Non-equilibrium turbulence scalings and self-similarity in turbulent planar jets

We study the self-similarity and dissipation scalings of a turbulent planar jet and the theoretically implied mean flow scalings. Unlike turbulent wakes where such studies have already been carried out (Dairay et al. 2015 J. Fluid Mech . 781 , 166–198. ( doi:10.1017/jfm.2015.493 ); Obligado et al. 2016 Phys. Rev. Fluids 1 , 044409. ( doi:10.1103/PhysRevFluids.1. 044409)), this is a boundary-free turbulent shear flow where the local Reynolds number increases with distance from inlet. The Townsend–George theory revised by (Dairay et al. 2015 J. Fluid Mech . 781 , 166–198. ( doi:10.1017/jfm.2015.493 )) is applied to turbulent planar jets. Only a few profiles need to be self-similar in this theory. The self-similarity of mean flow, turbulence dissipation, turbulent kinetic energy and Reynolds stress profiles is supported by our experimental results from 18 to at least 54 nozzle sizes, the furthermost location investigated in this work. Furthermore, the non-equilibrium dissipation scaling found in turbulent wakes, decaying grid-generated turbulence, various instances of periodic turbulence and turbulent boundary layers (Dairay et al. 2015 J. Fluid Mech . 781 , 166–198. ( doi:10.1017/jfm.2015.493 ); Vassilicos 2015 Annu. Rev. Fluid Mech . 95 , 114. ( doi:10.1146/annurev-fluid-010814-014637 ); Goto & Vassilicos 2015 Phys. Lett. A 3790 , 1144–1148. ( doi:10.1016/j.physleta.2015.02.025 ); Nedic et al. 2017 Phys. Rev. Fluids 2 , 032601. ( doi:10.1103/PhysRevFluids.2.032601 )) is also observed in the present turbulent planar jet and in the turbulent planar jet of (Antonia et al. 1980 Phys. Fluids 23 , 863055. ( doi:10.1063/1.863055 )). Given these observations, the theory implies new mean flow and jet width scalings which are found to be consistent with our data and the data of (Antonia et al. 1980 Phys. Fluids 23 , 863055. ( doi:10.1063/1.863055 )). In particular, it implies a hitherto unknown entrainment behaviour: the ratio of characteristic cross-stream to centreline streamwise mean flow velocities decays as the −1/3 power of streamwise distance in the region, where the non-equilibrium dissipation scaling holds.

Ship Wakes in Optical Images

Ship wakes are more distinct than the hulls and can be visually observed in optical images. In this paper the wakes of 2836 ships in 32 optical images with different resolutions are observed and summarized. The ships are divided into four types according to the hull and wake features: fishing vessels, motorboats, cargo ships, and warships. The results show that each ship type has characteristic wakes, and there are significant differences among the categories. The probabilities of occurrence of different types of wakes and their components are shown. Turbulent wakes are inevitable. The probability of occurrence of Kelvin wakes is small and less than 40%. The visibilities of internal waves that are generated by only cargo ships are very low as a result of the harsh formation conditions. Turbulent wakes should be preferentially detected. Low-resolution images are more suitable for the detection and positioning of hulls and wakes, while high-resolution images with more details are convenient for further analysis of the size, velocity, and draft of ships. The study on the cause of the formation of the features of ship wakes in optical images proves that the classification of the wakes is reasonable and that the features of wakes can be used to initially identify the type of ship.