The Technical Note series provides an outlet for a variety of NCAR manuscripts that contribute in specialized ways to the body of scientific knowledge but which are not suitable for journal, monograph, or book publication. Reports in this series are issued by the NCAR Scientific Divisions ; copies may be obtained on request from the Publications Office of NCAR. Designation symbols for the series include: Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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A Description of the Advanced Research WRF Version 3

One major drawback of the eddy viscosity subgrid‐scale stress models used in large‐eddy simulations is their inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes. In the present work a new eddy viscosity model is presented which alleviates many of these drawbacks. The model coefficient is computed dynamically as the calculation progresses rather than input a priori. The model is based on an algebraic identity between the subgrid‐scale stresses at two different filtered levels and the resolved turbulent stresses. The subgrid‐scale stresses obtained using the proposed model vanish in laminar flow and at a solid boundary, and have the correct asymptotic behavior in the near‐wall region of a turbulent boundary layer. The results of large‐eddy simulations of transitional and turbulent channel flow that use the proposed model are in good agreement with the direct simulation data.

A dynamic subgrid‐scale eddy viscosity model

Applications of second-moment turbulent closure hypotheses to geophysical fluid problems have developed rapidly since 1973, when genuine predictive skill in coping with the effects of stratification was demonstrated. The purpose here is to synthesize and organize material that has appeared in a number of articles and add new useful material so that a complete (and improved) description of a turbulence model from conception to application is condensed in a single article. It is hoped that this will be a useful reference to users of the model for application to either atmospheric or oceanic boundary layers.

http://fap.if.usp.br/~hbarbosa/uploads/Teaching/Modclim2010a/MellorYamada1982.pdf

Development of a turbulence closure model for geophysical fluid problems

A new technique is described for the numerical investigation of the time‐dependent flow of an incompressible fluid, the boundary of which is partially confined and partially free The full Navier‐Stokes equations are written in finite‐difference form, and the solution is accomplished by finite‐time‐step advancement The primary dependent variables are the pressure and the velocity components Also used is a set of marker particles which move with the fluid The technique is called the marker and cell method Some examples of the application of this method are presented All non‐linear effects are completely included, and the transient aspects can be computed for as much elapsed time as desired

Numerical Calculation of Time‐Dependent Viscous Incompressible Flow of Fluid with Free Surface

/pdf/turbulence-and-the-dynamics-of-coherent-structures-i-1o6o6m60fm.pdf

Turbulence and the dynamics of coherent structures. I. Coherent structures

The three-dimensional, primitive equations of motion have been integrated numerically in time for the case of turbulent, plane Poiseuille flow at very large Reynolds numbers. A total of 6720 uniform grid intervals were used, with sub-grid scale effects simulated with eddy coefficients proportional to the local velocity deformation. The agreement of calculated statistics against those measured by Laufer ranges from good to marginal. The eddy shapes are examined, and only the u-component, longitudinal eddies are found to be elongated in the downstream direction. However, the lateral v eddies have distinct downstream tilts. The turbulence energy balance is examined, including the separate effects of vertical diffusion of pressure and local kinetic energy.It is concluded that the numerical approach to the problem of turbulence at large Reynolds numbers is already profitable, with increased accuracy to be expected with modest increase of numerical resolution.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112070000691

A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers

Results of a three-dimensional numerical model are analysed in a study of turbulence and entrainment within mixed layers containing stratocumulus with or without parameterized cloud-top radiative cooling. The model eliminates most of the assumptions invoked in theories of cloud-capped mixed layers, but suffers disadvantages which include poor resolution and large truncation errors in and above the capping inversion. For relatively thick mixed layers with relatively thick capping inversions, the cloud-top radiative cooling is found to be lodged mostly within the capping inversion when the cooling is confined locally to the upper 50 m or less of the cloud. It does not then contribute substantially towards increased buoyancy flux and turbulence within the well mixed layer just below. The optimal means of correlating the entrainment rate, or mixed-layer growth rate, for mixed layers of variable amounts of stratocumulus is found to be through functional dependence upon an overall jump Richardson number, utilizing as scaling velocity the standard deviation of vertical velocity existing at the top of the mixed layer (near the center of the capping inversion). This velocity is found to be a fraction of the generalized convective velocity for the mixed layer as a whole which is greater for cloud-capped mixed layers than for clear mixed layers.

Stratocumulus-capped mixed layers derived from a three-dimensional model

Results of numerical integrations are presented for a neutrally stratified planetary boundary layer containing a passive scalar, and for three unstable cases with upward heat flux. The air is assumed unsaturated. A total of either 16,000 or 32,000 grid points was used in a three-dimensional region with length and width several times the height of the boundary layer. A key result is the irrelevance of the neutral height scale, u*/f, and its replacement by the height zi of the inversion base which confines the convective mixing when m and only for the two slightly unstable cases were the vertical velocity eddies distinctly elongated as in Ekman-layer theories. At large instabilities it is shown how the friction velocity u/* loses its influence upon the turbulence intensifies and a convective velocity wale becomes important. Vertical profiles of mean wind, potential tempe...

Numerical Investigation of Neutral and Unstable Planetary Boundary Layers

Convective Velocity and Temperature Scales for the Unstable Planetary Boundary Layer and for Rayleigh Convection

The heated boundary layer for DAY 33 of the Wangara data of southeast Australia (Clarke et al., 1971) is studied numerically with a three-dimensional model using 64000 grid points within a volume 5 km on a side and 2 km deep. Subgrid-scale transport equations were utilized in place of eddy-coefficient formulations. The rate of growth of the mixed layer is examined and parameterized, and the vertical profiles of heat flux, moisture flux and momentum fluxes are examined. The momentum boundary layer is found to coincide essentially with the mixed layer, and to grow with the latter during the hours of solar heating of the surface.

James W. Deardorff

Papers

A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers

Stratocumulus-capped mixed layers derived from a three-dimensional model

Numerical Investigation of Neutral and Unstable Planetary Boundary Layers

Convective Velocity and Temperature Scales for the Unstable Planetary Boundary Layer and for Rayleigh Convection

Three-dimensional numerical study of the height and mean structure of a heated planetary boundary layer