Proceedings with Extended Abstracts (single PDF file) - Radio ...

3.2.1 From v ′2 to ɛ kThe question is now to relate the turbulent KE to dissipation rate ɛ k . Two methods have beenproposed (discussed by Hocking (1999)).• If the radar volume is filled with homogeneous isotropic turbulence: (Frisch and Clifford,1974; Gossard and Strauch, 1983).[]ɛ k = 1 3/2v ′2(12)δ 1.35α[1 − β 2 /15]where{ δ = σb ; β 2 ≈ 1 − (σ r /σ b ) 2 if σ r < σ bδ = σ r ; β 2 ≈ 4(1 − (σ b /σ r ) 2 ) if σ b < σ r(13)• If the outer scale of turbulence is much smaller than any scale of the sampled volume : therelations between v ′2 and dissipation rate depends on the outer scale L m (Sato and Woodman,1982; Hocking, 1983; Weinstock, 1978, 1981).ɛ k ≈ 3 ( v ′ 2 ) 3/2/Lm (14)Several definition of such an outer scale exist. A commonly used expression, proposed by Weinstock(1978), relates the outer scale to the buoyancy scale L B : L m ≈ 1.5L B ≈ 3π (ɛ k /N 3 ) 1/2The relationship between turbulent KE and dissipation rate reads:ɛ k ≈ 0.5v ′2 N (15)• It should be noticed that the hypothesis of a constant ratio L m /L B has been questioned byIvey and Imberger (1991); Weinstock (1992); Smyth and Moum (2000). For instance, Weinstock(1992) suggests that the ratio L m /L B varies as a function of Ri: L m /L B ∼ (2Ri) 3/4 .3.3 Local MixingThe heat (or mass) flux can be inferred from the dissipation rates, by assuming homogeneousand steady state turbulence.Kθlocal = γ ɛ kand K localN 2 θ = ɛ p(16)N 2As the dissipations rates, these diffusivity estimates are local quantities, i.e. within theturbulent patches (or weighted averages of local quantities).4 Unknown parametersIn order to infer turbulence parameters from radar measurements, additional terms have to beevaluated, M, N, F T and γ.The Brunt-Väisälä frequency N, and the gradient of generalised potential index M, areusually evaluated from in-situ routine measurements (non co-located). Various evidences however,suggest that such in-situ estimates of gradients is likely dubious (e.g. Dalaudier et al.,2001) due to the large space and time variability of such gradients. Climatological temperatureand pressure can be used if humidity is negligible (e.g. Gage et al., 1980). Co-locatedmeasurements of temperature from RASS or lidar, sometimes possible, are anyway preferable.197