Lars Petter Røed

High Resolution Measurements of Turbulence, Velocity and Stress Using a Pulse-to-Pulse Coherent Sonar

Abstract Considered are the capabilities of a recently developed pulse-to-pulse coherent sonar called the High Resolution Current Profiler (HRCP). Special emphasis is placed on methods whereby reliable and accurate vertical profiles of turbulence parameters, such as turbulent kinetic energy and Reynolds stresses, may be extracted from such sonars. The prototype HRCP has been developed in order to obtain precise and reliable measurements of both the mean and the fluctuating components of the velocity vector profile in the bottom boundary layer (lowermost 10 m). The prototype HRCP developed through the project BSEX is a 307 KHz pulse-to-pulse coherent sonar with four beams mounted 30° off the vertical in 90° azimuthal increments. It has 50 range cells covering a vertical profiling distance of 10 meters. The data collected are radial speeds along the four acoustic beams. Thus, care has to be exercised in interpreting the measurements in terms of turbulence parameters. It is shown, based upon reasonable assum...

A Numerical Model for Long Barotropic Waves and Storm Surges along the Western Coast of Norway

Abstract A finite-difference scheme is used in order to study the generation and propagation of long barotropic waves and storm surges along the western coast of Norway. The performance of the numerical scheme is investigated by comparing with analytical solutions for a model with a straight coastline and a continental shelf of uniform depth and width. Simulations with a model of the west coast of Norway show that the wind stress and the atmospheric pressure are of about equal importance for the largest storm surges. The maximum elevation of the sea surface occurs at the coast and the sea level decreases nearly linearly over the shelf. The surge amplitude at the coast agrees well with observations. The sea level changes outside the shelf are small and for the most part due to the pressure. Shelf waves are mainly generated by the wind stress and Kelvin waves are mainly generated by the pressure field.

Open Boundary Conditions in Numerical Ocean Models

Conditions imposed on a class of computational boundaries sometimes referred to as “open” boundaries are reviewed. A possible definition of the term “open boundary” is suggested in order to limit the discussion. Some popular and recently suggested conditions are reviewed and discussed. Emphasis is on conditions based on the Sommerfeld radiation condition including the Orlanski type and modifications thereof, but also sponges are considered. In particular the modifications suggested to handle (i) oblique incidence and (ii) wind forcing at the open boundary are considered. Some sample experiments with a barotropic ocean model are shown. These experiments serve to illustrate the high sensitivity of the interior response to the implementation of different conditions at the model’s open sea boundaries.

Variability of the Denmark Strait overflow: A numerical study

Mesoscale variability in the Denmark Strait overflow is investigated using a version of the Miami Isopycnic Coordinate Ocean Model that includes a recently developed intermittent and vigorous, turbulent and diffusive diapycnal mixing scheme. Earlier idealized modeling work on the subject is further extended in that a realistic replica of the shelf-slope topography and irregular coastline geometry of the Denmark Strait area is also employed. Compared with earlier studies, our experiments reveal that (1) the introduction of the new diapycnal scheme and the true shelf-slope topography do not affect the formation of the intense cyclonic eddies south of the sill and along the continental slope and (2) the new diapycnal scheme has a significant effect on the bottom plume, in that the distribution, volume transport and properties of the bottom plume appear to be more realistic and more in line with what is observed. The first conclusion adds support to the vortex-stretching mechanism suggested in earlier studies as the cause for the formation of the cyclonic eddies. This mechanism is therefore a robust feature and provides an explanation for the observed variability in the Denmark Strait overflow. The second conclusion underscores the importance of including realistic parameterizations of diapycnal mixing in isopycnal coordinate ocean models. Specifically, the results show that the water that descends along the bottom south of the sill becomes lighter and is more voluminous compared to experiments without the new mixing scheme. Even when including the mixing scheme, the bottom plume separates into distinct boluses of enhanced thickness. Moreover, these boluses are also associated with water of anomalously high density, as well as with the cyclonic eddies in the upper water column.

Modelling Mesoscale Features in the Ocean

The dominant dynamic length scale in the ocean, as well as in the atmosphere, is the Rossby radius of deformation (e.g., Gill, 1982 pp. 191 – 203). In the atmosphere this length scale is the scale of the low pressure systems, i.e. about 100 –1000 km, which is referred to as the synoptic scale. In the ocean the Rossby radius of deformation varies from about 100 – 300 km in tropical waters down to 5–10 km in subpolar regions like the Norwegian Sea. Length scales such as the latter are commonly referred to as the mesoscale by meteorologists. This reference has also been adopted in the ocean, although from a dynamical point of view, it would have been natural to name it the oceanic synoptic scale. The name mesoscale is, therefore, traditionally associated with a particular range in kilometers rather than being associated with its similar dynamic atmospheric length scale. Oceanic features of the order of the Rossby deformation radius, which may be dubbed oceanic ‘weather’, are nevertheless referred to as mesoscale features. Examples of such features are upwelling jets, eddies and filaments. These features are clearly visible in almost any satellite image of the ocean surface.

A simple approach to adjust tidal forcing in fjord models

To model currents in a fjord accurate tidal forcing is of extreme importance. Due to complex topography with narrow and shallow straits, the tides in the innermost parts of a fjord are both shifted in phase and altered in amplitude compared to the tides in the open water outside the fjord. Commonly, coastal tide information extracted from global or regional models is used on the boundary of the fjord model. Since tides vary over short distances in shallower waters close to the coast, the global and regional tidal forcings are usually too coarse to achieve sufficiently accurate tides in fjords. We present a straightforward method to remedy this problem by simply adjusting the tides to fit the observed tides at the entrance of the fjord. To evaluate the method, we present results from the Oslofjord, Norway. A model for the fjord is first run using raw tidal forcing on its open boundary. By comparing modelled and observed time series of water level at a tidal gauge station close to the open boundary of the model, a factor for the amplitude and a shift in phase are computed. The amplitude factor and the phase shift are then applied to produce adjusted tidal forcing at the open boundary. Next, we rerun the fjord model using the adjusted tidal forcing. The results from the two runs are then compared to independent observations inside the fjord in terms of amplitude and phases of the various tidal components, the total tidal water level, and the depth integrated tidal currents. The results show improvements in the modelled tides in both the outer, and more importantly, the inner parts of the fjord.

Operational marine models at the Norwegian Meteorological Institute

The Norwegian Meteorological Institute (DNMI) runs an operational marine forecast system, which consists of 4 coupled marine numerical models: a numerical weather prediction model (HIRLAM), a wave model (WINCH), a primitive equation baroclinic ocean model (ECOM3D) which is run both in barotropic and baroclinic modes, and an oil drift model (NOROIL). A sketch of the system is shown in Figure 1. This activity addresses two of the goals of EuroGOOS: building on proven forecasting know-how and creating new marine operational services.

Two-Dimensional Problems

This chapter investigates the effect of including more than one dimension in space. In particular, it discusses the impact on numerical stability and the stability criterion. Extension to three dimensions is then straightforward.

Time Marching Problems

The purpose of this chapter is to present some properties inherent in the governing equations listed in Sect. 1.1. Most problems in the geophysical sciences, including atmospheres, oceans, seas, and lakes, involve solving so-called time marching problems. Typically, the state of the fluid in question is known at one specific time. As postulated by Bjerknes (Meteor Z 21:1–7, 1904) in his comments on weather forecasting (see quote in the preface), the aim is then to predict the state of the fluid at a later time. This is done by solving the governing equations listed in Sect. 1.1. Such problems are known in mathematics as initial value problems.

Shallow Water Problem

The purpose of this chapter is to learn how to solve a simple subset of the momentum equations ( 1.1) numerically. The focus is on the shallow water equations, and in particular their depth integrated versions ( 1.33) and ( 1.34). Despite their simplicity, the shallow water equations include the essence of the momentum equations. For instance, we retain the possibility of a geostrophic balance and the impact of nonlinear terms on the dynamics.