Richardson number

Additional near-surface measurements may also be required to support calculated quantities such as the bulk Richardson number (a stability parameter) ... 

Relates the nature of the fluid flow in and around bodies. Richardson Number... 

In this section primary attention is directed at the turbulent processes that occur in the mixed layer as a result of the interaction between shear-and buoyancy-driven flows. The flux Richardson number Rf gives a measure of the relative importance of the buoyancy terms in the equations of motion, (g/T)w d , as compared to the shear production terms, u w dutbz. 

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 / (, ... 

Fischer (1972) defined the estuarine Richardson number (Rig) by the following equation ... 

Figure 3.10 Contour lines represented by the ratio (v), defined as the diffusive salt transport (tidal driven) to the total landward salt flux as related to contours of Froude [Fm = Uf/(ghAp/p)1/2] Richardson numbers [Rig = (g[Ap/p][U( /b])/U ]. A clear decrease is found when moving from Type 1 to Type 3 estuaries (From Fisher, 1976, as modified by Jay et al., 2000, with permission.)...

Richardson number dimensionless number that expresses the ratio of potential to kinetic energy, also known as the Froude number. 

G is usually termed the buoyancy force parameter . It is a form of Richardson number. 

The value of Km depends on the properties of the mean flow at a particular location and time. To account for the contribution of thermal stratification (buoyancy) to the production or suppression of turbulent energy. Km is taken to be a function of the local value of the flux Richardson number, which expresses the ratio of the rate of generation of energy by buoyancy forces to the rate of generation of energy by the turbulent momentum fluxes. In this approach the influence of the past history of the turbulence on velocity field is not considered the approach is termed a local theory. 

The air over the SCS is highly unstable, because it contains heated and light humid air portions causing buoyancy and natural convection, and thus an additional turbidity (an unstable stratification). Monin and Obukhov [435] suggested to account this by adding a linear term to the logarithmic one (1.1). Here, an alternative way of Nickitin [466] is used that suggests the universal Karman constant to be a known empirical function of the 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... 

Jaeger [313] recorded wind speed measurements over a ten year period over stands of Scotch pine located in southern Germany as they grew from 3 to 8 m height. He made estimates of the variation in m, z0, d, /3 (Deacon parameter), and Richardson number, Ri, from wind and temperature data collected from meteorological towers placed within the forest stand. He found that the following correlations described the measurements ... 

Launiainen, J. (1995) Derivation of the Relationship between the Obukhov Stability Parameter and the Bulk Richardson Number for Flux-Profile Studies,... 

In a recent publication [646] concerning the same topic, the authors distinguished between the stirrer-controlled nd w 30 = const) and the gravity-controlled regime. However, a correlation of these data with the aid of Richardson number, Ri, see below, was not satisfactory. 

The flux Richardson number according to (16.68) is a function of the distance from the ground. Because it is dimensionless, it can actually be viewed as a dimensionless length... 

By definition the Monin-Obukhov length is the height at which the production of turbulence by both mechanical and buoyancy forces is equal. The parameter L, like the flux Richardson number, provides a measure of the stability of the surface layer. As we discussed, when Rf > 0 and therefore according to (16.69) L > 0 the atmosphere is stable. On the other hand, when the atmosphere is unstable, Rf < 0 and then L < 0. Because of the inverse relationship between Rf and L, an adiabatic atmosphere corresponds to very small (positive or negative) values of Rf and to very large (positive or negative) values of L. Typical values of L for different atmospheric stability conditions are given in Table 16.2. 

The dimensionless length C, is equal to the flux Richardson number, = Rf, only in the surface layer. Using once more the n theorem, we can write the second dimensionless group as a function of the first or... 

This ratio is called the flux Richardson number and is denoted by Rf. We can then rewrite... 

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