Modons in hyperbolically sheared zonal flow are analytically constructed in the equivalent barotropic system on a β plane. Linearity between the potential vorticity and the stream function, and circularity of the modon boundary are assumed. In the presence of the shear, the azimuthal velocity becomes discontinuous on the modon boundary. The flow inside of the modon boundary may have the same high-over-low dipole structure as the modon in uniform zonal flow. The outside flow rapidly approaches the sheared zonal background flow as receding from the modon boundary.
The propagation speed and depth of density currents in an arbitrarily sheared environmental flow with energy loss due to the cold-warm interfacial friction are analytically investigated in a 2-dimensional model. Only a case of small energy loss and small wind shear is examined. While there is only one solution for a conservative case, the energy loss generates two distinct solutions. One is strongly controlled by the energy loss, which does not exist for a conservative case. The other is not so much affected by it, which is connected with the conservative solution. The former depends on the energy loss on the cold-warm interface. The latter depends on the vertically integrated total energy loss. Both solutions are independent of its vertical profile.
Some strain steps which are often observed by the JMA strainmeters seem to occur prior to earthquakes. Therefore the strain steps have been considered to be a possible index of an earthquake occurrence. However, many other strain steps can occur unrelated to any earthquakes. It is statistically investigated whether these associations of strain steps with earthquake occurrences are causally related. The statistical method applied is based on Bayes' theorem which is useful when we have no prior information about the distribution of the parameters included in the study. There are two parameters in this study: one is π and the other is πH. The former is the probability of an earthquake or earthquakes occurring within an arbitary time interval of 48 hours, and the latter is the probability of an earthquake or earthquakes occurring within 48 hours after the occurrence of a strain step. The distributions of π and πH are given as posterior distributions in Bayes' theorem and the equality or the inequality of π and πH gives the statistical relationship between strain steps and earthquakes. The expectation of πH, i.e., E (πH) is larger than that of π, i.e., E (π) for M≥4 earthquakes. On the contrary, the former is less than the latter for M≥3 and M≥2 earthquakes. Besides the probability of πH≥π is estimated to be over 80% for M≥4 earthquakes but less than 20% for M≥3 and M≥2 earthquakes. These results show the possibility that the strain steps are the precursors of earthquake occurrence, especially for larger earthquakes, although those larger than M5 did not occur during the period of the data collection in this study.
The relations between the changes of the length of day (LOD) and variations of the atmospheric angular momentum (AAM) are studied. The results of the AAM calculations based on the U. S. NMC data from 1000hPa to 0.4hPa and the comparison with the LOD data for 1979-1992 are presented. It is shown that the changes of the LOD are in good agreement with the variations of the relative atmospheric angular momentum (AAM) on intra-annual time scale (in time scales less than one year) during 1979-1992. On decadal time scales, the LOD shows a large variation, while the AAM does not show a significant variation. This large discrepancy is considered to have a non-atmospheric origin.