" instructions direct the control flow to the left, right, up or down, and loops are constructed by sending the control flow in
Befunge
on an object. This may be a simple two-dimensional object, such as a circle or wing, or it may be a three-dimensional vehicle. A series of singularities
Aerodynamic potential-flow code
Aerodynamic_potential-flow_code
Fluid flow through a constant-area duct with friction
the flow is assumed to be steady and one-dimensional, and no mass is added within the duct. The Fanno flow model is considered an irreversible process
Fanno_flow
Type of fluid flow
both 2- and 3-dimensional flows. Hele-Shaw flow is an example of a geometry for which inertia forces are negligible. It is defined by two parallel plates
Stokes_flow
Motion characterized by chaotic changes in pressure and flow velocity
Turbulent flow is always rotational and three dimensional. For example, atmospheric cyclones are rotational but their substantially two-dimensional shapes
Turbulence
Programming language designed 1942 to 1945
using lines in the two-dimensional notation: Boolean values were represented as integers with FALSE=0 and TRUE=1. Conditional control flow took the form of
Plankalkül
Real-valued number of spatial dimensions
sets); 1 for sets describing lines (1-dimensional sets having length only); 2 for sets describing surfaces (2-dimensional sets having length and width); and
Fractal_dimension
On smallest surface enclosing two volumes
three-dimensional standard double bubble can be seen as a surface of revolution of this two-dimensional double bubble. In any higher dimension, the optimal
Double_bubble_theorem
Simultaneous flow of materials with two or more thermodynamic phases
flow, flows that were previously limited to one-dimensional problems could be pushed to three-dimensional models. Projects to develop multiphase flow
Multiphase_flow
Creek in Western Sydney, New South Wales, Australia
2D domain to correctly embody the in-channel hydraulics and each two-dimensional flow patterns on the floodplain, especially on the lower ends of the creek
Burns_Creek_(Sydney)
Vector field which is used to mathematically describe the motion of a continuum
average flow velocity u ¯ {\displaystyle {\bar {u}}} (with the usual dimension of length per time), defined as the quotient between the volume flow rate
Flow_velocity
TWO DIMENSIONAL-FLOW
TWO DIMENSIONAL-FLOW
Girl/Female
Tamil
Triguni | தà¯à®°à¯€à®•à¯‚நீ
The three dimensions
Triguni | தà¯à®°à¯€à®•à¯‚நீ
Surname or Lastname
English
English : perhaps, as Reaney proposes, a variant of Tough.
Boy/Male
Tamil
Dimensions
Girl/Female
Hindu
Three dimensional
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
The Three Dimensions
Boy/Male
Tamil
Trigun | தà¯à®°à®¿à®•à¯à®£
The three dimensions
Trigun | தà¯à®°à®¿à®•à¯à®£
Boy/Male
Hindu, Indian
Shining in Three Dimensions
Boy/Male
Welsh
gift from God'.
Boy/Male
Tamil
Triyog | தà¯à®°à¯€à®¯à¯‹à®•
Controlling all three dimension
Triyog | தà¯à®°à¯€à®¯à¯‹à®•
Girl/Female
Hindu, Indian
Three Dimension
Boy/Male
Spanish
God. Abbreviation of names like Mateo and Teodor.
Boy/Male
Hindu, Indian
Dimensions
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
The Three Dimensions
Girl/Female
Indian, Telugu
Uni-dimensional
Girl/Female
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
Three Dimentional
Girl/Female
Tamil
Trikaya | தà¯à®°à®¿à®•à®¾à®¯à®¾
Three dimensional
Trikaya | தà¯à®°à®¿à®•à®¾à®¯à®¾
Boy/Male
Hindu, Indian
Controlling All Three Dimension
Male
Welsh
Welsh form of English Tom, TWM means "twin."
Male
Polish
Polish form of Latin Ivo, IWO means "yew tree."
Girl/Female
Gujarati, Indian, Kannada
Dimension; Purity
TWO DIMENSIONAL-FLOW
TWO DIMENSIONAL-FLOW
Girl/Female
Indian
Young, Gentle
Boy/Male
English
From the Farm by the Spring
Girl/Female
Indian
Fem of nadi, Dew, Generosity
Boy/Male
Muslim
Servant of the Extender, Creator.
Boy/Male
Indian
Accepted, Popular
Boy/Male
Indian
Last, The devotee and God are one
Male
Welsh
 Modern Welsh form of Old Welsh Owain, OWEN means "born of yew." Compare with another form of Owen.
Boy/Male
Gujarati, Indian
King
Girl/Female
Arabic, Pashtun
Name of the Heaven; Garden
Male
English
Pet form of English Moses, MOE means "drawn out."
TWO DIMENSIONAL-FLOW
TWO DIMENSIONAL-FLOW
TWO DIMENSIONAL-FLOW
TWO DIMENSIONAL-FLOW
TWO DIMENSIONAL-FLOW
n.
The sum of one and one; the number next greater than one, and next less than three; two units or objects.
n.
A literal factor, as numbered in characterizing a term. The term dimensions forms with the cardinal numbers a phrase equivalent to degree with the ordinal; thus, a2b2c is a term of five dimensions, or of the fifth degree.
n.
Measure; dimensions; estimate.
a.
Having dimensions.
n.
Dimension.
n.
A symbol representing two units, as 2, II., or ii.
n.
Extent; reach; scope; importance; as, a project of large dimensions.
n.
The manifoldness with which the fundamental units of time, length, and mass are involved in determining the units of other physical quantities.
n.
Measure; dimension; size.
a.
Divided from the border to the base into two distinct parts; bipartite.
a.
Having two lips.
a.
Employing two hands; as, the two-hand alphabet. See Dactylology.
a.
Having but one dimension. See Dimension.
n.
The degree of manifoldness of a quantity; as, time is quantity having one dimension; volume has three dimensions, relative to extension.
a.
Divided about half way from the border to the base into two segments; bifid.
a.
Pertaining to dimension.
n.
One and one; twice one.
a.
Measuring two feet; two feet long, thick, or wide; as, a two-foot rule.
a.
Without dimensions; marking dimensions or the limits.
n.
Measure in a single line, as length, breadth, height, thickness, or circumference; extension; measurement; -- usually, in the plural, measure in length and breadth, or in length, breadth, and thickness; extent; size; as, the dimensions of a room, or of a ship; the dimensions of a farm, of a kingdom.