An exact, stratified model of a meddy

An exact model to describe submesoscale, coherent vortices in a uniformly stratified fluid is presented. The model allows for stratification of the eddy interior, so as to agree with observations. The closed set of equations governing the evolution of the eddy on the F-plane is derived. In the case that the interior isopycnal surfaces remain horizontal the stratified analogue of the ‘rodon’, a special solution of the ‘lens equations’ that govern the evolution of uniform-density, warm-core surface eddies, is obtained.     

Mapping of underground cavities by the passive seismic standing waves method: the case study of Barsukovskaya cave (Novosibirsk region,Russia)

This article presents the results of mapping a karst cave by the passive seismic standing waves method. Barsukovskaya cave is located about 100 km southeast of the city of Novosibirsk (Russia). The total length of the cave's passages and grottoes is estimated at about 200 m, the maximum depth from the earth's surface is about 19 m. The method for studying underground cavities used is based on the effect of the generation of standing waves by microtremor in the space between the earth's surface and the cave roof. The accumulation of amplitude spectra of a large number of microtremor records makes it possible to determine the frequencies of the first few modes of these waves. Areal passive seismic survey on the earth's surface above the cave made it possible to construct a map of the lowest mode frequency distribution over the cave roof. Since no standing waves were observed at other points, this map reflects the cave structure in plan, which confirms the comparison with the cave diagram drawn up earlier by one of the speleologists. A schematic map of the depth of the cave roof was constructed using the longitudinal wave velocity V_p = 3120 m/s determined by the rock samples selected near the entrance to the cave. This map at a qualitative level also agrees with the data of speleologists, which indicate that the cave, on average, gradually becomes deeper from the entrance to its dead‐end branches. The shallower depths in comparison with the data of speleologists are apparently explained by a very low estimate of the velocity determined from a rock sample taken near the entrance to the cave. The reliability of the obtained cave mapping results is confirmed by the numerical simulation results using the finite‐element method.