Flemming Bo Pedersen

Fronts in the Kattegat: The hydrodynamic regulating factor for biology

The recurrence since 1981 of oxygen depletion in the southern part of the Kattegat (the transition area between the Baltic Sea and the North Sea) initiated an interdisciplinary project in biological oceanography. More than 100 years of observations from light-vessels in the region are at our disposal for a hydrographic description. Nevertheless, it was first after the analysis of satellite images and the intensive in situ measurements that the great importance of the complicated front-dynamics in the region was appreciated. A phenomenological description of the interaction between the major physical phenomena encountered in the southern Kattegat such as fronts, leakage (detrainment), baroclinic circulation, wind mixing, entrainment, upwelling, and intrusions is given. The importance of these estuarine events to phytoplankton production is discussed. The importance of the hitherto unnoticed subsurface phytoplankton productions in connection with intrusions at the primary halocline is underlined.

Winddriven Stratified Flow

The wind is often one of the most important external forcing functions with respect to the currents and mixing processes in the ocean, in estuaries and lakes.

Interfacial Shear Stress (τi)

The shear stress at the boundaries of a flow (including the interface) is of crucial importance to the macro- as well as to the microstructure of the flow. The macrostructure — by which we mean the average velocity, the depth et cetera — is determined by the momentum equation or the energy equation. The microstructure — by which we mean the turbulent properties of the flow — is determined by the conservation equation for the kinetic energy, the mass flux et cetera. In all these equations, the shear stress plays a central role by governing the velocity and depth variations in the flow direction and by determining the mixing processes including the entrainment.

The Equations of Continuity and Motion for Miscible Stratified Flows

The motion of real fluids is associated with an energy loss, i.e. — as far as turbulent flow is concerned — with a production of turbulent kinetic energy, which in a homogeneous flow is dissipated into heat. In a stratified flow, part of this turbulent kinetic energy is used to mix the flowing water with the ambient water. Let us briefly illustrate this mixing process in a dense bottom current, see Fig. 4.1

Pressure Conditions and Potential Energy

From the basic course in hydraulics we know that the pressure conditions in a stagnant pool of water is hydrostatic, which means that the pressure equals the weight of the fluid column above it. On the assumption that we are concerned with the pressure normal to the flow direction, the pressure distribution is hydrostatic here too, but now the pressure balances the vertical component of the weight of the fluid column normal to the flow direction. Contrary to homogeneous fluids, this weight generally is a function of space and time due to the mixing of water masses of different temperature, salinities, concentration of suspended particles etc. The density of sea water is discussed in Appendix (read it!).

Free Penetrative Convection

Free penetrative convection is the disorganized movement without a mean velocity created by a source of buoyancy flux flowing into an ambient fluid.

Entrainment (V E )

Entrainment can be defined as: 1) The incorporation of non-turbulent, usually irrotational fluid into the turbulent region of the entraining fluid, or conversely: 2) The diffusion of the turbulent entraining fluid into the non-turbulent ambient fluid.

Horizontal Buoyant Flow

A horizontal buoyant flow is the flow created by a horizontally directed source of mass, momentum, and buoyancy into an ambient fluid. The horizontal direction is preserved by the existence of two stable density jumps embedding the flow, as for instance a free surface and an interface.

Dense Bottom Currents

A dense bottom current or a light roof current is the flow created by a source of mass, momentum, and buoyancy flowing into an ambient fluid in such a way that the flow is bounded by the fixed wall and the interface. The dense bottom currents and light roof currents are primarily driven by buoyancy forces.

ℝ f T = The Bulk Flux Richardson Number

1) IR f T is the ratio between the gain in potential as well as turbulent kinetic energy due to the entrained mass and the energy available for the turbulence, i.e. the production, corrected for the rate of change of the turbulent kinetic energy of the turbulent body.