# A Systematic Review of Ship Wake Detection Methods in Satellite Imagery
## 3 Results  
### Overview of Ship Wake Characteristics  
Although this report is not intended as a deep dive into the mechanisms behind wake formation, its modeling, or its imaging, it is deemed important to provide a basic overview of the phenomenon of interest and its basic structure, as this is often referenced in later sections. Wakes are generated by the movement of the hull of a ship through the sea surface. While the generation of wakes is a complex phenomenon which is affected by the sea state, ship characteristics, and the speed of the vessel, several common features can be generally identified in remote sensing imagery of high enough resolution. These features are highlighted in Figure 1.  
Figure 1: Schematic synthesis of the basic structure of a ship wake with the hypothesis of infinite depth. Divergent waves are divided into crests (continuous lines) and troughs (dotted lines). In general, the wake field of a ship is generated by the interaction of a stationary wave pattern and a turbulent wake. The stationary wave pattern travels at the same velocity as the ship and is formed by divergent and transverse waves. These are usually well-defined for displacement ships, which are, in general, slower. The propagation of these wave groups is bounded within the so-called Kelvin angle, which, under infinite depth conditions, is always equal to 19.47\({}^{\circ}\)[13]. In real conditions, this angle varies, becoming narrower with increasing speeds when above a threshold depending on the characteristics of the vessel. A turbulent wake, instead, is generated by the boundary layer effects of the hull of the ship. For ships mounted with propellers, the most common propulsion system in use, the turbulence is further increased. [PERSON] et al., in the \"Ship and Wake detection\" chapter of their \"Synthetic Aperture Radar Marine User's Manual\" [2], divide wake structures into four categories:  
* Turbulent wakes, which stretch directly behind the vessel. With favorable conditions, a turbulent wake can be observed for several kilometers behind the ship itself. * Kelvin wakes, formed by transverse and divergent waves. Divergent waves, as they propagate outwards from the track of the vessel, interact with transverse waves and generate a V-shaped pattern of cusp waves. These wave groups are strongly influenced by the depth of the seabed and the Froude number of the vessel, as shown in Equation (1): \[\text{Fr}=\frac{u}{\sqrt{gL}},\] (1) where u is the local flow velocity (in m/s), g is the local gravity field (in m/s\({}^{2}\)), and L is a characteristic length (in m) usually selected as the ship's length along the center-line [14]. * Narrow-V wakes, visible through Bragg scattering from short centimeter-scale waves along the vessel. * Internal wave wakes, generated under certain conditions of shallow stratification. Generally, the bow of the ship creates a system of waves whose wavelength is related to the ship speed but not necessarily to the ship length [14]. Before analyzing capabilities for detection of ship wakes using SAR, it is important to note that the detection and analysis of wakes in SAR images is further complicated by the fact that the wake image that is observed using SAR does not correspond to an instantaneous snapshot of the wake itself. The SAR collects data over a period of time, leading to phenomena such as hydrodynamic modulation and velocity bunching. Consequently, the wake characteristics that can be observed depend significantly on the relative geometry between the wake and the direction of motion of the SAR-mounting platform [15]. The other parameter that has a great effect on wake visualization in SAR imagery is wind speed, due to its influence over sea surface roughness [2]. In SAR imagery, turbulent wake is the most visible of the ship-related signatures after the ship itself. This type of wake appears as a dark line (due to its smooth surface) stretching from the ship and up to a few kilometers behind it.