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By James W. Deardorff.

Journal of Fluid Mechanics 41(2), 453–480 (1970). Author name and affiliation on printed p. 453; abstract describes integrated primitive equations, plane Poiseuille flow, statistical averages and comparison with experiments. Primary paper scan hosted as university course material.

James W. Deardorff was an atmospheric scientist whose numerical work helped establish large eddy simulation as a way to study turbulence. His 1970 study integrated three-dimensional equations for turbulent channel flow while representing subgrid effects through coefficients tied to resolved deformation. The primary paper identifies his affiliation as the National Center for Atmospheric Research.^[ref]

The calculation used 6720 uniform grid intervals and compared computed flow statistics with experimental measurements. The reported agreement ranged from good to marginal. This made the unresolved-motion model testable against quantities beyond the appearance of an evolving flow: the paper examined eddy structure and the kinetic energy balance as well as statistical averages.^[ref]

An elementary example explains why those separate statistics matter. Two equally likely velocities $U-a$ and $U+a$ have mean $U$ and variance $a^2$. A prediction that always returns $U$ has the correct mean but zero variance. Matching a mean velocity profile alone therefore cannot establish that a model captures turbulent fluctuations or their transport.

Deardorff's study illustrates a productive compromise: compute evolving resolved structures, model the missing influence with a subgrid-scale model, and compare predicted statistics with observations. Finer resolution and a different closure can change the prediction, so agreement remains a property of a specified calculation and test.

A large eddy simulation computes the time-dependent large-scale motion of a turbulent flow while representing the influence of unresolved motion through a subgrid-scale model. A spatial averaging filter specifies which information is retained. The distinction concerns spatial resolution, rather than simply replacing a fluctuating flow by its time average.^[ref]

For an elementary illustration, take one component of a periodic velocity field,An ideal filter retaining Fourier modes with integer index at most four keeps the first term and removes the second, whose index is ten. The removed term still contributes to products such as $u_x^2$. Filtering the nonlinear Navier-Stokes equations consequently introduces a subgrid-scale stress that cannot generally be reconstructed from the retained velocity field alone.

This gives a computational compromise. Direct numerical simulation must resolve the dynamically relevant dissipative motion, whereas a large eddy simulation resolves a chosen coarser field and models its missing influence. Doubling grid counts in all three directions multiplies the cell count by eight, before any additional time-step cost. The filter, numerical discretization and closure must work together; a coarse grid by itself does not certify a useful approximation.

An early concrete demonstration was James W. Deardorff's 1970 calculation of turbulent channel flow using 6720 uniform grid intervals and strain-dependent coefficients for subgrid effects. The paper compared computed statistics with experimental measurements and reported agreement ranging from good to marginal. That comparison tests a particular simulation, rather than establishing that every resolved structure or model is exact.^[ref]

Implementations can supply subgrid dissipation in different ways. The Cardinal documentation, for example, describes a spectral filter used to drain energy from the smallest retained wavelengths; that is a particular numerical treatment, not the definition of all large eddy simulation.^[ref]