Tarmo Soomere

Nonlinear Components of Ship Wake Waves

Nonlinear components of wakes from large high-speed ships at times carry a substantial part of the wake energy and behave completely differently compared to the classical Kelvin wave system. This overview makes an attempt to summarize the descriptions of nonlinear parts of a ship’s wake. For completeness, also the basic properties of the Kelvin wake are sketched. The central topic is the generation of solitons by ship motion both in channels and in unbounded sea areas. The discussion is mostly limited to disturbances on the surface of nonstratified water. The optional nonlinear components of the ship wake such as the very narrow V-like wake components, packets of monochromatic waves, ship-generated depression areas, and supercritical bores are also discussed. Specific features of solitonic ship waves and their interactions have numerous applications in naval and coastal engineering, and in adjacent areas of applied mechanics. An overview of the practical use of certain properties of phase shifts, and particularly high wave humps occurring during Mach reflection and nonlinear interaction of solitons in decreasing the wave resistance at supercritical speeds and in the freak wave theory, is also presented. The final part of the paper describes the results of studies of far-field properties of nonlinear wakes and possible consequences of the increase of local hydrodynamic activity. There are 263 references cited in this review article.

Runup of nonlinear asymmetric waves on a plane beach

The problem of the long wave runup on a beach is discussed in the framework of the rigorous solutions of the nonlinear shallow-water theory. The key and novel moment here is the analysis of the runup of a certain class of asymmetric waves, the face slope steepness of which exceeds the back slope steepness. Shown is that the runup height increases when the relative face slope steepness increases whereas the rundown weakly depends on the steepness. The results partially explain why the tsunami waves with the steep front (as it was for the 2004 tsunami in the Indian Ocean) penetrate deeper into inland compared with symmetric waves of the same height and length.

The use of Lagrangian trajectories for the identification of the environmentally safe fairways.

We propose and test a method for the optimisation of marine fairways to minimise the risk to high-value areas, based on statistical analysis of Lagrangian trajectories of current-driven pollution transport. The offshore areas are quantified according to the probability of pollution released in these areas to reach vulnerable regions. The method contains an eddy-resolving circulation model, a scheme for tracking of Lagrangian trajectories, a technique for the calculation of quantities characterising the potential of different sea areas to supply adverse impacts, and routines to construct the optimum fairway. The gain is expressed in terms of the probability of pollution transport to the nearshore and the associated time (particle age). The use of the optimum fairway would decrease the probability of coastal pollution by 40% or increase the average time of reaching the pollution to the coast from 5.3 to about 9 days in the Gulf of Finland, the Baltic Sea.

Extremes and Decadal Variations of the Northern Baltic Sea Wave Conditions

Average wave conditions, their seasonal cycle and decadal variations, and extreme wave storms in the northern Baltic Sea are studied on the basis of long-term time series from Almagrundet (1978–2003) and Vilsandi (1954–2005), and wave statistics from the middle of the northern Baltic Proper. The typical wave periods are 3–4 s in coastal areas and 4–6 s on the open sea. The monthly mean wave height varies from about 0.4 (0.5) m in April–July to 0.8 (1.3–1.4) m in January at Vilsandi (Almagrundet). The annual mean wave height varied insignificantly in the 1960s–1970s, considerably increased in the 1980s, was at highest in the mid-1990s, and rapidly decreases in 1998–2005. Significant wave heights H S ≥ 4m occur with a probability of about 1%. Extreme wave conditions with H S ≥ 7m have been registered five times since 1978. The records overlook 2–3 such cases. The overall recorded maximum H S is 7.8 m. The estimated maximum of H S was 9.5 m in cyclone Gudrun in January 2005.

Investigating the Marine Protected Areas most at risk of current-driven pollution in the Gulf of Finland, the Baltic Sea, using a Lagrangian transport model

The possibility of current-driven propagation of contaminants released along a major fairway polluting the Marine Protected Areas (MPAs) in the Gulf of Finland, the Baltic Sea, is examined using a 3D circulation model, a Lagrangian transport model and statistics. Not surprisingly, the number of hits to the MPA decreases almost linearly with its distance from the fairway. In addition, the potential pollution released during a ship accident with the pollutants carried by currents may affect MPAs at very large distances. Typically, a fairway section approximately 125 km long (covering about 1/3 of the approximate 400-km-long gulf) may serve as a source of pollution for each MPA. The largest MPA (in the Eastern Gulf of Finland) may receive pollution from an approximately 210-km-long section (covering about 1/2 of the entire length of the gulf). This information may be useful in assisting maritime management.

The potential of current- and wind-driven transport for environmental management of the Baltic Sea.

The ever increasing impact of the marine industry and transport on vulnerable sea areas puts the marine environment under exceptional pressure and calls for inspired methods for mitigating the impact of the related risks. We describe a method for preventive reduction of remote environmental risks caused by the shipping and maritime industry that are transported by surface currents and wind impact to the coasts. This method is based on characterizing systematically the damaging potential of the offshore areas in terms of potential transport to vulnerable regions of an oil spill or other pollution that has occurred in a particular area. The resulting maps of probabilities of pollution to be transported to the nearshore and the time it takes for the pollution to reach the nearshore are used to design environmentally optimized fairways for the Gulf of Finland, Baltic Proper, and south-western Baltic Sea.

Applied Wave Mathematics

CENS, CMA and the CENS-CMA Project: J.Engelbrecht, R.Winther, E.Quak.- Part I.Waves in Solids.- Overview: A.Berezovski.- Deformation Waves in Solids: J.Engelbrecht.- The Perturbation Technique for Wave Interaction in Prestressed Material: A.Ravasoo.- Waves in Inhomogeneous Solids: A.Berezovski, M.Berezovski, J. Engelbrecht.- Part II. Mesoscopic Theory.- Overview: W.Muschik.- Dynamics of Internal Variables from the Mesoscopic Background for the Example of Liquid Crystals and Ferrofluids: Ch.Papenfuss.- Towards a Description of Twist Waves in Mesoscopic Continuum Physics: H. Herrmann.- Part III.- Exploiting the Dissipation Inequality.- Overview: W. Muschik.- Weakly Nonlocal Non-equilibrium Thermodynamics - Variational Principles and Second Law: P. Van.- Part IV. Waves in Fluids.- Overview: T.Soomere.- Long Ship Waves in Shallow Water Bodies: T.Soomere.- Modelling of Ship Waves from High-speed Vessels: T. Torsvik.- New Trends in the Analytical Theory of Long Sea Wave Runup: I. Didenkulova.- Part V. Mathematical Methods.- Overview: E. Quak.- The Pseudospectral Method and Discrete Spectral Analysis: A. Salupere.- Foundations of Finite Element Methods for Wave Equations of Maxwell Type: S.H. Christiansen.- An Introduction to the Theory of Scalar Conservation Laws with Spatially Discontinuous Flux Functions: N.H. Risebro.- Index

Impact of horizontal eddy diffusivity on Lagrangian statistics for coastal pollution from a major marine fairway

Lagrangian trajectory methods are often applied as deterministic transport models, where transport is due strictly to advection without taking into account stochastic elements of particle dispersion, which raises questions about validity of the model results. The present work investigates the impact of horizontal eddy diffusivity for a case study of coastal pollution in the Gulf of Finland, where the pollutants are assumed to originate from a major fairway and are transported to the coast by surface currents. Lagrangian trajectories are calculated using the TRACMASS model from velocity fields calculated by the Rossby Centre circulation model for 1982 to 2001. Three cases are investigated: (1) trajectory calculation without eddy diffusivity, (2) stochastic modelling of eddy diffusivity with a constant diffusion coefficient and (3) stochastic modelling of eddy diffusivity with a time- and space-variable diffusion coefficient. It is found that the eddy diffusivity effect increases the spreading rate of initially closely packed trajectories and the number of trajectories that eventually reach the coast. The pattern of most frequently hit coastal sections, the probability of hit to each such section and the time the pollution spends offshore are virtually invariant with respect to inclusion of eddy diffusivity.

Recent Change—Sea Level and Wind Waves

This chapter describes observed changes in sea level and wind waves in the Baltic Sea basin over the past 200 years and the main climate drivers of this change. The datasets available for studying these are described in detail. Recent climate change and land uplift are causing changes in sea level. Relative sea level is falling by 8.2 mm year−1 in the Gulf of Bothnia and slightly rising in parts of the southern Baltic Sea. Absolute sea level (ASL) is rising by 1.3–1.8 mm year−1, which is within the range of recent global estimates. The 30-year trends of Baltic Sea tide gauge records tend to increase, but similar or even slightly higher rates were observed around 1900 and 1950. Sea level in the Baltic Sea shows higher values during winter and lower values during spring and this seasonal amplitude increased between 1800 and 2000. The intensity of storm surges (extreme sea levels) may have increased in recent decades in some parts of the Baltic Sea. This may be linked to a long-term shift in storm tracks.

Runup characteristics of symmetrical solitary tsunami waves of “unknown” shapes

The problem of tsunami wave runup on a beach is discussed in the framework of the rigorous solutions of the nonlinear shallow-water theory. We present an analysis of the runup characteristics for various shapes of the incoming symmetrical solitary tsunami waves. It will be demonstrated that the extreme (maximal) wave characteristics on a beach (runup and draw-down heights, runup and draw-down velocities and breaking parameter) are weakly dependent on the shape of incident wave if the definition of the “significant” wavelength determined on the 2/3 level of the maximum height is used. The universal analytical expressions for the extreme wave characteristics are derived for the runup of the solitary pulses. They can be directly applicable for tsunami warning because in many cases the shape of the incident tsunami wave is unknown.