K-Epsilon Models of Katul et al. (2004)

In Katul et al. (2004), three models that solve for the profiles of mean wind speed (U), Reynolds stress (uw), the turbulent kinetic energy (K), and the turbulent kinetic energy dissipation rate (Epsilson) inside dense canopies were proposed. One model uses a standard K-Epsilon relaxation time scale while the remaining 2 methods utilize a constant mixing length scale inside the canopy. As an example, we show how these three models are implemented in Matlab using the Duke pine forest data set described in Katul and Chang (1999). Towards this end, 7 matlab files must be downloaded and placed in the same directory:
  1. k_epsilon_example_shell.m, is the main program that loads the data, sets up the computational grid, and calls the Matlab functions responsible for the calculations.
  2. LPI_DATA.m is the data set from the Duke pine forest, and includes the measured leaf area density profile, the drag coefficient, and the measured flow statistics for which the K-Epsilon models will be tested against (see Figure 7 in Katul et al. (2004)).
  3. Thomas.m is a tri-diagonal solver needed for the implicit schemes used in solving the non-linear ODEs.
  4. closure_constants.m are the closure constants needed for the K-Epsilon models (see Table 1 and section 2.3). Note, the K-U model does not use all these constants (see section 2.4).
  5. k_U_CSL.m is the K-U model (equations 9 and 10).
  6. k_epsilon_CSL.m is the K-Epsilon model (equations 1-7) that uses a constant mixing length scale (see equation 4b).
  7. k_epsilon_CSL_e.m is the K-Epsilon model (equations 1-7) that uses standard TKE-dissipation relaxation time scales (see equation 4a, bottom).

Upon running k_epsilon_example_shell.m from the Matlab prompt, Figure 7 in Katul et al. (2004) is generated. The rationale for using a constant mixing length model is described in Poggi et al. (2004).