Hydrodynamic Characteristics of Undular Tidal Bores in the Qiantang River Based on Field Observations

Understanding the undular tidal bores in the Qiantang River is essential for effective river management and maintenance.While breaking tidal bores have been studied extensively, reports on undular tidal bores in the Qiantang Riverremain limited. Furthermore, observed data on undular tidal bores fulfilling the requirements of short measurementtime intervals, and spring, medium, and neap tide coverage, and providing detailed data for the global vertical stratificationof flow velocity are quite limited. Based on field observations at Qige in the Qiantang estuary, we analyzedthe characteristics of undular tidal bores. The results showed that the flooding amplitude (a) of the first wave isalways larger than its ebbing amplitude (b). Moreover, the vertical distribution of the maximum flood velocity exhibitesthree shapes, influenced by the tidal range, while that of the maximum ebb velocity exhibites a single shape. Duringthe initial phase of the flood tide in the spring and medium tides, the upper water body experiences multiple oscillatingchanges along the flow direction, corresponding to the alternating process of the crest and trough of the tide levelupon the arrival of the tidal bore. The tidal range is a crucial parameter in tidal bore hydrodynamics. By establishingthe relationship between hydrodynamic parameters and tidal range, other hydrodynamic parameters, such as the tidalbore height, maximum flood depth–averaged velocity, maximum flood stratified velocity at the measurement points,and duration of the flood tide current, can be effectively predicted, thereby providing an important reference for rivermanagement and maintenance.

Mediterranean Sea level trends from long-period tide gauge time series

The main purpose of this study is to highlight, on the basis of statistical tests, the significant long-term changes of the Mediterranean Sea level, through the analysis of historical tide gauge records. In this framework, 14 tide gauge monthly series selected from the Permanent Service of the Mean Sea Level(PSMSL) database were used. The search for the presence or not of trends within these series, that have a temporal coverage from 59 to 142 years, was carried out using the Mann-Kendall test and the Sen’s slope estimator. The obtained results show that the Split Rt Marjana series are the only ones which does not exhibit a significant trend. The other 13 series show significant increasing trends. This result seems sufficient to suppose the presence, in the past century, of a new climatic phase on the scale of the Mediterranean basin, where the rising sea level is one of the consequences.

Experimental hydrodynamic study of the Qiantang River tidal bore

To study the hydrodynamics of tidal bore, a physical modeling study is carried out in a rectangular flume with considera- tions of the tidal bore heights, the propagation speeds, the tidal current velocities, the front steepness, and the bore shapes. After the validation with the field observations, the experimental results are analyzed, and it is shown that： （1） the greater initial ebb velocity or the larger initial water depth impedes the tidal bore propagation, （2） the maximum bore height appears at an initial ebb velocity in the range of 0.5 m/s-l.5 m/s. （3） when the Froude number exceeds 1.2, an undular bore appears, atter it exceeds 1.3, a breaking bore occurs, and after it exceeds 1.7, the bore is broken.

Shape and gravitational field of the ellipsoidal satellites

The shape and gravitational field of ellipsoidal satellites are studied by using the tidal theory. For ellipsoidal satellites, the following conclusions were obtained: Firstly, in the early stage of the satellite formation, strong tidal friction allowed the satellites move in a synchronous orbit and evolve into a triaxial ellipsoidal shape. Because the tidal potential from the associated primary and the centrifugal potential from the satellite spin are nearly fixed at the surface, the early satellites are the viscoelastic celestial body, and their surfaces are nearly in the hydrostatic equilibrium state. The deformation is fixed in the surface of the satellite. By using the related parameters of primary and satellite, the tidal height and the theoretical lengths of three primary radii of the ellipsoidal satellite are calculated. Secondly, the current ellipsoidal satellites nearly maintain their ellipsoidal shape from solidification, which happened a few billion years ago. According to the satellite shape, we estimated the orbital period and spinning angular velocity, and then determined the evolution of the orbit. Lastly, assuming an ellipsoidal satellite originated in the hydrostatic equilibrium state, the surface shape could be determined by tidal, rotation, and additional potentials. However, the shape of the satellite's geoid differs from its surface shape. The relationship between these shapes is discussed and a formula for the gravitational harmonic coefficients is presented.