Fourier Image Methods for Evolution Equations of Deep-Water Waves

• Autorzy: Jankowski Jan , Leszczyński Henryk

Identyfikatory

DOI

10.17466/tq2019/23.3/a

• Języki publikacji: EN

Abstrakty

EN

The velocity potential of the fluid satisfies the Laplace equation with nonlocal boundary conditions on a free surface. This differential problem is transformed to an evolution equation in Fourier variables. The Fourier transform images of boundary functions are approximated by Picard's iterations and the method of lines on meshes related to roots of Hermite polynomials. Due to convolutions of sine and cosine functions the integral terms of Picard's iterations reveal unexpected instabilities for wave numbers in a neighborhood of zero.

Słowa kluczowe

EN

wave evolution; Laplace equation; Fourier transform; method of lines; Gauss-Hermite quadrature

• Wydawca: Politechnika Gdańska
• Czasopismo: TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
• Rocznik: 2019
• Tom: Vol. 23, No 3
• Strony: 261--268
• Opis fizyczny: Bibliogr. 8 poz., rys.

Twórcy

autor

Jankowski Jan

• Polish Register of Shipping, Gen. J. Hallera 126, 80-416 Gdańsk, Poland

autor

Leszczyński Henryk

• Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-308 Gdańsk, Poland

Bibliografia

• [1] Zakharov V E 1968 Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki 9(2)190
• [2] Stiassnie M and Shemer L 1984 J. Fluid Mech.47
• [3] Komen G J, Cavaleri L, Donelan M, Hasselmann K, Hasselmann S and Janssen P A E M1994 Dynamics and Modelling of Ocean Waves, Cambridge University Press
• [4] Lannes D 2013 AMS.188
• [5] Part VII: ECMWF Wave Model, IFS Documentation – Cy40r1, Operational implemen-tation 2013 [online:] https://www.ecmwf.int/sites/default/files/IFSCY40R1Part7.pdf
• [6] Mitsuyasu H 1968 On the growth of the spectrum of wind-generated waves. II, Rep. Res.Inst. Appl. Mech. (Kyushu Univ.)17(59)235
• [7] Hasselmann K, Barnett T P, Bouws E, Carlson H, Cartwright D E, Enke K, Ewing J A,Gienapp H, Hasselmann D E, Kruseman P, Meerburg A, Müller P, Olbers D J, Richter K,Sell W and Walden H 1973 Measurements of wind-wave growth and swell decay duringthe Joint North Sea Wave Project (JONSWAP), Dtsch. Hydrogr. Z. Suppl. A8(12)
• [8] Hasselmann S, Hasselmann K 1985 Journal of Physical Oceanography 15 1369

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).