3 The surface layer and the mean air-water interface

In this section we are concerned with the definition of the basic structure of the surface layer and lay the foundations for describing it as a particular type of two-phase flow.

We define a surface layer as the region occupied by two different phases (air and water) which, between them, fill the region. [Note the difference from some other authors who refer to the viscous boundary layer as a surface layer.] In the schematic sketch given in figure 1 the surface layer is the portion of volume enclosed by the two dashed lines which represent the lowest envelopes of bubbles and troughs in the liquid phase ( trough level ) and the envelope of the highest droplets and water ejections within the gas phase ( crest level ). For practical purposes in some flow regimes, this layer may be better defined by excluding the extreme regions, populated with few drops or bubbles.

Figure 1: Sketch of geometry adopted in the model for the two-phase surface layer. The upper and lower bounds of the two-phase layer are indicated with dashed lines. A possible choice of mean free surface is given with a solid line, but for our analysis a smooth lower bound of the layer is chosen.

Within the surface layer flow properties such as density are not represented by continuous functions of time and space. Hence it is desirable to use mean flow properties, which are assumed to be continuous and smooth, to describe the...