Observed relationship between the drag coefficient,Cd, and stability parameter, (−z/L)

Momentum and heat flux were measured with a sonic anemometer at the Marine Observation Tower in the port of ItÔ. Under unstable conditions (T _w -T _a =3C4C), using the eddy correlation method, results show thatCd=(1.2±0.3)×10^–3 andCh=(1.5±0.3)×10^–3 at 5.5 m above mean sea level except for the case of weak winds.An unexpected relationship betweenCd and (–z/L) was observed, that is,Cd decreases as (–z/L) increases. If roughness variation over the sea is taken into account, we can explain the decrease in the range of (–z/L) less than 1, but not in the range greater than 1. This is due to a strong instability effect and the change of roughness class, from moderately rough to smooth.     

A refinement of the previous hypothesis of turbulent energy spectrum

To refine the previous hypothesis of turbulent energy spectrum (Nan-niti, 1970), further theoretical consideration and a simple experiment using electric fans was carried out. From the hypothesis ofq=δε/δk andεq=const., the following relations are derived for the spectrumF, and the autocorrelation functionR:F(k)∼k _{−(5−2α)/3} andR(t)∼1−(t/τ)_2(1−α)/3, whereq is the local energy supply,ε the energy dissipation rate, andk the wavenumber,t the time,τ the lifetime of the largest eddy. The following further relations are also obtained:ε∼l _−α,v∼l _β,v∼τ _γ andγ=(1−α)/(2+α)=β/(1−β), wherel is the length scale of the phenomenon,v turbulent velocity,α=1/2,β=1/6, andγ=1/5. The experimental results support these relations.     

A hypothesis of turbulent energy spectrum

Based on the experimental result, ε∝l ^−0.5, previously obtained, a hypothesis of turbulent energy spectrum in steady state is presented by introducing local energy supply,q. The foundamental relations areq=δε/δκ and εq=const., wherek is the wave number. Meteorological Research Institute