would include sullicient resolution iii wove number space wtiilc itt the SiInIc
tinie rttiiitlinp sufficient complexity (i.c.. presence of shear. striltificiltit~n.
e ~ c . )
to be interesting practically. exceeds the capability of the largest computers now availuble or projected for the immediate future. Consequently.
n u n i h x l simulation of three-dimensional turbulent ffows for the purpose
of obtaining Lagrangian information must, of necessity, rely on the so-called
subgrid scale modeling. That is, analytically or heuristically obtained models
of small-scale wave number interaction must be incorporated in a deterministic way into the computer program. While such subgrid scale models can
cause consideruble dificulty in ccrtiiin aspects of flow simulation. particularly when used in the presence of strong stable stratification. they nevertheless are a necessity. and when using such models to study turbulent
diffusion one can rely on the hope that the subgrid scale modeling. a large
wave number approximation, will have minimal impact on quantities controlling diffusion since these quantities are determined primarily by the small
wave number portion of the spectrum.
In the case of twodimensional turbulent flows. computer capabilities are
such that subgrid scale approximation is not necessary. Of course. twodimensional turbulent flow is an idealization not yet shown to be a realistic
model of even the largest scale motions in the atmosphere. Nevertheless. as a
theoretical exercise, and as a possibly practical model for quasi-geostrophic
atmospheric turbulence there is some justification for studying the problem.
Herr: it is possible to undertake numerical simulation without use of the
subgrid scale model but by dealing with the basic Navier-Stokes equations
and truncating these at some sufficiently large wave number to have minimal
impact on the large wave number effects controlling diffusion.
In this paper two examples of numerical simulation of Lagrangian turhulence motion are considered. In the first, a two-dimensional simulation is
cxamincd using an Eulerian field generation truncated at a reasonably high
wwc number, In the second case, a three-dimensional simulation is
examined. namely, simulated. fully developed turbulent channel flow. Here
subgrid scalc approximation is essential. 1 n both cases, Lagrangian particles
are tracked in order to obtain information about such quantities as Lagrangian autocorrclation, mean-square displacement, relative two-point
displacement, and the effects of shear flow on diffusion.
2. SIMCILATION OF TLJHBUL.ENT DIFFUSION FOR
TWO-DIMENSIONAL FLOW
Two-dimensional turbulent flow is in a sense a misnomer inasmuch as the
two-dimensional restriction prohibits vortex strclchinp. In any event such an
idealiziition can be considered as an approximation to motions occurring on
iI large scale in thc oceans and atmospheres. ie.. quasi-gcostrophic tur-
tinie rttiiitlinp sufficient complexity (i.c.. presence of shear. striltificiltit~n.
e ~ c . )
to be interesting practically. exceeds the capability of the largest computers now availuble or projected for the immediate future. Consequently.
n u n i h x l simulation of three-dimensional turbulent ffows for the purpose
of obtaining Lagrangian information must, of necessity, rely on the so-called
subgrid scale modeling. That is, analytically or heuristically obtained models
of small-scale wave number interaction must be incorporated in a deterministic way into the computer program. While such subgrid scale models can
cause consideruble dificulty in ccrtiiin aspects of flow simulation. particularly when used in the presence of strong stable stratification. they nevertheless are a necessity. and when using such models to study turbulent
diffusion one can rely on the hope that the subgrid scale modeling. a large
wave number approximation, will have minimal impact on quantities controlling diffusion since these quantities are determined primarily by the small
wave number portion of the spectrum.
In the case of twodimensional turbulent flows. computer capabilities are
such that subgrid scale approximation is not necessary. Of course. twodimensional turbulent flow is an idealization not yet shown to be a realistic
model of even the largest scale motions in the atmosphere. Nevertheless. as a
theoretical exercise, and as a possibly practical model for quasi-geostrophic
atmospheric turbulence there is some justification for studying the problem.
Herr: it is possible to undertake numerical simulation without use of the
subgrid scale model but by dealing with the basic Navier-Stokes equations
and truncating these at some sufficiently large wave number to have minimal
impact on the large wave number effects controlling diffusion.
In this paper two examples of numerical simulation of Lagrangian turhulence motion are considered. In the first, a two-dimensional simulation is
cxamincd using an Eulerian field generation truncated at a reasonably high
wwc number, In the second case, a three-dimensional simulation is
examined. namely, simulated. fully developed turbulent channel flow. Here
subgrid scalc approximation is essential. 1 n both cases, Lagrangian particles
are tracked in order to obtain information about such quantities as Lagrangian autocorrclation, mean-square displacement, relative two-point
displacement, and the effects of shear flow on diffusion.
2. SIMCILATION OF TLJHBUL.ENT DIFFUSION FOR
TWO-DIMENSIONAL FLOW
Two-dimensional turbulent flow is in a sense a misnomer inasmuch as the
two-dimensional restriction prohibits vortex strclchinp. In any event such an
idealiziition can be considered as an approximation to motions occurring on
iI large scale in thc oceans and atmospheres. ie.. quasi-gcostrophic tur-