What is LES?
Short Answer:
A large-eddy simulation (LES) is a turbulence-resolving computational and numerical method that models fluid flow by solving the filtered equations of motion.
Long Answer:
Most geophysical flows are turbulent. Excluding subsurface flows, environmental fluids such as rivers, the atmosphere, and the ocean all have high Reynolds numbers (a dimensionless number characterizing the ratio between inertial and viscous forces), defined as . Once a fluid flow exceeds some critical Reynolds number, it becomes turbulent. In a nutshell, turbulence can be defined as the swirling motion of fluids that occurs irregularly in space and time. A decomposition can be performed that assumes superposition of a mean flow and a range of chaotic motions, known as Reynolds decomposition. However, there are still interactions between the mean flow and turbulent motions that cannot be neglected.
In the atmospheric boundary layer (ABL), the Reynolds number is very high, about 108, due to turbulence generated from both mechanical shear and buoyancy. To simulate the ABL, one could solve the Reynolds-Averaged Navier-Stokes (RANS) equations, in which only the dynamics of the mean flow are solved for, and the interaction of the mean flow with turbulence is parameterized. While computationally cheap, this technique essentially averages out the three-dimensional unsteady flow that is important in many applications. Turbulence not only drastically enhances mixing and transport, but it occurs mostly close to boundaries, which is important for studies in surface-atmosphere interactions. Bottom line: we want to resolve turbulence in these simulations.
Another method that is commonly used to simulate turbulence is a direct numerical simulation (DNS), which entails solving the full Navier-Stokes equations directly. However, to do this, the computational domain must capture all scales of motion from the largest scales (the integral scale, about 1 kilometer) to the smallest scales (the Kolmogorov scale, about 1 millimeter). In fact, it can be shown that the number of floating-point operations needed to perform a DNS scales with the third power of the Reynolds number of the flow being simulated (see quick derivation using length scales here). So, the number of floating point operations for a DNS of the entire ABL is about 1024! This is beyond what is computationally possible today.
A large eddy simulation (LES) provides a wonderfully useful middle ground. By only explicitly solving for the eddies larger than some filter scale (usually the grid scale), and parameterizing the eddies smaller than that same filter scale, the LES saves computational cost, while resolving high Reynolds number flows (such as that of the ABL). This works for ABL research purposes, because the underlying assumption in the ABL is that the largest eddies contain most of the energy, and are responsible for most of the transport of momentum, heat, moisture, and other scalars or interest. The unsteadiness and turbulence of these large structures are not filtered out (as they would be in RANS), allowing for investigation of three-dimensional flow structures and secondary circulations.
However, the eddies below the filter scale cannot be ignored, and the interaction between the filtered scale and sub-grid scale (SGS) appears as an additional term in the filtered Navier-Stokes equations. These are unknowns that induce the turbulence closure problem, so they must be parameterized. Models proposed by Smagorinsky (1963) or Germano et al. (1991) are widely-used today, however the current model used in my research is a Lagrangian scale-dependent dynamic (LASD) model - see Bou-Zeid (2005) for more details on the formulation and implementation of this model.