Zaitseva-Pärnaste, I., Soomere, T. and Tribštok, O., 2011. Spatial variations in the wave climate... more Zaitseva-Pärnaste, I., Soomere, T. and Tribštok, O., 2011. Spatial variations in the wave climate change in the eastern part of the Baltic Sea. The study presents new evidence of large spatial variations in wave properties along the eastern coast of the Baltic Sea. The short-term (1–3 years) interannual variability of the annual mean wave height is almost coherent along the entire eastern coast in 1958–1986. This coherence is completely lost from about 1987: since then the annual mean wave height at Narva-Jõesuu is in anti-phase with this height in the Baltic Proper. Also, in 1954– 1957 the mean wave height in the eastern part of the Baltic Proper gradually decreases but rapidly increases in the Gulf of Finland. The decadal course of wave activity match relatively well each other at Nida and Vilsandi until about 1992, after which the annual mean wave height behavior is completely different at these sites. The largest difference between the long-term course in the wave height is foun...
ABSTRACT Long weakly nonlinear finite-amplitude internal waves in a fluid consisting of three inv... more ABSTRACT Long weakly nonlinear finite-amplitude internal waves in a fluid consisting of three inviscid layers of arbitrary thickness and constant densities (stable configuration, Boussinesq approximation) bounded by a horizontal rigid bottom from below and by a rigid lid at the surface are described up to the second order of perturbation theory in small parameters of nonlinearity and dispersion. First, a pair of alternatives of appropriate KdV-type equations with the coefficients depending on the parameters of the fluid (layer positions and thickness, density jumps) are derived for the displacements of both modes of internal waves and for each interface between the layers. These equations are integrable for a very limited set of coefficients and do not allow for proper description of several near-critical cases when certain coefficients vanish. A more specific equation allowing for a variety of solitonic solutions and capable of resolving most near-critical situations is derived by means of the introduction of another small parameter that describes the properties of the medium and rescaling of the ratio of small parameters. This procedure leads to a pair of implicitly interrelated alternatives of Gardner equations (KdV-type equations with combined nonlinearity) for the two interfaces. We present a detailed analysis of the relationships for the solutions for the disturbances at both interfaces and various regimes of the appearance and propagation properties of soliton solutions to these equations depending on the combinations of the parameters of the fluid. It is shown that both the quadratic and the cubic nonlinear terms vanish for several realistic configurations of such a fluid.
The area between the Estonian and Finnish capitals, Tallinn and Helsinki, apparently has the heav... more The area between the Estonian and Finnish capitals, Tallinn and Helsinki, apparently has the heaviest fast ferry traffic among the open sea areas of the Baltic Sea. Nearly 70 crossings of the gulf take place daily during the high season. It is generally believed that ship wash is negligible in the open sea areas where natural waves are frequently much
ABSTRACT The properties of wave fields induced by high-speed ferries and recently introduced conv... more ABSTRACT The properties of wave fields induced by high-speed ferries and recently introduced conventional ferries with increased cruise speeds are analysed for a site in Tallinn Bay, the Gulf of Finland, the Baltic Sea, located about 3 km from the sailing line and up to 8 km from the wave production area. The analysis is based on high-resolution profiling of the water surface for about 650 wakes from fast ferries, measured during 4 weeks in June–July 2008. The new large conventional ferries with cruise speeds of 25–30 knots (~ 45–55 km/h) sail at near-critical speeds along extensive sections of eastern Tallinn Bay, and excite wakes equivalent to those of high-speed ferries. The peak periods of these wakes are between 10 and 13 s. The typical daily highest ship wave is approximately 1.2 m, measured prior to wake breaking. The largest recorded ship wave in calm conditions had a height of 1.5 m and in the presence of some wind wave background 1.7 m. The cumulative impact of ship wakes results in a gradual increase in the suspended matter concentration in near-bottom water over the course of a day. The largest and longest ship waves produce considerable wave runup at the coast and prevent several coastal sections from achieving an equilibrium state. The largest ship waves have an asymmetric shape both in terms of the water surface elevation above and below the mean level and in terms of the shape of the wave front and back. The overall intensity of anthropogenic waves has remained at the same level as it was in the year 2002, although the ships that produced the highest waves in the past are no longer in service.
Zaitseva-Pärnaste, I., Soomere, T. and Tribštok, O., 2011. Spatial variations in the wave climate... more Zaitseva-Pärnaste, I., Soomere, T. and Tribštok, O., 2011. Spatial variations in the wave climate change in the eastern part of the Baltic Sea. The study presents new evidence of large spatial variations in wave properties along the eastern coast of the Baltic Sea. The short-term (1–3 years) interannual variability of the annual mean wave height is almost coherent along the entire eastern coast in 1958–1986. This coherence is completely lost from about 1987: since then the annual mean wave height at Narva-Jõesuu is in anti-phase with this height in the Baltic Proper. Also, in 1954– 1957 the mean wave height in the eastern part of the Baltic Proper gradually decreases but rapidly increases in the Gulf of Finland. The decadal course of wave activity match relatively well each other at Nida and Vilsandi until about 1992, after which the annual mean wave height behavior is completely different at these sites. The largest difference between the long-term course in the wave height is foun...
ABSTRACT Long weakly nonlinear finite-amplitude internal waves in a fluid consisting of three inv... more ABSTRACT Long weakly nonlinear finite-amplitude internal waves in a fluid consisting of three inviscid layers of arbitrary thickness and constant densities (stable configuration, Boussinesq approximation) bounded by a horizontal rigid bottom from below and by a rigid lid at the surface are described up to the second order of perturbation theory in small parameters of nonlinearity and dispersion. First, a pair of alternatives of appropriate KdV-type equations with the coefficients depending on the parameters of the fluid (layer positions and thickness, density jumps) are derived for the displacements of both modes of internal waves and for each interface between the layers. These equations are integrable for a very limited set of coefficients and do not allow for proper description of several near-critical cases when certain coefficients vanish. A more specific equation allowing for a variety of solitonic solutions and capable of resolving most near-critical situations is derived by means of the introduction of another small parameter that describes the properties of the medium and rescaling of the ratio of small parameters. This procedure leads to a pair of implicitly interrelated alternatives of Gardner equations (KdV-type equations with combined nonlinearity) for the two interfaces. We present a detailed analysis of the relationships for the solutions for the disturbances at both interfaces and various regimes of the appearance and propagation properties of soliton solutions to these equations depending on the combinations of the parameters of the fluid. It is shown that both the quadratic and the cubic nonlinear terms vanish for several realistic configurations of such a fluid.
The area between the Estonian and Finnish capitals, Tallinn and Helsinki, apparently has the heav... more The area between the Estonian and Finnish capitals, Tallinn and Helsinki, apparently has the heaviest fast ferry traffic among the open sea areas of the Baltic Sea. Nearly 70 crossings of the gulf take place daily during the high season. It is generally believed that ship wash is negligible in the open sea areas where natural waves are frequently much
ABSTRACT The properties of wave fields induced by high-speed ferries and recently introduced conv... more ABSTRACT The properties of wave fields induced by high-speed ferries and recently introduced conventional ferries with increased cruise speeds are analysed for a site in Tallinn Bay, the Gulf of Finland, the Baltic Sea, located about 3 km from the sailing line and up to 8 km from the wave production area. The analysis is based on high-resolution profiling of the water surface for about 650 wakes from fast ferries, measured during 4 weeks in June–July 2008. The new large conventional ferries with cruise speeds of 25–30 knots (~ 45–55 km/h) sail at near-critical speeds along extensive sections of eastern Tallinn Bay, and excite wakes equivalent to those of high-speed ferries. The peak periods of these wakes are between 10 and 13 s. The typical daily highest ship wave is approximately 1.2 m, measured prior to wake breaking. The largest recorded ship wave in calm conditions had a height of 1.5 m and in the presence of some wind wave background 1.7 m. The cumulative impact of ship wakes results in a gradual increase in the suspended matter concentration in near-bottom water over the course of a day. The largest and longest ship waves produce considerable wave runup at the coast and prevent several coastal sections from achieving an equilibrium state. The largest ship waves have an asymmetric shape both in terms of the water surface elevation above and below the mean level and in terms of the shape of the wave front and back. The overall intensity of anthropogenic waves has remained at the same level as it was in the year 2002, although the ships that produced the highest waves in the past are no longer in service.
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