Toward Improved Closure Relations for the Turbulent Kinetic Energy Equation in Bubble-Driven Flows

2013 ◽  
Vol 85 (7) ◽  
pp. 1131-1136 ◽  
Author(s):  
Martin Wörner ◽  
Sercan Erdogan
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Energy Equation ◽  
Turbulent Kinetic Energy Equation ◽  
Closure Relations

Scaling the Turbulent Kinetic Energy Equation

2015 ◽  
pp. 239-242
Author(s):  
Jordi Vila-Guerau de Arellano ◽  
Chiel C. van Heerwaarden ◽  
Bart J. H. van Stratum ◽  
Kees van den Dries
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Energy Equation ◽  
Turbulent Kinetic Energy Equation

scholarly journals Scaling and modelling of turbulence in variable property channel flows

2017 ◽  
Vol 823 ◽  
Author(s):  
Rene Pecnik ◽  
Ashish Patel
Keyword(s):  
Mach Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Energy Equation ◽  
Stokes Equations ◽  
Channel Flows ◽  
Alternative Formulation ◽  
Variable Property ◽  
Budget Analysis ◽  
Turbulent Kinetic Energy Equation

We derive an alternative formulation of the turbulent kinetic energy equation for flows with strong near-wall density and viscosity gradients. The derivation is based on a scaling transformation of the Navier–Stokes equations using semi-local quantities. A budget analysis of the semi-locally scaled turbulent kinetic energy equation shows that, for several variable property low-Mach-number channel flows, the ‘leading-order effect’ of variable density and viscosity on turbulence in wall bounded flows can effectively be characterized by the semi-local Reynolds number. Moreover, if a turbulence model is solved in its semi-locally scaled form, we show that an excellent agreement with direct numerical simulations is obtained for both low- and high-Mach-number flows, where conventional modelling approaches fail.

Spectra and Cospectra Over Flat Uniform Terrain

1994 ◽  
Author(s):  
J. C. Kaimal ◽  
J. J. Finnigan
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Turbulent Flows ◽  
Energy Equation ◽  
Spatial Scales ◽  
Random Forcing ◽  
Dissipation Term ◽  
Turbulent Kinetic Energy Equation

Turbulent flows like those in the atmospheric boundary layer can be thought of as a superposition of eddies—coherent patterns of velocity, vorticity, and pressure— spread over a wide range of sizes. These eddies interact continuously with the mean flow, from which they derive their energy, and also with each other. The large “energy-containing” eddies, which contain most of the kinetic energy and are responsible for most of the transport in the turbulence, arise through instabilities in the background flow. The random forcing that provokes these instabilities is provided by the existing turbulence. This is the process represented in the production terms of the turbulent kinetic energy equation (1.59) in Chapter 1. The energy-containing eddies themselves are also subject to instabilities, which in their case are provoked by other eddies. This imposes upon them a finite lifetime before they too break up into yet smaller eddies. This process is repeated at all scales until the eddies become sufficiently small that viscosity can affect them directly and convert their kinetic energy to internal energy (heat). The action of viscosity is captured in the dissipation term of the turbulent kinetic energy equation. The second-moment budget equations presented in Chapter 1, of which (1.59) is one example, describe the summed behavior of all the eddies in the turbulent flow. To understand the conversion of mean kinetic energy into turbulent kinetic energy in the large eddies, the handing down of this energy to eddies of smaller and smaller scale in an “eddy cascade” process, and its ultimate conversion to heat by viscosity, we must isolate the different scales of turbulent motion and separately observe their behavior. Taking Fourier spectra and cospectra of the turbulence offers a convenient way of doing this. The spectral representation associates with each scale of motion the amount of kinetic energy, variance, or eddy flux it contributes to the whole and provides a new and invaluable perspective on boundary layer structure. The spectrum of boundary layer fluctuations covers a range of more than five decades: millimeters to kilometers in spatial scales and fractions of a second to hours in temporal scales.

A new model for the CBL growth based on the turbulent kinetic energy equation

2007 ◽  
Vol 7 (5) ◽  
pp. 409-419 ◽  
Author(s):  
Antonio G. Goulart ◽  
Davidson M. Moreira ◽  
Marco T. Vilhena ◽  
Gervásio A. Degrazia ◽  
Sergej S. Zilitinkevich
Keyword(s):  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Energy Equation ◽  
New Model ◽  
Turbulent Kinetic Energy Equation
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