Turbulent Kinetic Energy (TKE)

Slides:



Advertisements
Similar presentations
Introduction Irina Surface layer and surface fluxes Anton
Advertisements

Institut für Meteorologie und Klimatologie Universität Hannover
Canopy Spectra and Dissipation John Finnigan CSIRO Atmospheric Research Canberra, Australia.
LARGE EDDY SIMULATION Chin-Hoh Moeng NCAR.
Turbulent Mixing During an Admiralty Inlet Bottom Water Intrusion Philip Orton Hats off to the A-Team: Sally, Erin, Karin and Christie! Profs extraordinaire:
Continuity Equation. Continuity Equation Continuity Equation Net outflow in x direction.
Convection.
Louisiana Tech University Ruston, LA Slide 1 Time Averaging Steven A. Jones BIEN 501 Monday, April 14, 2008.
..perhaps the hardest place to use Bernoulli’s equation (so don’t)
LES of Turbulent Flows: Lecture 10 (ME EN )
Dynamics V: response of the ocean to wind (Langmuir circulation, mixed layer, Ekman layer) L. Talley Fall, 2014 Surface mixed layer - Langmuir circulation.
Direct numerical simulation study of a turbulent stably stratified air flow above the wavy water surface. O. A. Druzhinin, Y. I. Troitskaya Institute of.
Convection Convection Matt Penrice Astronomy 501 University of Victoria.
Turbulence and mixing in estuaries
Sensible heat flux Latent heat flux Radiation Ground heat flux Surface Energy Budget The exchanges of heat, moisture and momentum between the air and the.
Introduction to surface ocean modelling SOPRAN GOTM School Warnemünde: Hans Burchard Baltic Sea Research Institute Warnemünde, Germany.
Evidence for a mixing transition in fully-developed pipe flow Beverley McKeon, Jonathan Morrison DEPT AERONAUTICS IMPERIAL COLLEGE.
Engineering H191 - Drafting / CAD The Ohio State University Gateway Engineering Education Coalition Lab 4P. 1Autumn Quarter Transport Phenomena Lab 4.
Eddy Viscosity Model Jordanian-German Winter Academy February 5 th -11 th 2006 Participant Name : Eng. Tareq Salameh Mechanical Engineering Department.
1 Physics of turbulence muna Al_khaswneh Dr.Ahmad Al-salaymeh.
Boundary Layer Meteorology Lecture 4 Turbulent Fluxes Energy Cascades Turbulence closures TKE Budgets.
California State University, Chico
Modelling of the particle suspension in turbulent pipe flow
0 Local and nonlocal conditional strain rates along gradient trajectories from various scalar fields in turbulence Lipo Wang Institut für Technische Verbrennung.
Xin Xi. 1946: Obukhov Length, as a universal length scale for exchange processes in surface layer. 1954: Monin-Obukhov Similarity Theory, as a starting.
Reynolds-Averaged Navier-Stokes Equations -- RANS
Equations that allow a quantitative look at the OCEAN
Momentum Equations in a Fluid (PD) Pressure difference (Co) Coriolis Force (Fr) Friction Total Force acting on a body = mass times its acceleration (W)
Turbulent properties: - vary chaotically in time around a mean value - exhibit a wide, continuous range of scale variations - cascade energy from large.
Budgets of second order moments for cloudy boundary layers 1 Systematische Untersuchung höherer statistischer Momente und ihrer Bilanzen 1 LES der atmosphärischen.
Mass Transfer Coefficient
Modeling the Atmospheric Boundary Layer (2). Review of last lecture Reynolds averaging: Separation of mean and turbulent components u = U + u’, = 0 Intensity.
LES of Turbulent Flows: Lecture 2 (ME EN )
Mixing From Stresses Wind stresses Bottom stresses Internal stresses Non-stress Instabilities Cooling Double Diffusion Tidal Straining Shear ProductionBuoyancy.
Physics of turbulence at small scales Turbulence is a property of the flow not the fluid. 1. Can only be described statistically. 2. Dissipates energy.
Typical Mean Dynamic Balances in Estuaries Along-Estuary Component 1. Barotropic pressure gradient vs. friction Steady state, linear motion, no rotation,
Further steps towards a scale separated turbulence scheme: Matthias Raschendorfer DWD Aim: General valid (consistent) description of sub grid scale (SGS)
1 Marginal Thermobaric Stability in the Weddell Sea Miles McPhee McPhee Research Company.
Matthias Raschendorfer DWD Recent extensions of the COSMO TKE scheme related to the interaction with non turbulent scales COSMO Offenbach 2009 Matthias.
Quantification of the Infection & its Effect on Mean Fow.... P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Modeling of Turbulent.
Conservation of Salt: Conservation of Heat: Equation of State: Conservation of Mass or Continuity: Equations that allow a quantitative look at the OCEAN.
INTRODUCTION TO CONVECTION
Turbulence Modeling In FLOTRAN Chapter 5 Training Manual May 15, 2001 Inventory # Questions about Turbulence What is turbulence and what are.
ARSM -ASFM reduction RANSLESDNS 2-eqn. RANS Averaging Invariance Application DNS 7-eqn. RANS Body force effects Linear Theories: RDT Realizability, Consistency.
Lecture Guidelines for GEOF110 Chapter 7 Until Re-averaging + movie = 2 h scaling/ hydrostatic equation = 2 h Ilker Fer Guiding for blackboard presentation.
Viscosità Equazioni di Navier Stokes. Viscous stresses are surface forces per unit area. (Similar to pressure) (Viscous stresses)
Direct numerical simulation has to solve all the turbulence scales from the large eddies down to the smallest Kolmogorov scales. They are based on a three-dimensional.
Turbulent Fluid Flow daVinci [1510].
The Standard, RNG, and Realizable k- Models. The major differences in the models are as follows: the method of calculating turbulent viscosity the turbulent.
Meteorological Variables 1. Local right-hand Cartesian coordinate 2. Polar coordinate x y U V W O O East North Up Dynamic variable: Wind.
Simulation of a self-propelled wake with small excess momentum in a stratified fluid Matthew de Stadler and Sutanu Sarkar University of California San.
Introduction to the Turbulence Models
Development of the two-equation second-order turbulence-convection model (dry version): analytical formulation, single-column numerical results, and.
Coastal Ocean Dynamics Baltic Sea Research Warnemünde
Reynolds-Averaged Navier-Stokes Equations -- RANS
Introduction to Symmetry Analysis
Connecting Observations With Theory
C. F. Panagiotou and Y. Hasegawa
The k-ε model The k-ε model focuses on the mechanisms that affect the turbulent kinetic energy (per unit mass) k. The instantaneous kinetic energy k(t)
Isotropy Kinetic Energy Spectrum.
SCALING AND NON-DIMENSIONAL NUMBERS
Particle (s) motion.
Fundamentals of Convection
Characteristics of Turbulence:
New insights into turbulence dynamics under stabilizing
Lake Iseo Field Experiment
Lecture 1: Introduction
Convective Heat Transfer
Turbulent properties:
  Robin Robertson Lamont-Doherty Earth Observatory
Presentation transcript:

Turbulent Kinetic Energy (TKE) An equation to describe TKE is obtained by multiplying the momentum equation for turbulent flow times the flow itself (scalar product) Total flow = Mean plus turbulent parts = Same for a scalar:

- Use these properties of turbulent flows in the Navier Stokes equations The only terms that have products of fluctuations are the advection terms All other terms remain the same, e.g.,

are the Reynolds stresses arise from advective (non-linear or inertial) terms

Turbulent Kinetic Energy (TKE) Equation Multiplying turbulent flow times ui and dropping the primes Total changes of TKE Transport of TKE Shear Production Buoyancy Production Viscous Dissipation fluctuating strain rate Transport of TKE. Has a flux divergence form and represents spatial transport of TKE. The first two terms are transport of turbulence by turbulence itself: pressure fluctuations (waves) and turbulent transport by eddies; the third term is viscous transport

interaction of Reynolds stresses with mean shear; represents gain of TKE represents gain or loss of TKE, depending on covariance of density and w fluctuations represents loss of TKE

In many ocean applications, the TKE balance is approximated as:

Shear production from bottom stress z u Vertical Shears (vertical gradients) bottom

Shear production from wind stress z W u Vertical Shears (vertical gradients)

Shear production from internal stresses z Vertical Shears (vertical gradients) u1 u2 Flux of momentum from regions of fast flow to regions of slow flow

Parameterizations and representations of Shear Production Near the bottom Bottom stress:

Law of the wall may be widely applicable (Monismith’s Lectures) Law of the wall may be widely applicable

(Monismith’s Lectures) Ralph Obtained from velocity profiles and best fitting them to the values of z0 and u*

Shear Production from Reynolds’ stresses Mixing of property S Mixing of momentum With ADCP: and θ is the angle of ADCP’s transducers -- 20º Lohrmann et al. (1990, J. Oc. Atmos. Tech., 7, 19)

Souza et al. (2004, Geophys. Res. Lett., 31, L20309) (2002)

Souza et al. (2004, Geophys. Res. Lett., 31, L20309) Day of the year (2002)

Souza et al. (2004, Geophys. Res. Lett., 31, L20309)

Buoyancy Production from Cooling and Double Diffusion S1, T1 S2, T2 S2 > S1 T2 > T1

Layering Experiment http://www.phys.ocean.dal.ca/programs/doubdiff/labdemos.html

Data from the Arctic From Kelley et al. (2002, The Diffusive Regime of Double-Diffusive Convection)

Layers in Seno Gala

Dissipation from strain in the flow (m2/s3) (Jennifer MacKinnon’s webpage)

Production of TKE Dissipation of TKE From: Rippeth et al. (2003, JPO, 1889) Dissipation of TKE

Other ways to determine dissipation (indirectly) Az Other ways to determine dissipation (indirectly) (Monismith’s Lectures)

(Monismith’s Lectures)

Inertial subrange – transfer of energy by inertial forces (responsible for dissipation of TKE) Inertial subrange – transfer of energy by inertial forces (Monismith’s Lectures)

P Kolmogorov’s K-5/3 law (Monismith’s Lectures) equilibrium range inertial dissipating range

Stratification kills turbulence In stratified flow, buoyancy tends to: i) inhibit range of scales in the subinertial range ii) “kill” the turbulence

(Monismith’s Lectures)

(Monismith’s Lectures)

(Monismith’s Lectures)

(Monismith’s Lectures)