Abstract
The kinematics of two-dimensional focusing wave trains on a shearing flow in water of finite depth are investigated analytically. In the absence of waves, the vorticity due to the vertical gradient of the horizontal current velocity is assumed constant. A linear kinematic model based on the spatio-temporal evolution of the frequency is derived predicting the focusing distance and time of a chirped wave packet in the presence of constant vorticity, and surface current. Based on this model, the kinematic behavior of the transient wave packet is analyzed, and described in terms of spreading of the focusing point into a wider area. The effects of bathymetry, vorticity, and surface current are analyzed and discussed. Two main results are obtained: (i) the combined effects of surface current and vorticity, in deep water, are nontrivial, highly depending on the presence of surface current (ii) the effects of bathymetry, in the presence of shear, are also counterintuitive in the presence of vorticity, since significant effects can be observed when considering high values of the depth parameter.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
