Basics concepts of the tides are discussed: the tidal movement of sea level, tidal currents, the tide as a wave phenomenon. A qualitative explanation of tidal generation is given. The connection between tidal dissipation and changes in the length of day and lunar recession is explained. An example of a tide-gauge record serves to illustrate the main semidiurnal signal, the spring-neap cycle, and the diurnal inequality. The chapter is concluded with a discussion on the scope of the book and an overview of the contents of the chapters, followed by a further reading section.

Based on the overview from the previous chapter, the main tidal constituents are understood intuitively when their frequencies are derived. This involves the three species of long-period, diurnal, and semidiurnal tides. The corrections needed for the lunar nodal cycle are discussed. The effect of the main constituents on the tidal signal are illustrated (modulation due to elliptic orbit, diurnal inequality, spring-neap, and related cycles). The principle of the method of harmonic analysis is explained. For the tidal signal as a whole, the notion of the tidal period is discussed, including its variability and long-term mean, as well as the presence of circa-tidal clocks in marine organisms.

In this chapter, expressions are derived for the tide-generating force and the associated tide-generating potential. The Moon and Sun act as the tide-generating bodies. The declination is introduced followed by an alternative expression for the tide-generating potential in terms of terrestrial coordinates, which serves as a starting point for Chapter 4. The Moon and Sun act as tide-generating bodies; their combined effect is qualitatively shown to result in a spring-neap cycle.

The propagation of waves at tidal frequencies is studied analytically for simple configurations involving a wall, a channel, semi-enclosed basins, or a continental slope with adjacent shelf sea. The equations of motions are presented, and are simplified using the linear and hydrostatic approximations. The fundamental wave types (Poincaré and Kelvin waves) are derived. The appearance of amphidromic points is explained. A detailed analysis is provided of the solution of the Taylor problem in the case of perfect reflection. The parameter space is explored for modified Kelvin waves in the presence of a shelf sea. As a special case, the double Kelvin wave is obtained.

This chapter provides a systematic qualitative overview of the periodicities involved in the motions of the Earth and Moon that are relevant for tides. Key features are the ellipticity of the orbits and the declination. The celestial origin of the different years (sidereal, tropical, anomalistic) is explained, and the same for months (sidereal, tropical, anomalistic, synodic) and days (sidereal, solar, lunar). The long-period variations (lunar apsidal precession and lunar nodal cycle) are also explained. The implications of the solar tide-generating force on the Earth–Moon system are outlined (evection and variation). The chapter ends with a convenient list of all the relevant periods.

This chapter focuses on tides in coastal seas and basins, where nonlinear and frictional effects are generally important. The depth-averaged shallow-water constituents are derived (Appendix B). The origin of shallow-water constituents is explained. A simple example is analyzed of tidal flow over a bank to explain the principles behind tide-induced residual circulation. Implications for chaotic stirring are discussed. Co-oscillation and resonance in tidal basins are analyzed for simple configurations, including the effects of frictional and radiation damping. The Helmholtz oscillator is explained.Finally, the focus shifts from depth-averaged currents to the vertical structure (Ekman dynamics, tidal straining, strain-induced periodic stratification in estuaries). The decomposition of tidal currents in phasors (rotary components) is elucidated.

The vertical stratification of density in the ocean is illustrated and the key quantity, the buoyancy frequency, is defined. A governing set of linear equations to describe internal tides is derived, followed by an explanation of the two principal ways of solving them: the method of vertical modes and the method of characteristics. The strengths and limitations of both are discussed. Simple examples are provided for constant stratification and a three-layer system. The notions of group velocity of phase speed of internal waves (tides) are introduced. The solutions for reflection from a linearly sloping bottom is derived; an example the distribution of the steepness in ocean bathymetry is shown. Finally, an analytical solution of the generation of internal tides is given for a simple model set-up involving a small-amplitude sill; this is followed by a numerical example in a more realistic setting.