Mathematical methods for modeling wind wave anomalies on the ocean surface

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Abstract

The work is devoted to the construction of a mathematical model of the effect of currents on wind waves on the ocean surface and the study of fluctuations in sea waves by non-contact means (radar, radiometry, optical sensing devices).A review of numerous publications in this field is given and a new approach to calculating wind wave fluctuations using a special asymptotic method is proposed. This method allows us to obtain explicit analytical formulas for wind disturbance disturbances. At the same time, it is possible to analytically calculate the mentioned disturbances in both spectral and coordinate forms. This, in turn, allows us to explicitly calculate the perturbations of reflected radar signals and of the self-radiation from the agitated sea surface under the influence of currents.

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About the authors

D. Yu. Knyazkov

Ishlinsky Institute for Problems in Mechanics of the RAS

Author for correspondence.
Email: knyaz@ipmnet.ru
Russian Federation, Moscow

A. S. Shamaev

Ishlinsky Institute for Problems in Mechanics of the RAS

Email: sham@rambler.ru
Russian Federation, Moscow

References

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Supplementary files

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2. Fig. 1. Radar image obtained by the Almaz-1 spacecraft in the North Sea and a bathymetric diagram of the survey area

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3. Fig. 2. Phenomenon of resonant scattering on a periodic surface

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4. Fig. 3. Processing of a radar frame using the averaging procedure. Comparison of different scales of the problem

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5. Fig. 4. Scheme of flow around an underwater obstacle

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6. Fig. 5. Transformation of wind ripples over streamlined bottom irregularities

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7. Fig. 6. Velocity field on the water surface directly above a moving body

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8. Fig. 7. Maps of the components vx, vy of the flow velocity field on the surface of the liquid in coordinate representation

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9. Fig. 8. Real components of the Fourier transforms of the flow velocity components on the liquid surface: component a: in the region [2,2]×[2,2] and b: in the region [0.25,0.25]×[0.25,0.25] near the origin (isometric projection); component c: in the region [2,2]×[2,2] and d: in the region [0.25,0.25]×[0.25,0.25] near the origin (isometric projection)

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