Cooperative Institute for Research in Environmental Sciences

Research Applications
Turbulence Statistics

Accurate measurements of turbulence statistics require sufficiently long stationary time series. Such data were collected by the TLS while it was parked at constant altitude in the shear region below a ~6 m s^-1 nocturnal jet.

In general, the small-scale statistics of the velocity and temperature fields are well described by their structure functions D_U(s) and D_T(s) from which various statistics are computed: dissipation scales η_U and η_T, outer scales L_U and L_T, temperature structure constant C_T², energy dissipation rate ε, and temperature and velocity variances σ_U and σ_T.

The structure functions shown below were computed from 10 seconds-long time series of the 200 Hz TLS temperature and velocity signals. Each regime can be clearly identified on these plots:

• The s^2/3 scaling in the inertial range (η < s < L):

D_u(s) = C_K ε^2/3s^2/3 ; D_T(s) = C_T²s^2/3

• The s² scaling in the dissipation range (s < η):

D_u(s) = (ε / 15 υ) s² ; D_T(s) = (N / 3 χ) s²

• The flat region at large separations (L < s) where:

L_U = σ U² / ε ; L_T = 2^3/2 σ T³ / C_T^3/2

These structure functions provide estimates of key turbulence statistics: C_T², ε, η_U, η_T, L_U, L_T, l₀ and l_U. Note that estimates of the turbulent kinetic energy (TKE) can be deduced assuming isotropy from C_T², ε, L_U, and L_T, using:

Click on image for larger version.

For further details see the related publication:

2004 - Frehlich R, Meillier Y, Jensen ML, et al.: "A statistical description of small-scale turbulence in the low-level nocturnal jet". Journal of the Atmospheric Sciences 61 (9): 1079-1085 May 2004.