Convective velocity scale

In this expression, w is a typical velocity scale and d a typical length scale, for example the diameter of a micro charmel. The Peclet number represents the ratio of the diffusive and the convective time-scales, i.e. flows with large Peclet numbers are dominated by convection. 

Velocity and temperature gradients are confined to the surface layer defined by z < I-. Above L the wind velocity and potential temperature are virtually uniform with height. Venkatram (1978) has presented a method to estimate the value of the convective velocity scale w,. On the basis of this method, he showed that convective conditions in the planetary boundary layer are a common occurrence (Venkatram, 1980). In particular, the planetary boundary layer is convective during the daytime hours for a substantial fraction of each year ( 7 months). For example, for a wind speed of 5 m sec , a kinematic heat flux Qo as small as O.PC sec can drive the planetary boundary layer into a convective state. 

Venkatram, A. (1978). Estimating the convective velocity scale for diffusion applications. Boundary Layer Meteorol. 15, 447-452. 

In nature, it is likely to encounter convective dissolution of many crystals. In this case, if their boundary layers do not overlap and the flow velocity fields do not overlap, each crystal may be viewed as dissolving individually without interacting with other crystals. However, if their boundary layers overlap or their flow velocity fields overlap, the above treatment would not be accurate. Furthermore, when there are many crystals, the whole parcel of crystal-containing fluid may sink or rise (large-scale convection), leading to completely different fluid dynamics. Such problems remain to be solved. 

The velocity field is caused in free convection by the temperature field. Therefore, the thickness 8 of the thermal boundary layer can be used as the single length scale that characterizes both the temperature and velocity fields. Denoting the velocity scale in the x direction by u0, the continuity equation [Eq. (39)] shows that the velocity scale v0 in the y direction is of the order of u08/x. 

We may note that the thermal boundary layer in this case is asymptotically thin relative to the boundary layer for a solid body. This is a consequence of the fact that the tangential velocity near the surface is larger, and hence convection is relatively more efficient. From a simplistic point of view, the larger velocity means that convection parallel to the surface is more efficient, and hence the time available for conduction (or diffusion) normal to the surface is reduced. Thus, the dimension of the fluid region that is heated (or within which solute resides) is also reduced. Indeed, if we define Pe by using a characteristic length scale lc and a characteristic velocity scale uc, heat can be conducted a distance... 

Diffusive flow for neutrals The importance of convective vs. diffusive flow of neutrals is determined by the Peclet number Pe = uL/D, where L is a characteristic dimension of the system. Away from inlet and exit ports, the characteristic length will be on the order of the reactor dimension. The system will be primarily diffusive when Pe 1. For CI2 gas in a reactor with L 0.1 m and a neutral species diffusivity of D 5m s at 20mtorr, the Peclet number will be Pe 1 when M = 50ms. Convective gas velocities are not likely to be that high, except for a small region near the gas inlet ports. It follows that gas flow can be approximated as diffusive this obviates the need for solving the full Navier-Stokes equations which adds to the computational burden. It should be noted that both the diffusivity and the convective velocity scale inversely with gas pressure, so the Pe number is independent of pressure. However, as the pressure is lowered to the point of free molecular flow, the gas diffusion coefficient has no meaning any more. Direct Simulation Monte Carlo (DSMC) [41, 143] can then be applied to solve for the fluid velocity profiles. 

The variables on which Fy and F, are assumed to depend are the friction velocity u, the Monin-Obukhov length L, the Coriolis parameter /, the mixed-layer depth zt, the convective velocity scale w, the surface roughness z.a, and the height of pollutant release above the ground h.s... 

Unstable Conditions In unstable conditions there is usually an inversion base height at z = Zi that defines the extent of the mixed layer. The two parameters that are key in determining Kzz are the convective velocity scale wr and Zi- We expect that a dimensionless profile Kzz = Kzz/w,z., which is a function only of z/z., should be applicable. This form should be valid as long as Kzz is independent of the nature of the source distribution. Lamb and Duran (1977) determined that Kzz does depend on the source height. With the proviso that the result be applied when emissions are at or near ground level, Lamb et al. (1975) and Lamb and Duran (1977) derived an empirical expression for Kzz under unstable conditions, using the numerical turbulence model of Deardorff (1970) ... 

Convective storm, 1027, 1029 Convective velocity scale, 87d Coordinate systems ... 

Heat convection from the ground to a cold dense gas cloud is an additional source of turbulent kinetic energy. The velocity scale for this process is defined by... 

Because Eq. (133) is widely used for predicting particle transfer rates, it is instructive to perform its dimensional analysis by introducing the characteristic length scale convection velocity and migration velocity Then, Eq. (133) can be expressed as... 

Chemical constraints on the water abundance in the deep atmosphere of Saturn were given by Visscher and Channon, 2005 [346]. Saturn is known to develop the largest scale convective storms in the Solar System. Water storms that also occur in the atmosphere of Jupiter may develop velocities up to 150 m/s (Hueso and Sanchez-Lavega, 2004 [167]). 

After detachment of the flame from the walls, the narrow ever-diminishing hot product zone behind the flame moves owing to the free convection in the centrifugal acceleration field toward the axis of rotation, with a speed scaling with circumferential velocity at the flame location, which reduces the observed flame speed to very low values, and in some cases negative ones. 

---