Freely floating structures trapping time-harmonic water waves (revisited)

Preprint English OPEN
Kuznetsov, Nikolay ; Motygin, Oleg (2014)
  • Subject: Mathematical Physics | 76B15, 35Q35

We study the coupled small-amplitude motion of the mechanical system consisting of infinitely deep water and a structure immersed in it. The former is bounded above by a free surface, whereas the latter is formed by an arbitrary finite number of surface-piercing bodies floating freely. The mathematical model of time-harmonic motion is a spectral problem in which the frequency of oscillations serves as the spectral parameter. It is proved that there exist axisymmetric structures consisting of $N \geq 2$ bodies; every structure has the following properties: (i) a time-harmonic wave mode is trapped by it; (ii) some of its bodies (may be none) are motionless, whereas the rest of the bodies (may be none) are heaving at the same frequency as water. The construction of these structures is based on a generalization of the semi-inverse procedure applied earlier for obtaining trapping bodies that are motionless although float freely.
  • References (23)
    23 references, page 1 of 3

    [1] M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions, Dover, 1965.

    [2] J. T. Beale, Eigenfunction expansions for objects floating in an open sea. Comm. Pure Appl. Math. 30 (1977), 283-313.

    [3] D. V., Evans, R. Porter, Wave-free motions of isolated bodies and the existence of motion-trapped modes. J. Fluid Mech. 584 (2007), 225-234.

    [4] C. J. Fitzgerald, P. McIver, Passive trapped modes in the water-wave problem for a floating structure. J. Fluid Mech. 657 (2010), 456-477.

    [5] F. John, On the motion of floating bodies, I. Comm. Pure Appl. Math. 2 (1949), 13-57.

    [6] F. John, On the motion of floating bodies, II. Comm. Pure Appl. Math. 3 (1950), 45-101.

    [7] N. Kuznetsov, On uniqueness of a solution to the plane problem on interaction of surface waves with obstacle. J. Math. Sciences 150 (2008), 1860-1868.

    [8] N. Kuznetsov, On the problem of time-harmonic water waves in the presence of a freelyfloating structure. St. Petersburg Math. J. 22 (2011), 985-995.

    [9] N. Kuznetsov, V. Maz'ya, B. Vainberg, Linear Water Waves: A Mathematical Approach. (Cambridge University Press, Cambridge 2002).

    [10] N. Kuznetsov, O. Motygin, On the coupled time-harmonic motion of water and a body freely floating in it. J. Fluid Mech. 679 (2011), 616-627.

  • Metrics
    No metrics available
Share - Bookmark