Zygmunt Kowalik

Numerical Modeling of Ocean Dynamics

While there are several excellent books dealing with numerical analysis and analytical theory, students and faculty in numerical applications to ocean dynamics have to sift through hundreds of references. This monograph is an attempt to partly rectify this situation. Major chapters (II, III and IV) deal first with the basics and then go on to various applications. Instead of covering the vast field of ocean dynamics, this book focuses on transport equations (diffusion and advection), shallow water phenomena - tides, storm surges and tsunamis; three-dimensional time dependent oceanic motion; natural oscillations; and steady state phenomena. The aim of this book is two-fold; it gives an introduction to the application of finite-difference methods to ocean dynamics, and it also reviews more complex methods.

Tides in the Sea of Okhotsk

Eight major tidal constituents in the Sea of Okhotsk have been investigated using a numerical solution of tidal equations on a 59 space grid. The tides are dominated by the diurnal constituents. Diurnal tidal currents are enhanced in Shelikhov Bay and Penzhinskaya Guba, at Kashevarov Bank, in proximity to the Kuril Islands and at a few smaller locations. The major energy sink for diurnal tides (over 60% of the total energy) is Shelikhov Bay and Penzhinskaya Guba. The major portion of semidiurnal tide energy is dissipated in the northwestern region of the Sea of Okhotsk and in Shelikhov Bay and Penzhinskaya Guba. Nonlinear interactions of diurnal currents are investigated through K1 and O1 constituent behavior over Kashevarov Bank. These interactions generate residual circulation of the order of 10 cm s 21, major oscillations at semidiurnal and fortnightly periods (13.66 days), and higher harmonics of basic tidal periods. The M2 tidal current, caused by the nonlinear interaction of the diurnal constituents over Kashevarov Bank, constitutes approximately a half of the total M2 tide current there. The fortnightly current, through nonlinear interactions, also influences basic diurnal tidal currents by inducing fortnightly variations in the amplitude of these currents.

Diurnal tides in the Arctic Ocean

A two-dimensional numerical model with a space grid of about 14 km is applied to calculate diurnal tidal constituents K1 and O1 in the Arctic Ocean. Calculated corange and cotidal charts show that along the continental slope, local regions of increased sea level amplitude, highly variable phase and enhanced currents occur. It is shown that in these local regions, shelf waves (topographic waves) of tidal origin are generated. In the Arctic Ocean and Northern Atlantic Ocean more than 30 regions of enhanced currents are identified. To prove the near-resonant interaction of the diurnal tides with the local bottom topography, the natural periods of oscillations for all regions have been calculated. The flux of energy averaged over the tidal period depicts the gyres of semitrapped energy, suggesting that the shelf waves are partially trapped over the irregularities of the bottom topography. It is shown that the occurrence of near-resonance phenomenon changes the energy flow in the tidal waves. First, the flux of energy from the astronomical sources is amplified in the shelf wave regions, and afterwards the tidal energy is strongly dissipated in the same regions.

Topographic enhancement of tidal motion in the western Barents Sea

A high-resolution numerical lattice is used to study a topographically trapped motion around islands and shallow banks of the western Barents Sea caused both by the semidiurnal and diurnal tidal waves. Observations and model computations in the vicinity of Bear Island show well-developed trapped motion with distinctive tidal oscillatory motion. Numerical investigations demonstrate that one source of the trapped motion is tidal current rectification over shallow topography. Tidal motion supports residual currents of the order of 8 cm s−1 around Bear Island and shallow Spitsbergenbanken. The structures of enhanced tidal currents for the semidiurnal components are generated in the shallow areas due to topographic amplification. In the diurnal band of oscillations the maximum current is associated with the shelf wave occurrence. Residual currents due to diurnal tides occur at both the shallow areas and the shelf slope in regions of maximum topographic gradients. Surface manifestation of the diurnal current enhancement is the local maximum of tidal amplitude at the shelf break of the order of 5 to 10 cm. Tidal current enhancement and tidally generated residual currents in the Bear Island and Spitsbergenbanken regions cause an increased generation of ice leads, ridges and, trapped motion of the ice floes.

Tsunamis Generated by Eruptions from Mount St. Augustine Volcano, Alaska

During an eruption of the Alaskan volcano Mount St. Augustine in the spring of 1986, there was concern about the possibility that a tsunami might be generated by the collapse of a portion of the volcano into the shallow water of Cook Inlet. A similar edifice collapse of the volcano and ensuing sea wave occurred during an eruption in 1883. Other sea waves resulting in great loss of life and property have been generated by the eruption of coastal volcanos around the world. Although Mount St. Augustine remained intact during this eruptive cycle, a possible recurrence of the 1883 events spurred a numerical simulation of the 1883 sea wave. This simulation, which yielded a forecast of potential wave heights and travel times, was based on a method that could be applied generally to other coastal volcanos.

Kuril Islands tsunami of November 2006: 2. Impact at Crescent City by local enhancement

[1] Crescent City (CC) is particularly susceptible to tsunami attack. The combination of tsunami signal enhancement by both distant bathymetric features and local nearshore resonance seems to be responsible for this behavior. Application of global tsunami propagation models to the Kuril Islands Tsunami of November 2006 in the companion paper (Kowalik et al., 2008) delineated the importance of distant bathymetric features for both tsunami wave amplification and for increased duration of the tsunami arriving at CC. These distant features were responsible for delivering the late, high-energy signal, which was delayed by 2 hours from the predicted arrival time. Additional local amplification and increased duration are caused by the shelf bathymetry adjacent to CC. As the initial tsunami arrives at CC, the shelf trapping mechanism tends to excite the gravest of the natural modes. This oscillation is slowly shifted toward the natural mode closest to the period of the incident tsunami wave packet. Short-duration wave trains tend to influence the tsunami response at CC harbor in such a way that 1 hour after the first wave arrival a much stronger wave will be generated owing to the tendency of the shelf to initially ring at the frequency of the gravest mode. Practical implications of distant and local amplification relate to the potential hazard near CC, highlighting the need for awareness of the tsunami signal duration. In this respect, two timescales are important for this event: the 2-hour time delay due to distant bathymetric features and the 1-hour delay due to local offshore bathymetry.

Wave Dispersion Study in the Indian Ocean-Tsunami of December 26, 2004

A numerical study which takes into account wave dispersion effects has been carried out in the Indian Ocean to reproduce the initial stage of wave propagation of the tsunami event that occurred on December 26, 2004. Three different numerical models have been used: the nonlinear shallow water (nondispersive), the nonlinear Boussinesq, and the full Navier-Stokes aided by the volume of fluid method to track the free surface. Numerical model results are compared against each other. General features of the wave propagation agreed very well in all numerical studies. However some important differences are observed in the wave patterns, i.e., the development in time of the wave front is shown to be strongly connected to the dispersion effects. Discussions and conclusions are made about the spatial and temporal distribution of the free surface reaffirming that the dispersion mechanism is important for tsunami hazard mitigation.

Numerical simulation of two‐dimensional tsunami runup

Abstract The hydrodynamic and mathematical problems connected with discontinuity between wet and dry domains, nonlinearity, friction, and computational instability are the main problems that have to be sorted out in the runup computation. A variety of runup models are analyzed, including the boundary conditions used to move the shoreline. Based on the initial experiments one‐dimensional and two‐dimensional algorithms are constructed. These models are tested against analytical solutions obtained by others. The extent of inundation along Alaska, British Columbia, Washington, and Oregon coasts caused by the 1964 Alaska earthquake tsunami is well documented. The data gathered at Alberni Inlet, British Columbia, Canada, is used to test the numerical model and the boundary conditions set at the mouth of the inlet. The computed extent of flooding turned out to be in satisfactory agreement with the data obtained from the observations.

Preface to special section on Arctic Ocean Model Intercomparison Project (AOMIP) Studies and Results

] More than 130years ago,theAustrian Arctic explorer,Carl Weyprecht [Weyprecht and Ihne, 1913] (who discov-ered Franz Josef Land, an archipelago north of Russia, andwho advanced a successful scheme for international coop-eration in polar science—the International Polar Year con-cept) postulated that a number of fundamental problems ofmeteorology and geophysics could be solved near theEarth’spoles.Thishypothesisisstillvalidinthe21stcenturybecause the Arctic is recognized as a region where globalclimate change signals are amplified. The model-basedconclusion of Manabe and Stouffer [1994] that the firstsigns of climate change could be detected in the Arctic hasbeen corroborated by numerous other model results [e.g.,Holland and Bitz, 2003; Symon et al., 2005]. On the otherhand, it has been demonstrated that model conclusions maybe highly uncertain and that model estimates of futureclimate change differ significantly from model to model.In order to reduce these uncertainties, it is important tovalidate and to improve models. The latter is the first majorgoal of the Arctic Ocean Model Intercomparison Project(AOMIP). The second major AOMIP goal is to investigatevariability of the Arctic Ocean and sea ice at seasonal todecadal timescales, and identify mechanisms responsible forthe observed changes. Some of the latest AOMIP activitiesassociated with these project goals arereflected inthe papersof this special section.[

Modeling of Topographically Amplified Diurnal Tides in the Nordic Seas

Abstract Diurnal tidal constituents K1 and O1 are calculated in the Nordic seas with a numerical space grid of about 10 km. This allows resolution of the structure of enhanced tidal currents generated by near-resonant topographic vorticity waves at the Yermak Plateau. The resonance properties of the Yermak Plateau are investigated in the period range 20–30 h. The main resonance peak is close to the 26-h period, and the resonance curve envelops a wide range of periods. This broad resonance peak explains the enhancement of both diurnal tidal components separated by a 2-h difference and the stability of the resonance phenomena. The model results describe well the observed flow pattern over the Yermak Plateau, including the current ellipse rotation.