Impact of a circular disk onto a liquid of shallow depth

Impact of a disk on shallow water

“…5 to show the dependence of the added mass coefficient C m ¼ m=r w R 3 on h=R for different drop heights H. The solid line in Fig. 5 corresponds to the theoretical dependence given in Chebakov (1974) …”

“…The measured values include the velocity of the body motion and the pressure at the bottom under the center of the falling disk. The data on the body velocity before and after the impact onto the free surface are used to evaluate the dependence of added mass on fluid depth, which is compared with theoretical predictions by Chebakov (1974). The pressure time-histories are analyzed with the help of wavelet transforms (Farge, 1992).…”

Impact of two circular plates one of which is floating on a thin layer of liquid

“…We use another idea assuming that Equations (1)(2)(3)(4)(5) are valid during both the interaction and the acceleration stages. If so, the initial conditions for Equation (6) have the form…”

“…The duration of this stage is unknown in advance and has to be determined together with the solution of the problem. Initial conditions for Equation (6) can be obtained by matching the solution at the interaction stage with that at the acceleration stage. We use another idea assuming that Equations (1)(2)(3)(4)(5) are valid during both the interaction and the acceleration stages.…”

“…The velocity potentialφ(r, z) was obtained by Vorovich and Yudovich [5] in the case of large thickness of the liquid layer, h/R > 2 π log 2, and by Chebakov [6] for a liquid layer of small thickness, h/R < 1. The second-order approximation of the potentialφ(r, z) as h/R → 0 is derived below by means of an asymptotic method which can be helpful to treat more complicated shapes of a plate floating on a thin liquid layer.…”