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A constant tidal form factor, defined by the ratio of the sum of K 1 and O 1 tidal amplitudes to the sum of M 2 and S 2 tidal amplitudes, has been widely used to represent tidal feature for nearly 120 years. Tides can be classified as semi-diurnal, mixed semi-diurnal, mixed diurnal and diurnal regimes based on tidal form factors. It is well-known that K 1 and O 1 tidal amplitudes have significant 18.61-year nodal variations. Therefore, the relative strength of semi-diurnal and diurnal tides changes during the 18.61-year nodal cycle. Consequently, local tidal regimes in some sea areas are not fixed, but periodically change during the 18.61-year nodal cycle. Such periodical tidal regime shift cannot be reflected by constant tidal form factor, which motivates present research. The purpose of this study is to propose a time-varying tidal form factor which considers the 18.61-year nodal modulations of main constituents based on the equilibrium tidal theory. 1249 tide gauges and a global tide model (EOT20) derived from multi-satellite altimeters are used to detect potential tidal regime shift related to the 18.61-year nodal cycle in the global ocean. It is found that there are 154 tide gauges and 17.32% ocean grid points in EOT20 model which exist tidal regime shift caused by the 18.61-year nodal cycle. Tidal form factor can be modified by ∼17% during the 18.61-year cycle in the global ocean. Furthermore, the deviations between theoretical and actual nodal modulations in some coastal resonant areas do not significantly influence the calculation of temporal tidal form factors. • Constant tidal from factors cannot reflect periodically tidal regime shift. • A temporal tidal form factor is proposed. • Tidal regime shift related to the nodal cycle widely exists in the global ocean. [ABSTRACT FROM AUTHOR]

Radiational tides derived from solar radiation are important components of ocean tides. Understanding dynamical features of radiational tides can be beneficial for further promoting the accuracy of water level prediction. Generally, radiational S 2 amplitudes are only 10%–30% of gravitational S 2 amplitudes, which has been verified by numerous studies. However, a previous study indicated that radidational S 2 amplitudes can reach 60% of gravitational S 2 amplitudes in the Gulf of Tonkin and related physical processes are unknown. In this paper, we revisit this abnormal phenomenon and find that such large radiational S 2 amplitudes are not real, but artifacts induced by the inadaptation of the method based on the credo of smoothness. Specifically, observed semi-diurnal tidal admittances in the Gulf of Tonkin are not smooth due to strong nonlinear interactions between large main diurnal tides. We quantitatively estimate and remove the contributions of quadratic and quartic nonlinear interactions to main semi-diurnal tides and find that the real ratio of radiational S 2 amplitude to astronomical S 2 amplitude is only 0.17 at Beihai, which is basically consistent with previous model results. Our study highlights the importance of eliminating the interference of nonlinear interactions to semi-diurnal tidal admittances in all diurnal resonant sea areas like the Gulf of Tonkin and the Gulf of Thailand when extracting radiational S 2 tides from sea level observations. • Large radiational S2 amplitudes in the Gulf of Tonkin are not real. • Observed semi-diurnal tidal admittances are distorted by nonlinear interactions. • Our method is universal for all diurnal resonant sea areas. [ABSTRACT FROM AUTHOR]

Highlights • Oceanic tidal heating from eccentricity forcing is strongly suppressed on Enceladus and other small satellites by the ice shell's mechanical forcing. • For large satellites, oceanic tidal heating from eccentricity forcing is enhanced due to the ice shell's self-gravity. • An ice shell increases oceanic obliquity tide heating on most satellites, except Triton, due to self-gravity and the flow properties of Rossby-Haurwitz waves. • Non-linear tidal heating in barotropic ocean tides is still found to be small compared to radiogenic decay, except for Triton. • Dynamic tidal forcing drives a time-varying pressure excess at the ocean surface due to the restrictive nature of the ice shell. Abstract Subsurface ocean tides act as a mechanism to dissipate tidal energy in icy satellite interiors. We numerically model the effect of an ice shell on ocean tides using non-linear bottom drag for the first time. We demonstrate that subsurface oceans experience tidal pressurization due to the confining nature of the ice shell, and find that Enceladus' eccentricity forcing can generate up to 2.2 kPa of pressure excess at the ocean surface. Existing free-surface oceanic energy dissipation scaling laws are extended to subsurface oceans, and are benchmarked against our numerical results to within 10 %. We show that for the large bodies Ganymede, Europa and Titan, an ice shell increases eccentricity tidal heating due to self-gravity, whereas the shell's suppressive mechanical forcing reduces eccentricity tide dissipation on Enceladus and Dione by several orders of magnitude due to their high effective rigidities. In contrast, the ice shell enhances obliquity-forced dissipation in all satellites investigated, except Triton, because the largely divergence-free ocean response is unaffected by the shell's rigidity but is still enhanced by self-gravity. We conclude that the fundamental difference in ocean response to obliquity and eccentricity forcing, combined with self-gravity, results in increased obliquity heating and suppressed eccentricity heating in small satellites. For large satellites with low effective rigidities, the type of ocean response is less important because the shell's mechanical forcing has little impact on the flow, whereas self-gravity will enhance the response, and consequently dissipation, regardless of the forcing. Overall, obliquity tides are likely to dominate the tidal heating budget of icy satellite oceans, remaining the most prominent source of fluid dissipation in subsurface barotropic ocean tides. [ABSTRACT FROM AUTHOR]

Icy satellites that contain subsurface oceans require sufficient thermal energy to prevent the liquid portion of their interiors from freezing. We develop a numerical finite difference model to solve the Laplace Tidal Equations on a sphere in order to simulate tidal flow and thermal energy dissipation in these oceans, neglecting the presence of an icy lid. The model is applied to Titan and Enceladus, where we explore how Rayleigh (linear) and bottom (quadratic) drag terms affect dissipation. The latter drag regime can only be applied numerically. We find excellent agreement between our results and recent analytical work. Obliquity tide Rossby-wave resonant features become independent of ocean thickness under the bottom drag regime for thick oceans. We show that for Titan, dissipation from this Rossby-wave resonance can act to dampen the rate of outward orbital migration by up to 40% for Earth-like values of bottom drag coefficient. Gravity-wave resonances can act to cause inward migration, although this is unlikely due to the thin oceans required to form such resonances. The same is true of all eccentricity tide resonances on Enceladus, such that dissipation becomes negligible for thick oceans under the bottom drag regime. [ABSTRACT FROM AUTHOR]

Understanding seasonal tidal changes is vital for accurate tidal prediction which is essential for numerous practical purposes, such as flood warning and navigation. It is common knowledge that main constituents show significant seasonal modulations in the global ocean due to non-astronomical factors such as river discharge, sea ice and ocean stratification. Less known, and less studied, is the seasonal variability of shallow water constituents. In this paper, we revisit the abnormally large semi-annual modulation of shallow water constituents at Lamu indicated by a previous study. We find that large semi-annual modulations of shallow water tides at Lamu are mostly not physical, but artifacts induced by unresolved nearby nonlinear shallow water tides due to short length of records. We also propose a novel method based on the 'credo of smoothness' to extract real semi-annual modulations of shallow water tides. Tidal harmonic analysis and other widely-used time series methods are generally frequency-depend, which means that they can only extract the amplitude and phase of one specific tidal frequency, but cannot distinguish different origins of a tidal constituent. It is suggested that care must be taken to ensure the obtained tidal amplitude/phase series are really reflecting tidal changes and are not artifacts of frequency-depend methods. • The seasonal variations of shallow water constituents at Lamu are revisited. • A novel method is proposed to extract real semi-annual modulations of shallow water tides. • The real semi-annual cycles in shallow water tides are very weak. [ABSTRACT FROM AUTHOR]

Abstract: This short paper explores some of the reasons for the asymmetries observed in tidal probability distribution functions in areas of predominantly semi-diurnal tide. It shows that contributions to asymmetry can arise from shallow water, diurnal and long period tidal constituents, with the diurnal terms likely to be the most important source of asymmetry at many locations. We consider this observation worthy of note due to the relatively little discussion of the topic in the literature hitherto. [Copyright &y& Elsevier]