Abstract
We derive the explicit analytic expression for the Stokes' drift in one dimension in the presence of a dichotomic Markov forcing. For small amplitudes of the forcing, the drift is enhanced, but the enhancement is reduced with increasing frequency of the forcing. On the other hand, a reduction of the drift or even a flux reversal can be induced at larger amplitudes, while the flux is now found to be an increasing function of the perturbation frequency.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
G. G. Stokes, Trans. Camb. Philos. Soc. 8:441 (1847); O. M. Phillips, The Dynamics of the Upper Ocean, Cambridge University Press, Cambridge, 1977; J. Lightwill, Waves in Fluids, Cambridge University Press, Cambridge, 1978.
A few recent papers from a rich bibliography on the subject: A. M. Bratseth, Tellus 50A:451 (1998); S. M. Cox, Fluid Dyn. Res. 19:149 (1997); H. C. Graber, B. K. Haus, R. D. Chapman, and L. K. Shay, J. Geophys. Res. 102:18749 (1997) (experimental); J. C. McWilliams, P. P. Sullivan, and Chin-Hoh Moeng, J. Fluid Mech. 334:1 (1997); M. Nordsveen and A. F. Bertelsen, Int. J. Multiphase Flow 23:503 (1997); V. Polonichko, J. Geophys. Res. 102:15773 (1997); S. A. Thorpe, J. Phys. Oceanogr. 27:62 and 2072 (1997).
See e.g. a recent paper of C. P. Lee, Phys. of Fluids 10:2765 (1998) and references therein.
K. Herterich and K. Hasselmann, J. Phys. Oceanogr. 12:704 (1982); O. N. Mesquita, S. Kane, and J. P. Gollub, Phys. Rev. A 45:3700 (1992).
K. M. Janson and G. D. Lythe, Phys. Rev. Lett. 81:3136 (1998); ibid., J. Stat. Phys. 90:227 (1998).
C. Van den Broeck, Europhys. Lett. 46:1 (1999).
R. Landauer and M. Büttiker, Physica Scripta T9:155 (1985).
M. O. Magnasco, Phys. Rev. Lett. 71:1477 (1993); M. Bier, Phys. Lett. A 211:12 (1996); P. Hänggi and R. Bartussek, in Lect. Notes in Phys., Vol. 476, ed. by J. Parisi et al., Springer, Berlin, 1996; R. D. Astumian, Science 276:917 (1997); F. Julicher, A. Ajdari, and J. Prost, Rev. Mod. Phys. 69, 1269 (1997).
C. R. Doering, W. Horsthemke, and J. Riordan, Phys. Rev. Lett. 72:2984 (1994); K. W. Kehr, K. Mussawisade, T. Wichmann, and W. Dieterich, Phys. Rev. E 56:R2351 (1997).
N. G. Van Kampen, Stochastic Processes in Physics and Chemistry, North Holland, Amsterdam, 1981.
W. Horsthemke and R. Lefever, Noise-Induced Transitions: Theory and Applications in Physics, Chemistry and Biology, Springer Verlag, 1984.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bena, I., Copelli, M. & Van den Broeck, C. Stokes' Drift: A Rocking Ratchet. Journal of Statistical Physics 101, 415–424 (2000). https://doi.org/10.1023/A:1026466206162
Issue Date:
DOI: https://doi.org/10.1023/A:1026466206162