Richardson number gradient

Stability is the need for simultaneous determinations of both the heat and momentum fluxes. Another approach is to deflne a quantity similar to Eq. (7.1) called the gradient Richardson number R ... 

The Monin-Obukhov length L is not a parameter that is routinely measured. Colder (1972), however, established a relation between the stability classes of Pasquill, the roughness height zo (see Section VII,B), and L. The results of his investigation are shown in Fig. 4. Alternatively, the local wind speed and cloud cover measurements are used to estimate the Pasquill stability class (Table IV). In addition, Colder developed a nonogram for relating the gradient Richardson number R-, to the more easily determined bulk Richardson number / (, ... 

With Fr 1 globally, the flow in the Wind Tunnel model study divided into two distinct flow regimes. Above the canopy the flow remained fully turbulent but stably stratified with a gradient Richardson number Ri 0.1. Within the canopy, the flow was laminar with Ri 10 and flowed downhill as gravity currents on both the windward... 

Aside from Kt and Km, / /now involves quantities that can be measured rather easily. In order to isolate the ratio AT7-/Km we define the gradient Richardson number Ri by... 

When the gas accumulated in the top-carving area reaches a state of dynamic equilibrium, the gas concentration no longer varies with time, at time of dddt = 0. About the stability of stratified fluid, Planck pointed out that the stability of stratified fluid depends on gradient and Richardson Number in 1929,... 

The results of Sumer s work show that the transverse mixing in a uniform channel is decreased by the existence of a stable density gradient in about the same proportion as the vertical mixing is reduced. In addition, a relationship between the coefficient and a Richardson number can be discerned. However, few natural channels are uniform, and Sumer s results show that Dj, is increased if the channel is irregular. Sumer and Fischer (90) note that it seems likely that the same holds for but they did not investigate this aspect Most numerical models of stratified estuaries hypothesize a relationship between mixing coefficients and some form of Richardson number. The results of this study suggest that in natural channels no such relationship may exist, or if it does, it may be in the opposite direction from what has usually been assumed. ... 

It turns out that Eq. (59) applies well at both low and high Reynolds numbers, but underpredicts Re (and hence U) at intermediate values of Re, particularly at the lower values of s (Khan and Richardson, 1990 Di Felice, 1995). It shares this characteristic with an equation similar in form obtained by equating the relationship for pressure gradient proposed later by Foscolo et al. (1983) with the pressure gradient as given by Eq. (8), viz.. 

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