Unstable and neutrally stable modes in barotropic and baroclinic shelf slope currents.

The stability of barotropic and baroclinic shelf slope currents currents is investigated. Assuming periodic small amplitude perturbation in along shelf direction the stability problem is reduced to an eigenvalue problem by discretization in the across shelf direction. The eigenvalue problem for the wave frequency when along shelf wave number is specified is solved numerically by using NAG-routines. Two applications are considered, one corresponding to the conditions along the Catalan shelf, northwestern Mediterranean, the other to the shelf slope west of Norway

Analysis of current and sea level observations from Trondheimsleia

Sea level and current measurements from Trondheimsleia have been analysed and the parameters of the tidal ellipses for the major tidal components M2, S2, N SUB>2, and K1 have been calculated. Harmonic constants for sea level and tidal ellipse parameters have been compared with the corresponding data from a high resolution tidal model in order to validate the performance of the model. Short periodic oscillations with period about 40 minutes are observed at the time of peak tidal current at one station located in a channel with relatively strong tidal currents

Characterizing chaotic dispersion in a coastal tidal model

Abstract Diverse Lagrangian methods are used to study dispersion and mixing in a model in the Norwegian Trondheim fjord. We focus on the tidally driven currents, neglecting wind-forcing, and generate a large number of particle trajectories. We first consider traditional measures (absolute and relative dispersion) involving averages over all particles. We then contour those measures, to gauge the spatial variations. Then we examine a more recently developed measure, the direct Lyapunov exponent (DLE), to further refine the description of the spatial variability. The results suggest regions of strong mixing adjacent to regions with weak mixing, so that particles in nearby regions may experience very distinct evolutions. And M2 dominates the dispersion; adding additional tidal components affects mainly the amplitude of the particle excursions rather than the character of the mixing

Barotropic instability in the West Spitsbergen Current

Barotropic instability in the shoreward branch of the West Spitsbergen Current is investigated on the basis of data from an array of current meter moorings along 78.83°N, across the upper continental slope and shelf break west of Svalbard. The slowly varying background current profile is modeled as an along‐slope, asymmetric jet anchored to the shelf break. Numerical linear stability analyses are performed on the idealized current profile and topography, revealing the characteristic period, wavelength, and growth rate of unstable vorticity waves. Detailed analysis of the ambient current profile in 2007–2008 shows that unstable conditions are present during ∼40% of the 10 month measurement record, depending on the localization, width, and amplitude of the current jet. The resulting vorticity waves are localized at the shelf break and are able to exchange water masses across the oceanic Arctic front. Typical wavelengths and periods are 20–40 km and 40–70 h, respectively. Wavelet, coherence, and complex demodulation analyses of the current meter data confirm that transient signals of similar periodicity as predicted by the stability analysis exist in the data record, prominently during the winter and spring months. Estimates of the heat loss contribution from isopycnal diffusion reach 1.4 TW during the time intervals when unstable vorticity waves are active at the shelf break, implying that the dynamics of the West Spitsbergen Current play a significant role in the cooling process of the Atlantic water on the way to the Arctic Ocean. This cooling corresponds to an along‐shelf cooling rate of −0.08°C per 100 km

Mid term report for GITEC-TWO

The report summarizes the work performed at the Department of Mathematics, during the first year of the European research project GITEC-TWO (contract ENV4-U96-0297). Some of the result will subsequently be published elsewhere in a more complete form. We start with the brief presentation of hydrostatic and dispersive long wave equations, in Eulerian as well as Lagrangian description, and a family of somewhat related numerical techniques. The effect of dispersion on the 1969 tsunami, originating in deep sea south-west of Portugal, is extensively discussed in relation to numerical solutions and discretization errors. We find strong indications that dispersive effects are significant for this tsunami. In the project work emphasis has been put on the analysis of numerical methods by analytic tools. To the knowledge of the writers this is a new approach. First an optical theory for discrete waves is established. Then the effects of a staircase boundary on run-up is investigated through separation of variables in a non-orthogonal coordinate system. Two finite element model are presented: a technique for solution of the Boussinesq equations in Eulerian coordinates and a run-up model in Lagrangian description. The latter is verified through comparison to analytic results and a previously developed finite difference method. The results are promising

Modellsimuleringer av tidevannstrømmen i Tjeldsundet og Ramsundet

Tidevannsstrømmen i Tjeldsundet og Ramsundet i Ofoten er simulert med en numerisk havmodell med horisontal gitteroppløsning 25-50 meter. Middelstrømmen i vannsøylen er beregnet for de tre viktigste halvdaglige tidevannskomponentene M2, S2, og N2, og den største heldaglige komponenten K1. For å vise resultatene, er det tegnet strømkart for områdene med sterkeste strøm; Ballstadstraumen, Sandtorgstraumen og Steinslandsstraumen i Tjeldsundet og Spannbogstraumen i Ramsundet. Kartene viser strømfeltene hver time gjennom en tidevannsyklus. I tillegg er det tegnet konturkart for sterkest strøm ved middels stor flo. Kartene viser at det er store variasjoner i strømstyrke og at det i forskjellige faser av tidevannsyklusen opptrer virvler og bakevjer i strømfeltene. Det opptrer virvler flere steder blant annet i nordgående flostrøm ved Evenskjœr nord for Sandtorg, i området ved Tjeldsundbrua, langs land øst og vest Ballstad, og i kjølvannet av Holsflua i Tjeldsundet, nord for innløpet til Ramsund ved sørvestgående fallstrøm. Noen av disse virvelstrukturene er dokumentert også ved observasjoner. Det er foretatt sammenlikninger med både vannstands- og strømmålinger. Modellen viser god overensstemmelse med vannstandsmålingene og prediksjoner av tidspunktene for strømvending mellom nordgående flostrøm og sørgående fallstrøm stemmer også godt overens med målinger. Strømstyrken i modellen viser dessuten god overenstemmelse med tidligere målinger av strømmen i overflatelaget (øvre 10-15 meter av vannsøylen). Strømmålingene utført under prosjektperioden av FFI i dypere vannlag (10-20 meter over bunnen) viser derimot vesentlig lavere strøm enn den middelstrømmen for vannsøylen som modellen predikterer. FFI-målingene er periodevis beheftet med stor usikkerhet på grunn av nedbøyninger og svingninger i måleriggen. Strømfeltene fra modellsimuleringene er forsøksvis implementert for visning i Forsvarets kartsystem MARIA og i serveren METOC WMS for å gjøre resultatene tilgjengelige for operativt bruk

Implementation of Non-Linear Advection Terms in a High Resolution Tidal Model

Various methods for approximating the non-linear advection terms in a high resolution tidal model with complex coastal boundaries have been implemented and tested. The model, driven by the dominant M2 tidal component at the open boundaries, has been applied to a model domain with 100 meter grid resolution for the Tjeldsundet channel in northern Norway. Overtides, intensivated jets and eddy structures appear in the current fields of the full non-linear simulations. How these flow features depend on the way the friction terms are calculated and the way the non-linear advection terms are calculated in a zone near the coastal boundaries, are discussed. Some comparison with field measurements have also been made