Skip to main content

Nonlinearity as the missing link between wavelets and currents

  • Chapter
Radar Scattering from Modulated Wind Waves
  • 119 Accesses

Abstract

To describe the large modulation of short surface waves by nonuniform currents as encountered for weak winds a two timescale technique is applied to the energy balance for short waves. A scaling is assumed in which wind input, nonlinear interactions, dissipation and horizontal current shear are all of the same strength. This approach leads to modulations correct in order of magnitude.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Alpers, W., and I. Hennings, A theory of the imaging mechanism of underwater bottom topography by real and synthetic aperture radar, J. Geophys. Res 89(C6),10,529-10,546,1984.

    Article  Google Scholar 

  • Alpers, W., D.B. Ross, and C.L. Rufenach, On the detectability of ocean surface waves by real and synthetic aperature radar, J. Geophys. Res., 81(C7), 6481-6498,1981.

    Article  Google Scholar 

  • Eckhaus, W., Asymptotic analysis of singular perturbations, North-Holland, Amsterdam 1919.

    Google Scholar 

  • Ermakov, S.A., and E.N. Pelinovsky, Variations of the spectrum of wind ripples on coastal waters under the action of internal waves, Dyn. Atmos. Oceans, 8,95-100,1984.

    Article  Google Scholar 

  • Gastel K. van, Nonlinear interactions of gravity-capillary waves: Lagrangian theory and effects on the spectrum, J. Fluid Mech., 182,449-523,1987A.

    Google Scholar 

  • Gastel, K. van, Imaging by X band radar of subsurface features: a nonlinear phenomenon, J. Geophys. Res. 92(C11), 11,851-11,865,1981B.

    Google Scholar 

  • Gastel K. van, P.A.E.M. Janssen, and G.J. Komen, On phase velocity and growth rate of wind-induced gravity-capillary waves, J. Fluid Mech., 161,199-216,1985.

    Article  Google Scholar 

  • Halsema D., van, A.L. Gray, S.J. Hughes and B.A. Hughes, C- and Ku-band scatterometer results from the scattmod internal wave experiment, Eur. Space Agency Spec. Publ., ESA SP-254,311-311, 1986.

    Google Scholar 

  • Hasselman, K., Grundgleichungen der Seegangsvorhersage, Schiffstechnik,7,191-195,1960.

    Google Scholar 

  • Hughes, B.A., The effect of internal waves on surface wind waves, 2, Theoretical analysis, J. Geophys. Res.,83(C1),455-465,1918.

    Article  Google Scholar 

  • Kasischke, E.S., Characterisation of internal wave surface patterns on airborne SAR imagery, Eur. Space Agency Spec. Publ., ESA SP-254, 1055-1060,1986.

    Google Scholar 

  • Kwoh, D.S.W., B.M. Lake and H. Rungaldier, Identification of the contribution of Bragg-scattering and specular reflection to X-band microwave backscattering in an ocean experiment, Space and Technol. Group, TRW, Redondo Beach, Calif. 1986.

    Google Scholar 

  • Lyzenga, D.R., R.A. Shuchman, E.S. Kasischke and G.A. Meadows, Modeling of bottom-related surface patterns imaged by synthetic aperture radar, paper presented at International Geoscience and Remote Sensing Symposium ’83, IEEE, San Francisco, Calif., 1983.

    Google Scholar 

  • Philips, O.M., On the response of short ocean wave components at fixed wavenumber to ocean current variations, J. Phys. Oceanogr., 14,1425-1488,1984.

    Article  Google Scholar 

  • Valenzuela, G.R., W.J. Plant, D.L. Schuler, D.T. Chen and W.C. Keller Microwave probing of shallow water bottom topography in the Nantucket Shoals, J. Geophys. Res. 90(C8),4982- 4942,1985.

    Google Scholar 

  • Willebrand, J., Energy transport in a nonlinear and inhomogeneous random gravity wave field, J. Fluid Mech., 70,118- 126,1975.

    Article  Google Scholar 

  • Yuen, H.C., D.R. Crawford and P.G. Saffman, SAR image of bottom topography in the ocean: Results from an improved model, Eur. Space Agency Spec. Publ., ESA SP-254,807-812,1986.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Kluwer Academic Publishers

About this chapter

Cite this chapter

van Gastel, K. (1989). Nonlinearity as the missing link between wavelets and currents. In: Komen, G.J., Oost, W.A. (eds) Radar Scattering from Modulated Wind Waves. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2309-6_18

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-2309-6_18

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7537-4

  • Online ISBN: 978-94-009-2309-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics