Trapped waves within the blocking frequency under compressed sea ice and two-dimensional current

The existence of trapped modes due to a horizontal submerged rigid cylinder placed below a compressed ice-covered surface is shown to exist within the frequency band of wave blocking by employing linearized water wave theory and with the inclusion of the effects of a two-dimensional current and the obliqueness of the propagating wave. A new modified multipole expansion method catering to the multiple propagating modes is proposed. The impact of different choices of propagating modes at a fixed frequency within the above-mentioned band on the trapped modes is detailed. Multiple trapped modes whose number depends on the direction and magnitude of the current exist within the frequency band. Out of the three choices of current types considered, while two of them result in the generation of trapped modes for all three possible choices of the propagating wave, the remaining one shows that only one propagating mode can generate a trapped wave. A break in the continuous spectrum of the trapped mode frequency due to the wave blocking and at the point of inflexion is presented. There exists a region of angle of propagation within which an abundance of the trapped mode is shown. The surface profiles for different angles of propagation and choices of propagating modes are illustrated graphically. The trapped modes associated with a higher angle of propagation decay at a faster rate.