Friction, atmospheric drag

The orbits of artificial satellites of the Earth or other bodies with atmospheres whose orbits come close to their surfaces are very complicated. The orbits of these satellites are influenced by atmospheric drag, which tends to bring the satellite down into the lower atmosphere, where it is either vaporized by atmospheric friction or falls to the planet s surface. In addition, the shape of Earth and many other bodies is not perfectly spherical. The bulge that forms at the equator, due to the planet s spinning motion, causes a stronger gravitational attraction. When the satellite passes by the equator, it may be slowed enough to pull it to earth. 

Momentum boundary layer calculations are useful to estimate the skin friction on a number of objects, such as on a ship hull, airplane fuselage and wings, a water surface, and a terrestrial surface. Once we know the boundary layer thickness, occurring where the velocity is 99% of the free-stream velocity, skin friction coefficient and the skin friction drag on the solid surface can be calculated. Estimate the laminar boundary layer thickness of a 1-m-long, thin flat plate moving through a calm atmosphere at 20 m/s. 

The early conductance theories given by Debye and Hiickel in 1926, Onsager in 1927 and Fuoss and Onsager in 1932 used a model which assumed all the postulates of the Debye-Hiickel theory (see Section 10.3). The factors which have to be considered in addition are the effects of the asymmetric ionic atmosphere, i.e. relaxation and electrophoresis, and viscous drag due to the frictional effects of the solvent on the movement of an ion under an applied external field. These effects result in a decreased ionic velocity and decreased ionic molar conductivity and become greater as the concentration increases. 

With respect to urban air pollution, the region of the atmosphere governing transport and dispersion is the so-called planetary boundary layer, roughly the lowest 1000 m. The planetary boundary layer represents the extent of influence of the Earth s surface on wind structure in the atmosphere. Within the planetary boundary layer, winds are influenced by the prevailing high-level flows and the frictional drag of the surface. 

The transition region between the turbulent surface layer and the normally nonturbulent free atmosphere This region is about 1 km in thickness and is characterized by a well-developed mixing generated by frictional drag as the air masses move over the Earth s surface. This layer contains approximately 10% of the mass of the atmosphere. Also called the atmospheric boundary layer or frictional layer, plankton... 

FIGURE 20.2 Forces acting on a charged particle. The particle is negatively charged and surrounded by a positively charged ionic atmosphere, indicated by the dashed circle. Fi is the electrical force, F2 is Stokes frictional drag, F3 is electrophoretic retardation, and F4 is the relaxation effect. 

Let us consider a neutral surface layer in stationary and horizontal homogeneous conditions. In that case, de/dt = 0, B = 0 (because of the adiabatic temperature profile and a zero heat flux at the surface), and usually also D = 0. Then, Eq. (3) provides a balance between shear production S and dissipation of kinetic ener s. In the neutral surface layer with mean wind speed U in the x-direction, we have S = - wo dU jdz, where wwo represents the vertical flux of horizontal momentum near the surface. This momentum flux is directly related to a friction force on the atmospheric motion by the drag of the surface. Since the momentum flux plays a dominant role in the surface-layer turbulence, it is used to define a characteristic turbulent velocity scale o by... 

---