Hodograph

Abstract: The concept of a spatial-velocity hodograph is introduced to describe quantitatively the extrusion of a carbon tubule from a catalytic particle. The conditions under which a continuous tubular surface can be generated are discussed in terms of this hodograph, the shape of which determines the geometry of the initial nanotube. The model is consistent with all observed tubular shapes and explains why the formation process induces stresses that may lead to "spontaneous" plastic deformation of the tubule. This result is due to the violation of the continuity condition, that is, to the mismatch between the extrusion velocity by the catalytic particle, required to generate a continuous tubular surface, and the rate of carbon deposition.

Abstract: It is proved that there exists an infinite involutive family of integrals of hydrodynamic type for diagonal Hamiltonian systems of quasilinear equations; the completeness of the family is also proved, and a basis for it is constructed for Whitham's equation. Higher integrals and symmetries of these systems are found.

Abstract: A physically based, shear-relative, and Galilean invariant method for predicting supercell motion using a hodograph is presented. It is founded on numerous observational and modeling studies since the 1940s, which suggest a consistent pattern to supercell motion exists. Two components are assumed to be largely responsible for supercell motion: (i) advection of the storm by a representative mean wind, and (ii) propagation away from the mean wind either toward the right or toward the left of the vertical wind shear—due to internal supercell dynamics. Using 290 supercell hodographs, this new method is shown to be statistically superior to existing methods in predicting supercell motion for both right- and left-moving storms. Other external factors such as interaction with atmospheric boundaries and orography can have a pronounced effect on supercell motion, but these are difficult to quantify prior to storm development using only a hodograph.

Abstract: The meteorology equipment carried by the Viking landers was intended to measure atmospheric temperature, wind speed, wind direction, and pressure. During the summer months, the winds were a few meters per second, with a complex hodograph and the Lander-1 site, dominated by counterclockwise turning of the wind, and a simpler hodograph at the Lander-2 site, marked by clockwise turning of the wind. With advancing season, the repetitive wind pattern began to break down, and protracted northeasterly winds were recorded on several occasions (some of which are associated with lower than normal temperatures). Examples are given of wind and temperature traces over short periods, illustrating the effects of convection, static stability, and lander interference. A theoretical argument, based on the horizontal scale dictated by heating of slopes and on vertical mixing of momentum, is presented to explain the different sense of wind rotation at the two lander sites.