Curvilinear Coordinate System for Mathematical Analysis of Inclined Buoyant Jets Using the Integral Method

The development of a local system of orthogonal curvilinear coordinates, which is appropriate to monitor the flow of an inclined buoyant jet with reference to the basic Cartesian coordinate system is presented. Such a system is necessary for the correct application of the integral method, since the well-known Gaussian profiles should be integrated on the cross-sectional area of inclined buoyant jet, where they are valid. This is the major advantage of the present work compared to all other integral methods using Cartesian coordinate systems. Consequently, the flow and mixing governing partial differential equations (PDE), i.e., continuity, momentum, buoyancy, and/or tracer conservation, are written in the local orthogonal curvilinear coordinate system and, then, the Reynolds substitution regarding mean and fluctuating components of all dependent variables is applied. After averaging with respect to time, the mean flow PDEs are taken, omitting second-order terms, as the dynamic pressure and molecular viscosity, compared to the mean flow and mixing contributions of turbulent terms. The latter are introduced through empirical coefficients. The Boussinesq’s approximation regarding small density differences is taken into consideration. The system of PDEs is closed by assuming known spreading coefficients along with Gaussian similarity profiles. The methodology is applied in the inclined two-dimensional buoyant jet; thus, PDEs are integrated on the jet cross-sectional area resulting in ordinary differential equations (ODE), which are appropriate to be solved by applying the 4th order Runge-Kutta algorithm coded in either FORTRAN or EXCEL. The numerical solution of ODEs, concerning trajectory of the inclined two-dimensional buoyant jet, as well as longitudinal variations of the mean axial velocity, mean concentration, minimum dilution, and entrainment velocity or entrainment coefficient, occurs quickly, saving computer memory and effort. The satisfactory agreement of results with experimental data available in the literature empowers the usefulness of the proposed methodology in inclined buoyant jets

Correlation between seismicity and barometric tidal exalting

Changes of barometric pressure in the area of Thessaloniki in Northern Greece were studied by analyzing a sample of 31 years of hourly measurements. The results of this analysis on the periodicities of tidal components are expressed in terms of amplitude and phases variability. An earlier investigation revealed a detectable correlation between the exalting of the amplitude parameters of the tidal waves with strong seismic events. A problem of this work was that we had compared the tidal parameters resulting from the analysis of data covering the period of one year with instantaneous seismic events, although the earthquake is the final result of a tectonic process of the upper lithosphere. Consequently, in order to increase the resolution of our method we had analyzed our data in groups of 3-months extent and the resulted amplitudes were compared with seismicity index for corresponding time periods. A stronger correlation was found in the last case. However, the estimation of tidal parameters in this case was restricted to short period (from one day down to eight hours) constituents. Therefore, a new analysis was performed, retaining the one-year length of each data block but shifting the one year window by steps of three months from the beginning to the end of the 31 years period. This way, we are able to estimate again tidal parameters ranging from periods of one year (Sa) down to eight hours (M3). The resulting correlation between these tidal parameters with a cumulative seismicity index for corresponding time intervals was remarkably increased

Atmospheric tide disturbances as Earthquake precursory phenomena

International audienceThe tidal changes of the barometric pressure in the area of Thessaloniki were studied by analysing a sample of 21 years of hourly measurements. The resulted tidal parameters (amplitude and phase difference) were considered as "mean values" of the corresponding parameters for this long time period. Using these parameters, barometric changes were computed and subtracted from the observations. Assuming that the residuals might include local (in terms of time) information,the residual time series was split in 21 blocks and a new analysis was performed for each block separately. The 21 amplitude values computed for each tidal wave were considered as the amplitude variation with respect to the correspondingmean value. An observable correlation of the amplitude exalting of the most of the tidal waves was found to Earthquakes of magnitude >4, occurred close to Thessaloniki in the test period