The nonlinear stage starts when the amplitude of the unstable flow feature becomes significant. This chapter first studies the nonlinear growth of the interface amplitude and its associated terminal velocity with potential flow models, both for RM and RT. Next, one describes several models intended to predict the evolution of the bubble and spike heights, and the corresponding velocities, for the nonlinear stage. The success and limitations of each model are assessed with comparison to experiments and numerical simulations. The sensitivities to viscosity, density ratio and Mach number are discussed.

This chapter briefly introduces the application of similarity theory and dimensional analysis in fluid mechanics. The concept of flow similarity is discussed at first to give the readers a brief idea what similarity means. Then some important dimensionless number is listed and discussed, which includes Reynolds number, Mach number, Strouhal number, Froude number, Euler number and Weber number. Next, the governing equations are transformed to a dimensionless form to shows how the dimensionless numbers act in the equations. In the end, some flow examples are provided to show the role of the dimensionless numbers.

The stability of river channel adjustment toward equilibrium is controlled by a set of factors governed by the Froude number. When the channel is subjected to water discharge, sediment load, and sediment particle size, it tends to attain stability which corresponds to the minimum Froude number and minimum bed material motion. Field observations and computer simulations for sand-bed rivers show that a river in equilibrium tends to acquire a stable geometry with minimum Froude number. This leads to the hypothesis of minimum Froude number, which is presented in this chapter.

Channels are a vital part of irrigation systems. They are the link between the source of water and the irrigation field. Channels used in irrigation systems can be either erodible or non-erodible, or earthen or lined. Flow in channels is governed by the principles of hydraulics. This chapter discusses rudimentary aspects of hydraulics and the design of open channels.

This chapter considers interactions between different forcings. It first describes the interaction between tidal currents and density gradients at intratidal (within one tidal cycle) time scales. One outcome of this interaction is the phenomenon known as tidal straining. The chapter continues with the treatment of intratidal variations of density that can also result from the interaction of density fields with tides and bathymetry. Subsequently, the chapter presents a description of the interaction between tides and density gradients at subtidal time scales, that is, at periods greater than one tidal cycle. The chapter then describes how advective accelerations from tidal currents can interact with density gradients to modify residual flows. It follows with a description of the competition between tidal stresses and density gradients in driving residual flows. It then deals with the competition between density gradients and wind stresses, to later add tidal forcing. The chapter then includes the influence of river discharge on estuarine circulation. The last two subsections present salt (or solute) budgets and their linkage to hydrodynamics and approaches to study saltwater intrusion