Guest lectures and seminars - Page 203

Jan Erik H. Weber, Department of Geosciences, University of Oslo Göran Broström, Norwegian Meteorological Institute, Oslo Nonlinear density-driven convection in a conditionally unstable fluid is studied theoretically. The novelty here is that the destabilizing basic density gradient is expressed in terms of the vertical perturbation velocity through a unit step function. This is done by introducing a one-way source step function due to phase transitions in the equation for the perturbation density. Then we can model the fact that the density-gradient is unstable when the perturbation vertical velocity is upward (positive), and stable when the vertical perturbation velocity is downward (negative), characterizing conditional stability. Linear analytical solutions as well as numerical results for nonlinear two-dimensional steady convection are presented.

Jan Erik Weber is professor at Department of Geosciences

A theoretical model for propagation of internal waves under an ice cover is developed. The sea water is considered to be inviscid, non-rotating, and incompressible and the Brunt-Väisälä frequency is supposed to be constant. The ice is considered of uniform thickness, with constant values of Young's modulus, Poisson's ratio, density and compressive stress in the ice. The boundary conditions are such that the normal velocity at the bottom is zero and, at the undersurface of the ice, the linearized kinematical and dynamic boundary conditions are satisfied. We present and analyze explicit solutions for the internal waves under the ice cover and the dispersion equations. It is shown that when the frequency is near, but smaller than the Brunt-Vaisela frequency the ice deflections can be considerable. The theoretical results are compared with experimental data for the Arctic regions.

Sergey Muzylev is at the Shirsov Institute of Oceanology, Moscow

The study is based on field measurements since 2002. We analyze the transport of Antarctic Bottom Water in Deep Channels of the Atlantic: Vema Channel (31deg S), Romanche Fracture Zone (0 deg) and Vema Fracture Zone (11 deg N). The flow of bottom water in the Vema Channel can reach 4 mln. sq. m per second and the velocity is as high as 60 cm/s. The transport and velocities in the Romanche Fracture Zone and Vema Fracture Zone are smaller and do not exceed 500 th. sq. m per sec. The major penetration of bottom waters to the Northeastern Atlantic basins occurs through the Vema FZ but not through the Romanche FZ because strong tidal internal waves on the slopes of the Mid-Atlantic Ridge near Romanche FZ exceed 50 m, while at the Vema FZ they are approximately 20 m. Such difference in mixing of bottom waters with the overlying North Atlantic Deep water results in the fact the deep Northeastern Atlantic basins are filled with the bottom water transported through the Vema FZ.

Eugene Morozov is proessor at the Shirshov Institute of Oceanology, Moscow

This presentation concerns the mathematical formulation of steady surface gravity waves in a Lagrangian description of motion. It will be demonstrated that classical second-order Lagrangian Stokes-like approximations do not represent a steady wave motion in the presence of net mass transport (Stokes drift). A general mathematically correct formulation is then derived. This derivation leads naturally to a Lagrangian Stokes-like perturbation scheme that is uniformly valid for all time, i.e. without secular terms. This scheme is illustrated, both for irrotational waves, with seventh-order and third-order approximations in deep water and finite depth, respectively, and for rotational waves with a third-order approximation of the Gerstner-like wave on finite depth. It is also shown that the Lagrangian approximations are more accurate than their Eulerian counterparts of same order.

Didier Clamond has been a post.-doc. at the Department at Mathematics, UiO. He is now faculty member at the University of Nice, Sophia-Antipolis.