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Use of mathematical models to simulate turbulent flow
In fluid dynamics, turbulence modeling is the construction and use of a mathematical model to predict the effects of turbulence. Turbulent flows are commonplace
Turbulence_modeling
Model used in computational fluid dynamics
The k-epsilon (k-ε) turbulence model is one of the most common models used in computational fluid dynamics (CFD) to simulate mean flow characteristics
K-epsilon_turbulence_model
One-equation turbulence model for computational fluid dynamics
Spalart–Allmaras model is a popular mathematical model used in computational fluid dynamics (CFD) to simulate the effects of turbulence. It is a one-equation model, meaning
Spalart–Allmaras turbulence model
Spalart–Allmaras_turbulence_model
Tool in computational fluid dynamics
computational fluid dynamics, the k–omega (k–ω) turbulence model is a common two-equation turbulence model, that is used as an approximation for the Reynolds-averaged
K–omega_turbulence_model
Motion characterized by chaotic changes in pressure and flow velocity
bowling Taylor microscale Turbulence modeling Velocimetry Vertical draft Vortex Vortex generator Wake turbulence Wave turbulence Wingtip vortices Wind tunnel
Turbulence
Mathematical model of continuous gusts
The Dryden wind turbulence model, also known as Dryden gusts, is a mathematical model of continuous gusts accepted for use by the United States Department
Dryden_Wind_Turbulence_Model
Mathematical model of turbulence
stress equation model (RSM), also referred to as second moment closures are the most complete classical turbulence model. In these models, the eddy-viscosity
Reynolds stress equation model
Reynolds_stress_equation_model
French-Chilean born American fluid dynamicist
born American fluid dynamicist, known for his work on turbulence, including turbulence modeling and computational fluid dynamics. Charles Meneveau, the
Charles_Meneveau
Mathematical equations to describe fluid flow
gamma-Re transition model has two equations and is based on the two-equation turbulence models in the context of turbulence modeling. This way both local
Gamma-Re_Transition_Model
Mathematical model of continuous gusts
The von Kármán wind turbulence model (also known as von Kármán gusts) is a mathematical model of continuous gusts. It matches observed continuous gusts
Von Kármán wind turbulence model
Von_Kármán_wind_turbulence_model
dynamics, smoothed particle hydrodynamics, direct numerical simulation, turbulence modeling, aerodynamic potential-flow code, thermal hydraulics, lattice Boltzmann
List of computational fluid dynamics software
List_of_computational_fluid_dynamics_software
Analysis and solving of problems that involve fluid flows
system being modeled. For turbulent flows, the range of length scales and complexity of phenomena involved in turbulence make most modeling approaches prohibitively
Computational_fluid_dynamics
Mean kinetic energy per unit mass of eddies in turbulent flow
Navier Stokes equations, the turbulence kinetic energy can be calculated based on the closure method, i.e. a turbulence model. The TKE can be defined to
Turbulence_kinetic_energy
Mathematical model for turbulence
Large eddy simulation (LES) is a mathematical model for turbulence used in computational fluid dynamics. It was initially proposed in 1963 by Joseph Smagorinsky
Large_eddy_simulation
Scientific journal
theoretical, numerical and experimental research in turbulence, including but not limited to turbulence modeling and geophysical fluid dynamics. Its current editor-in-chief
Journal_of_Turbulence
Turbulence model
Transport turbulence model, or SST, is a widely used and robust 2-equation eddy-viscosity turbulence model used in Computational Fluid Dynamics. The model combines
Menter's Shear Stress Transport
Menter's_Shear_Stress_Transport
Turbulence modeling approach
requires additional modeling to close the RANS equation for solving, and has led to the creation of many different turbulence models. The time-average operator
Reynolds-averaged Navier–Stokes equations
Reynolds-averaged_Navier–Stokes_equations
C., 1998. Turbulence Modeling for CFD. ISBN 1-928729-10-X, 2nd Ed., DCW Industries, Inc. This article was based on the Cebeci Smith model article in
Cebeci–Smith_model
Turbulent movement of transparent air masses
In meteorology, clear-air turbulence (CAT) is the turbulent movement of air masses in the absence of any visual clues such as clouds, and is caused when
Clear-air_turbulence
Transition modeling is the use of a model to predict the change from laminar and turbulent flows in fluids and their respective effects on the overall
Transition_modeling
models of hydrostatics, hydrodynamics and aerodynamics. Hydraulics Elasticity Mechanical waves and acoustics Valves and fluidics Gas laws Turbulence modeling
Timeline of fluid and continuum mechanics
Timeline_of_fluid_and_continuum_mechanics
Simulation in computational fluid dynamics
numerically solved without any turbulence model. This means that the whole range of spatial and temporal scales of the turbulence must be resolved. All the
Direct_numerical_simulation
Canadian engineer
contributions to the field of computational fluid dynamics, particularly in turbulence modeling and large-eddy simulation. He is currently a professor at Queen's
Ugo_Piomelli
Turbulence that concerns the regimes of magnetofluid flow at high Reynolds number
Magnetohydrodynamic turbulence concerns the chaotic regimes of magnetofluid flow at high Reynolds number. Magnetohydrodynamics (MHD) deals with quasi-neutral
Magnetohydrodynamic turbulence
Magnetohydrodynamic_turbulence
Constant in fluid dynamics
} with ρ the fluid density. The Kármán constant is often used in turbulence modeling, for instance in boundary-layer meteorology to calculate fluxes of
Von_Kármán_constant
Highly agitated, chaotic fluid motion
the RNG k–ε model for liquid turbulence[citation needed]. Several approaches have been carried out, including single-sized bubble modeling, double-sized
Churn_turbulent_flow
wave Turbulence modeling Turbulence kinetic energy (TKE) K-epsilon turbulence model k–omega turbulence model Spalart–Allmaras turbulence model Vorticity
List of named differential equations
List_of_named_differential_equations
Winds that vary randomly in space and time
randomly in space and time. Models of continuous gusts are used to represent atmospheric turbulence, especially clear air turbulence and turbulent winds in
Continuous_gusts
particle model used to study turbulence in two-dimensional ideal fluids. The two-dimensional guiding-center plasma is a completely equivalent model used in
Two-dimensional point vortex gas
Two-dimensional_point_vortex_gas
Set of partial differential equations on fluid flow
all channel flow scenarios. The dynamic wave is used for modeling transient storms in modeling programs including Mascaret (EDF), SIC (Irstea), HEC-RAS
Shallow_water_equations
Force perpendicular to flow of surrounding fluid
averaged over time, and the effects of the turbulence on the time-averaged flow represented by turbulence modeling (an additional set of equations based on
Lift_(force)
American mechanical engineer
hybrid model, enhancing predictions of spray characteristics and the temperature dependence of fuel penetration. Reitz applied turbulence modeling, including
Rolf_Reitz
Swirling and reverse current in a turbulent flow regime
tensorial algebra purposes when solving for two-equation turbulence models (or any other turbulence model that solves a transport equation for κ {\displaystyle
Eddy_(fluid_dynamics)
Repeating pattern of swirling vortices
SST, k-omega and Reynolds stress, and large eddy simulation (LES) turbulence models, by numerically solving some dynamic equations such as the Ginzburg–Landau
Kármán_vortex_street
Topics referred to by the same term
fluid layer under the action of gravity Turbulence modeling and eddy viscosity: in modelling the turbulence Reynolds stresses, the Boussinesq approximation
Boussinesq_approximation
Term in fluid dynamics
simulations are often undertaken to model wake flows, although such modeling has uncertainties associated with turbulence modeling (for example RANS versus LES
Wake_(physics)
Mathematical modeling of chemical processes
reaction model. Most fuels are fast burning and the overall rate of reaction is controlled by turbulence mixing. In the non-premixed flames, turbulence slowly
Chemical_reaction_model
x {\displaystyle \int _{\Omega }u\,dx} exactly. The idea of VMS turbulence modeling for Large Eddy Simulations(LES) of incompressible Navier–Stokes equations
Variational_multiscale_method
Aspects of fluid mechanics involving fluid flow
requires turbulence models for the foreseeable future. Reynolds-averaged Navier–Stokes equations (RANS) combined with turbulence modelling provides a model of
Fluid_dynamics
British academic
known for his work in the field of turbulent flows in general and turbulence modelling in particular. In 1994, he became a Fellow of the Royal Society.
Brian_Launder
Model in fluid dynamics
modification of a Reynolds-averaged Navier–Stokes equations (RANS) model in which the model switches to a subgrid scale formulation in regions fine enough
Detached_eddy_simulation
Ratio of inertial to viscous forces acting on a liquid
such as between an aircraft model in a wind tunnel and the full-size version. The predictions of the onset of turbulence and the ability to calculate
Reynolds_number
Mathematical method in fluid dynamics
G. (July 2009). "Reynolds-Averaged Navier–Stokes Equations for Turbulence Modeling". Applied Mechanics Reviews. 62 (4): 040802. doi:10.1115/1.3124648
Reynolds_decomposition
Software for simulating water flow within rivers
unsteady flow, two dimensional modeling, sediment transport and water quality modeling, and distributed hydrologic modeling (Rain-on-Grid.) The program is
HEC-RAS
Technique for managing measurement of fluid flows
equations for turbulence and porous flow are solved for the honeycomb using commercial CFD. RANS type RNG k-ε model is used for the turbulence modeling. Boundary
Flow_conditioning
Numerical simulations of physical problems via computers
computational contact mechanics. Computational electrodynamics is the process of modeling the interaction of electromagnetic fields with physical objects and the
Computational_physics
Baldwin–Lomax model is a 0-equation turbulence model used in computational fluid dynamics analysis of turbulent boundary layer flows. Baldwin-Lomax model at cfd-online
Baldwin–Lomax_model
subgrid-scale models, which reconstruct the effect of the sub-filter scales (the highest frequencies). One of the challenges in subgrid modeling is to effectively
Filter (large eddy simulation)
Filter_(large_eddy_simulation)
Cornell University professor of mechanical engineering
contributions of archival value to probability-density-function methods in turbulence modeling, to understanding of the geometry and distortion of surfaces in turbulent
Stephen_B._Pope
Mathematical simulation of how air pollutants disperse in the ambient atmosphere
dispersion models Portable Emissions Measurement System (PEMS) Roadway air dispersion modeling Useful conversions and formulas for air dispersion modeling Air
Atmospheric dispersion modeling
Atmospheric_dispersion_modeling
American engineer
Hussain (University of Houston, 1976) Academic work Main interests Heat transfer; combustion; numerical methods; turbulence modeling; materials processing
Bakhtier_Farouk
Structure to channel water past an obstacle
Fish-Turbulence Interplay?". 37th IAHR World Congress, IAHR & USAINS, Kuala Lumpur, Malaysia. 3: 2586–2595. Wang, H.; Chanson, H. (2018). "Modelling Upstream
Culvert
Weight classification for aircraft for purposes of take-off and landing
Wake turbulence categories and wake turbulence groups are defined by the International Civil Aviation Organization for the purpose of separating aircraft
Wake_turbulence_category
Type of algebraic integer
yields Pisot numbers that approach φ from above. Two-dimensional turbulence modeling using logarithmic spiral chains with self-similarity defined by a
Pisot–Vijayaraghavan_number
Lowest part of the atmosphere directly influenced by contact with the planetary surface
flow velocity, temperature, and moisture display rapid fluctuations (turbulence) and vertical mixing is strong. Above the PBL is the "free atmosphere"
Planetary_boundary_layer
Hypothesized depth at which phytoplankton growth is matched by losses
by Taylor & Ferrari (2011) using 3D Large eddy simulation (LES) turbulence modeling to study how the shutdown of thermal convection (i.e. convective
Critical_depth
Energy transfer between scales of motion
also important for wind waves in the theory of wave turbulence. Consider for instance turbulence generated by the air flow around a tall building: the
Energy_cascade
Dutch theoretical physicist
(1997). "Boundary-layer turbulence modeling and vorticity dynamics: II. Towards a theory of turbulent shear flow?". Turbulence Modeling and Vortex Dynamics
Hans_Dekker
French scientist
and Industrial Flow Laboratory. Marcel Lesieur's work focused on turbulence modeling and simulation. He performed direct numerical simulations of large
Marcel_Lesieur
French mathematician and physicist (1842–1929)
gravity Turbulence modeling and eddy viscosity for the Boussinesq approximation resulting in the use of an eddy viscosity to model the turbulence Reynolds
Joseph_Valentin_Boussinesq
School in Oxford, England
Olympic silver medallist Lord Hunt (born 1941), leading authority on turbulence modelling Tim Hunt, biochemist and Nobel laureate Edward Impey (born 1962)
Dragon_School
Computational fluid dynamics software package
incompressible or compressible. The software provides a wide range of turbulence models covering the following approaches: RANS (Reynolds-Averaged Navier–Stokes);
Code_Saturne
focus, but during this period, research topics broadened to include turbulence modeling and the study of transport phenomena in porous media. The introduction
Institut de Mécanique des Fluides de Toulouse
Institut_de_Mécanique_des_Fluides_de_Toulouse
French information technology service company
dissipation and dispersion errors combined with state-of-the-art turbulence modeling approaches (Large Eddy Simulations), allow ProLB to perform high-fidelity
CS_Communication_&_Systèmes
Laboratory in Princeton, New Jersey, United States
General Fusion and Microsoft, working on projects ranging from plasma turbulence modeling to machine learning for predicting tokamak disruptions. In 2025,
Princeton Plasma Physics Laboratory
Princeton_Plasma_Physics_Laboratory
Underwater current of sediment-laden water moving downslope
to mention. Both Direct numerical simulation (DNS) and Turbulence modeling are used to model these currents. Within minutes after the 1929 Grand Banks
Turbidity_current
American scientist (1948–1999)
turbulence and focused his research on turbulence modeling. His latest work had been published on the turbulence modelling of computing non-equilibrium turbulent
Charles_Speziale
Probabilistic problem-solving algorithm
as well as in modeling radiation transport for radiation dosimetry calculations. In statistical physics, Monte Carlo molecular modeling is an alternative
Monte_Carlo_method
Equations of motion for viscous fluids
supplemented with turbulence models, are used in practical computational fluid dynamics (CFD) applications when modeling turbulent flows. Some models include the
Navier–Stokes_equations
Data analysis is the process of inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, informing conclusions
Data_analysis
of state, viscosity and thermal conductivity models, turbulence models, multi-species chemistry models, and electromagnetics Time-dependent flow, including
CGNS
American academic
Wray-Agarwal one-equation turbulence model in 2015 which is a linear eddy viscosity model, derived from a k–omega turbulence model closure. Agarwal has been
Ramesh_K._Agarwal
Simulation of multiple aspects of physics
In computational modelling, multiphysics simulation (often shortened to simply "multiphysics") is defined as the simultaneous simulation of different
Multiphysics_simulation
Concept in fluid mechanics
study. Further u i ′ {\displaystyle u'_{i}} denotes the fluctuating (turbulence) part of the velocity. We consider a homogeneous fluid, whose density
Reynolds_stress
Ocean currents simulation system
The model incorporates the Mellor–Yamada turbulence scheme developed in the early 1970s by George Mellor and Ted Yamada; this turbulence sub-model is widely
Princeton_Ocean_Model
uses the k-epsilon model for turbulence modelling, the Eddy Dissipation Concept (EDC) for combustion modelling, and a radiation model based on the Discrete
Kameleon_FireEx_KFX
Set of nonlinear waves deviated far from thermal equilibrium
In continuum mechanics, wave turbulence is a set of nonlinear waves deviated far from thermal equilibrium. Such a state is usually accompanied by dissipation
Wave_turbulence
Model representing the dynamics of a long-chained polymer
such as polymer turbulence drag reduction and shear thinning. It is the most commonly used polymer model that can be used in a turbulence simulation since
FENE_model
Public engineering institution in Meghalaya, India
Computing Techniques in Machining, Computational Fluid Dynamics, Turbulence Modeling, Fluid Mechanics etc. The department is planning to start M.Tech
National Institute of Technology, Meghalaya
National_Institute_of_Technology,_Meghalaya
for astronomy research and education List of software for nanostructures modeling List of software for nuclear engineering Multiphysics simulation "GitHub
List of computational physics software
List_of_computational_physics_software
Mixing of fluids due to eddy currents
(see the section on Gradient based theories). See turbulence modeling for more. The simplest model of turbulent diffusion can be constructed by drawing
Eddy_diffusion
Australian nuclear scientist
Jiyuan (2014), "Solution Methods and Turbulence Modeling", Multiphase Flow Analysis Using Population Balance Modeling, Elsevier, pp. 169–261, doi:10
Guan_Heng_Yeoh
Column of one fluid moving through another
mushroom-shaped thermal plume. Atmospheric dispersion modeling Bibliography of atmospheric dispersion modeling Outline of air pollution dispersion Cryovolcano
Plume_(fluid_dynamics)
Soviet and American physicist
of the USSR Academy of Sciences in Moscow. His early research on turbulence modeling was influenced by the work of Soviet scientists like Andrey Kolmogorov
Valerian_Tatarskii
Software for numerical solution of partial differential equations
incompressible flow problems, preconditioning methods are used. Turbulence & Transition Modeling: RANS Models: Includes several variants of the Spalart-Allmaras (SA)
SU2_code
Abrupt reduction in lift due to flow separation
Taha, Haithem E. (2021). "Comparing the performance of different turbulence models in predicting dynamic stall". AIAA Scitech 2021 Forum: 1651. doi:10
Stall_(fluid_dynamics)
American theoretical physicist (1928–2008)
physicist (fluid dynamicist) best known for his work on the theory of fluid turbulence. Kraichnan received his B.S. and Ph.D. in physics from MIT, graduating
Robert_Kraichnan
Field of mathematics and science based on non-linear systems and initial conditions
as possible. Better models of warning signs of fetal hypoxia can be obtained through chaotic modeling. As Perry points out, modeling of chaotic time series
Chaos_theory
Camassa-Holm equation), turbulence (modelled by the LANS-alpha equation), template marching for biomedical images (modelled by the EPDiff equation) and
Darryl_Holm
Technique in mathematical modeling
turbulence and large coherent structures present in fluid flow problems. Model order reduction also finds modern applications in aeronautics to model
Model_order_reduction
Modelling financial risks
Financial risk management. Risk modeling is one of many subtasks within the broader area of financial modeling. Risk modeling uses a variety of techniques
Financial_risk_modeling
Mathematical expression for the stability of rocks in water currents
inertia, and the turbulence of the current. Hence, the application of this coefficient is limited to conditions where turbulence is predominantly induced
Izbash_formula
proper models are adopted, and some promising results have been presented in the literature. However, to utilize this method precisely, proper turbulence models
Dynamic stall on helicopter rotors
Dynamic_stall_on_helicopter_rotors
Integral expressing the amount of overlap of one function as it is shifted over another
In computational fluid dynamics, the large eddy simulation (LES) turbulence model uses the convolution operation to lower the range of length scales
Convolution
Canadian actress and model
Pratt (born December 18, 1970) is a Canadian actress, author and fitness model. Pratt grew up in Chesley, Ontario, a self described "tomboy at heart."[citation
Victoria_Pratt
2024 aviation accident over Myanmar
flight, carrying 211 passengers and 18 crew members, encountered severe turbulence over the Irrawaddy River, Myanmar, resulting in the death of a passenger
Singapore_Airlines_Flight_321
Model for the potential energy of a diatomic molecule
after physicist Philip M. Morse, is a convenient interatomic interaction model for the potential energy of a diatomic molecule. It is a better approximation
Morse_potential
2001 aviation accident in New York
to the first officer's overuse of rudder controls in response to wake turbulence from a preceding Japan Airlines Boeing 747-400 that took off minutes before
American_Airlines_Flight_587
Type of computer benchmarking tool
potential field. 110.applu Partial differential equations. 125.turb3d Turbulence modeling. 141.apsi Weather prediction. 145.fpppp Image From Gaussian series
SPECfp
Software model
example, turbulence prediction). Unlike models that focus on individual aspects such as mean radiant temperature or wind flows and turbulence, ENVI-met
ENVI-met
TURBULENCE MODELING
TURBULENCE MODELING
Girl/Female
Irish
From the Latin name Rosa and means “little rose.†Records show that the name has been in use in Ireland since the sixteenth century. When the expression of Irish patriotic poetry and song was outlawed during Ireland’s troubled and turbulent past, the Irish bards would disguise their nationalistic verse as love songs. In the figure of Roisin Dubh (“Dark Rosaleenâ€), a Gaelic poem translated by James Clarence Mangan in 1835, the name became a poetic symbol of Ireland, reflecting the Irish tradition of disguising outlawed patriotic verse as love songs where she is told not to be downhearted for her friends are returning from abroad to come to her aid.
Girl/Female
Irish
From the Latin name Rosa and means “little rose.†Records show that the name has been in use in Ireland since the sixteenth century. When the expression of Irish patriotic poetry and song was outlawed during Ireland’s troubled and turbulent past, the Irish bards would disguise their nationalistic verse as love songs. In the figure of Roisin Dubh (“Dark Rosaleenâ€), a Gaelic poem translated by James Clarence Mangan in 1835, the name became a poetic symbol of Ireland, reflecting the Irish tradition of disguising outlawed patriotic verse as love songs where she is told not to be downhearted for her friends are returning from abroad to come to her aid.
Girl/Female
English
Turbulent; stormy.
Girl/Female
American, Australian, British, Christian, English, French
Turbulent; Stormy; Tempest; Violent Storm
Surname or Lastname
English
English : nickname for a noisy or troublesome person, from Anglo-French de(s)rei ‘noise’, ‘trouble’, ‘turbulence’ (from Old French desroi).English : topographic for someone who lived by a deer enclosure, from Old English dēor ‘deer’ + (ge)hæg ‘enclosure’.
TURBULENCE MODELING
TURBULENCE MODELING
Boy/Male
Hindu, Indian, Marathi
Happy
Surname or Lastname
English
English : habitational name from Great or Little Blencow in Cumbria, named with a Celtic word blain ‘summit’ and an obscure second element to which Old Norse haugr ‘hill’ has been added.
Boy/Male
Indian, Telugu
Excellent
Male
Russian
(Дима) Pet form of Russian Dmitri, DIMA means "loves the earth" or "follower of Demeter."
Female
English
English variant spelling of Latin Leona, LEONE means "lion." Compare with masculine Leone.
Boy/Male
Muslim/Islamic
Director guide
Boy/Male
Tamil
Gods jewel, Lord Rama
Surname or Lastname
English
English : from Middle English Godmer, a blend of two names, Old English Godmær and Old Northern French Godmar, both composed of the Germanic elements gÅd ‘good’ or god ‘god’ + mÄ“ri, mÄri ‘famous’.
Girl/Female
Arabic, Gujarati, Hindu, Indian, Marathi, Muslim, Pashtun
Name of Prophet Muhammad's Wife; Happiness Giver
Girl/Female
Celtic American
From Ireland.
TURBULENCE MODELING
TURBULENCE MODELING
TURBULENCE MODELING
TURBULENCE MODELING
TURBULENCE MODELING
n.
Turbulence.
n.
A blustering, turbulent fellow.
n.
The quality or state of being turbulent; a disturbed state; tumult; disorder; agitation.
a.
Turbulent; violent; as, a tumultuous speech.
n.
Alt. of Truculency
adv.
In a turbulent manner.
n.
A noisy, turbulent quarrel or disturbance; a brawl.
a.
Disturbed; agitated; tumultuous; roused to violent commotion; as, the turbulent ocean.
n.
The state or quality of being boisterous; turbulence; disorder; tumultuousness.
v. i.
To grow rough, boisterous, or turbulent.
a.
Full of tumult; characterized by tumult; disorderly; turbulent.
adv.
In a scambling manner; with turbulence and noise; with bold intrusiveness.
a.
Producing commotion; disturbing; exciting.
a.
Noisy; rough; turbulent; as, boisterous mirth; boisterous behavior.
a.
Tumultuous; turbulent; boisterous; furious; quarrelsome; scolding.
n.
An uncivil, turbulent fellow.
a.
Exhibiting tumultuous violence and fury; acting with noisy turbulence; violent; rough; stormy.
n.
Stormy; turbulent; tempestuous; rude.
n.
Alt. of Purulency
a.
Disposed to insubordination and disorder; restless; unquiet; refractory; as, turbulent spirits.