Topic
Turbulence kinetic energy
About: Turbulence kinetic energy is a research topic. Over the lifetime, 16622 publications have been published within this topic receiving 470847 citations.
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TL;DR: In this paper, the authors present a review of the applicability and applicability of numerical predictions of turbulent flow, and advocate that computational economy, range of applicability, and physical realism are best served by turbulence models in which the magnitudes of two turbulence quantities, the turbulence kinetic energy k and its dissipation rate ϵ, are calculated from transport equations solved simultaneously with those governing the mean flow behaviour.
Abstract: The paper reviews the problem of making numerical predictions of turbulent flow. It advocates that computational economy, range of applicability and physical realism are best served at present by turbulence models in which the magnitudes of two turbulence quantities, the turbulence kinetic energy k and its dissipation rate ϵ, are calculated from transport equations solved simultaneously with those governing the mean flow behaviour. The width of applicability of the model is demonstrated by reference to numerical computations of nine substantially different kinds of turbulent flow.
11,866 citations
Book•
31 Jul 1988
TL;DR: In this article, the boundary layer is defined as the boundary of a boundary layer, and the spectral gap is used to measure the spectral properties of the boundary layers of a turbulent flow.
Abstract: 1 Mean Boundary Layer Characteristics.- 1.1 A boundary-layer definition.- 1.2 Wind and flow.- 1.3 Turbulent transport.- 1.4 Taylor's hypothesis.- 1.5 Virtual potential temperature.- 1.6 Boundaiy layer depth and structure.- 1.7 Micrometeorology.- 1.8 Significance of the boundary layer.- 1.9 General references.- 1.10 References for this chapter.- 1.11 Exercises.- 2 Some Mathematical and Conceptual Tools: Part 1. Statistics.- 2.1 The significance of turbulence and its spectrum.- 2.2 The spectral gap.- 2.3 Mean and turbulent parts.- 2.4 Some basic statistical methods.- 2.5 Turbulence kinetic energy.- 2.6 Kinematic flux.- 2.7 Eddy flux.- 2.8 Summation notation.- 2.9 Stress.- 2.10 Friction velocity.- 2.11 References.- 2.12 Exercises.- 3 Application of the Governing Equations to Turbulent Flow.- 3.1 Methodology.- 3.2 Basic governing equations.- 3.3 Simplifications, approximations, and scaling arguments.- 3.4 Equations for mean variables in a turbulent flow.- 3.5 Summary of equations, with simplifications.- 3.6 Case studies.- 3.7 References.- 3.8 Exercises.- 4 Prognostic Equations for Turbulent Fluxes and Variances.- 4.1 Prognostic equations for the turbulent departures.- 4.2 Free convection scaling variables.- 4.3 Prognostic equations for variances.- 4.4 Prognostic equations for turbulent fluxes.- 4.5 References.- 4.6 Exercises.- 5 Turbulence Kinetic Energy, Stability, and Scaling.- 5.1 The TKE budget derivation.- 5.2 Contributions to the TKE budget.- 5.3 TKE budget contributions as a function of eddy size.- 5.4 Mean kinetic energy and its interaction with turbulence.- 5.5 Stability concepts.- 5.6 The Richardson number.- 5.7 The Obukhov length.- 5.8 Dimensionless gradients.- 5.9 Miscellaneous scaling parameters.- 5.10 Combined stability tables.- 5.11 References.- 5.12 Exercises.- 6 Turbulence Closure Techniques.- 6.1 The closure problem.- 6.2 Parameterization rules.- 6.3 Local closure - zero and half order.- 6.4 Local closure - first order.- 6.5 Local closure - one-and-a-half order.- 6.6 Local closure - second order.- 6.7 Local closure - third order.- 6.8 Nonlocal closure - transilient turbulence theory.- 6.9 Nonlocal closure - spectral diffusivity theory.- 6.10 References.- 6.11 Exercises.- 7 Boundary Conditions and External Forcings.- 7.1 Effective surface turbulent flux.- 7.2 Heat budget at the surface.- 7.3 Radiation budget.- 7.4 Fluxes at interfaces.- 7.5 Partitioning of flux into sensible and latent portions.- 7.6 Flux to and from the ground.- 7.7 References.- 7.8 Exercises.- 8 Some Mathematical and Conceptual Tools: Part 2. Time Series.- 8.1 Time and space series.- 8.2 Autocorrelation.- 8.3 Structure function.- 8.4 Discrete Fourier transform.- 8.5 Fast Fourier Transform.- 8.6 Energy spectrum.- 8.7 Spectral characteristics.- 8.8 Spectra of two variables.- 8.9 Periodogram.- 8.10 Nonlocal spectra.- 8.11 Spectral decomposition of the TKE equation.- 8.12 References.- 8.13 Exercises.- 9 Similarity Theory.- 9.1 An overview.- 9.2 Buckingham Pi dimensional analysis methods.- 9.3 Scaling variables.- 9.4 Stable boundary layer similarity relationship lists.- 9.5 Neutral boundary layer similarity relationship lists.- 9.6 Convective boundary layer similarity relationship lists.- 9.7 The log wind profile.- 9.8 Rossby-number similarity and profile matching.- 9.9 Spectral similarity.- 9.10 Similarity scaling domains.- 9.11 References.- 9.12 Exercises.- 10 Measurement and Simulation Techniques.- 10.1 Sensor and measurement categories.- 10.2 Sensor lists.- 10.3 Active remote sensor observations of morphology.- 10.4 Instrument platforms.- 10.5 Field experiments.- 10.6 Simulation methods.- 10.7 Analysis methods.- 10.8 References.- 10.9 Exercises.- 11 Convective Mixed Layer.- 11.1 The unstable surface layer.- 11.2 The mixed layer.- 11.3 Entrainment zone.- 11.4 Entrainment velocity and its parameterization.- 11.5 Subsidence and advection.- 11.6 References.- 11.7 Exercises.- 12 Stable Boundary Layer.- 12.1 Mean Characteristics.- 12.2 Processes.- 12.3 Evolution.- 12.4 Other Depth Models.- 12.5 Low-level (nocturnal) jet.- 12.6 Buoyancy (gravity) waves.- 12.7 Terrain slope and drainage winds.- 12.8 References.- 12.9 Exercises.- 13 Boundary Layer Clouds.- 13.1 Thermodynamics.- 13.2 Radiation.- 13.3 Cloud entrainment mechanisms.- 13.4 Fair-weather cumulus.- 13.5 Stratocumulus.- 13.6 Fog.- 13.7 References.- 13.8 Exercises.- 14 Geographic Effects.- 14.1 Geographically generated local winds.- 14.2 Geographically modified flow.- 14.3 Urban heat island.- 14.4 References.- 14.5 Exercises.- Appendices.- A. Scaling variables and dimensionless groups.- B. Notation.- C. Useful constants parameters and conversion factors.- D. Derivation of virtual potential temperature.- Errata section.
9,111 citations
TL;DR: In this article, the local turbulent viscosity is determined from the solution of transport equations for the turbulence kinetic energy and the energy dissipation rate, and the predicted hydrodynamic and heat-transfer development of the boundary layers is in close agreement with the measured behaviour.
Abstract: The paper presents a new model of turbulence in which the local turbulent viscosity is determined from the solution of transport equations for the turbulence kinetic energy and the energy dissipation rate. The major component of this work has been the provision of a suitable form of the model for regions where the turbulence Reynolds number is low. The model has been applied to the prediction of wall boundary-layer flows in which streamwise accelerations are so severe that the boundary layer reverts partially towards laminar. In all cases, the predicted hydrodynamic and heat-transfer development of the boundary layers is in close agreement with the measured behaviour.
3,999 citations
Book•
01 Jan 1953
TL;DR: In this article, the kinematics of the field of homogeneous turbulence and the universal equilibrium theory of decay of the energy-containing eddies are discussed. But the authors focus on the dynamics of decay and not on the probability distribution of u(x).
Abstract: Preface 1 Introduction 2 Mathematics representation of the field of turbulence 3 The kinematics of homogeneous turbulence 4 Some linear problems 5 General dynamics of decay 6 The universal equilibrium theory 7 Decay of the energy-containing eddies 8 The probability distribution of u(x) Bibliography of research on homogeneous turbulence Index
3,121 citations