A Boundary-Layer Scaling for Turbulent Katabatic Flow

Scaling relationships are proposed for the turbulent katabatic flow of a stably stratified fluid down a homogeneously cooled planar slope—the turbulent analogue of a Prandtl-type slope flow. The \(\Pi \) Theorem predicts that such flows are controlled by three non-dimensional parameters: the slope angle, the Prandtl number, and a Reynolds number defined in terms of the surface thermal forcing (surface buoyancy or surface buoyancy flux), Brunt-Väisälä frequency, slope angle, and molecular viscosity and diffusivity coefficients. However, by exploiting the structure of the governing differential equations in a boundary-layer form, scaled equations are deduced that involve only two non-dimensional parameters: the Prandtl number and a modified Reynolds number. In the proposed scaling framework, the slope angle does not appear as an independent governing parameter, but merely acts as a stretching factor in the scales for the dependent and independent variables, and appears in the Reynolds number. Based on the boundary-layer analysis, we hypothesize that the full katabatic-flow problem is largely controlled by two rather than three parameters. Preliminary tests of the scaling hypothesis using data from direct numerical simulations provide encouraging results.     

Wave propagation in elastic media with stress-induced anisotropy

Summary. The effect of initial stress on the velocities of plane elastic waves is considered and corrections to the first order in terms of initial stress for P -and S -waves are obtained. The results are compared with those of Dahlen, who found that to the first order the initial stress had no effect on P -wave velocities: this conclusion is shown to be correct only when the unstressed material is isotropic.     

Shear-wave polarizations in the Peter the First Range indicating crack-induced anisotropy in a thrust-fault regime

Summary. Three-component seismograms of small local earthquakes recorded in the Peter the First Range of mountains near Garm, Tadzhikistan SSR, display shear-wave splitting similar to that previously observed near the North Anatolian Fault in Turkey. The Peter the First Range is in a region of compressional tectonics, whereas the North Anatolian Fault is a comparatively simple strike-slip fault. Detailed analysis of the Turkish records suggests that the splitting is diagnostic of crack-induced anisotropy caused by vertical microcracks aligned parallel to the direction of maximum compression. Preliminary examination of paper records from Garm shows that most shear waves arriving within the shear-wave window display shear-wave splitting, and that the polarizations of leading shear-waves are consistently aligned in a NE/SW direction. The area is complicated and the tectonics are not well-understood, but the NE/SW direction is approximately perpendicular to the compressional axis in many of the fault-plane mechanisms of the earthquakes. These earthquakes are usually at depths between 5 and 12 km, although there are some deeper events nearby.
Parallel shear-wave polarizations, such as those observed, are expected to indicate the strike of nearly vertical parallel microcracks, which would be aligned parallel to the direction of maximum compression. Thus the shear-wave polarizations in the Peter the First Range indicate that the directions of principal stress are reversed in the rock above the earthquake foci where thrust faulting is taking place.     

Liparitic volcanism of some regional volcanic structures in Kazakhstan,Middle Asia and Caucasus

Liparitic volcanism is a typical feature of the orogenic phase giving rise to the Kazakhstan, Middle Asia and Caucasus folded systems. The main characteristics of the liparitic volcanism common to these three regions are the following:

1. Geo-structural zonation of the volcanic structures.
2. Dismembered Moho surface within the volcanic structures.
3. Synchronous, yet independent evolution of liparitic and andesitic volcanisms.
4. Ignimbritic character of the liparitic volcanism.
5. Lateral petrochemical zonation with some features common to the liparitic and andesitic rock series.

Geo-structural and petrochemical zonations are likely governed in the regions studied by a deep-seated plutonic body.