A NON-HYDROSTATIC MODEL OF DENSE WATER FORMATION IN THE PARTIALLY ICE-COVERED OCEAN
Naosuke Okada1*, Shoshiro Minobe2 and Motoyoshi Ikeda1
1Graduate School of Environmental Earth Science,
Hokkaido University, Sapporo, Japan
2Graduate School of Science, Hokkaido University, Sapporo, Japan
1 INTRODUCTION
In the ocean partially covered by sea ice, nearly uniform atmospheric cooling can induce much more intense cooling through an open water area, and hence, more rapid brine rejection from ice formation than the ice-covered portion. This nonuniform negative buoyancy flux produces a unique situation of convection: an area of convection is comparable with a convective plume. The density of the water made by this situation may depend on the size of an area of convection. To make clear this problem, we carry out numerical experiments using a three-dimensional non-hydrostatic model.
2 MODEL
A three-dimensional ocean model is developed without a hydrostatic assumption for Businesq incompressible fluid under rotation. The model domain is a square in the plan view with the side lengths of 12.8km and a depth of 1000m. The spatial resolution is 100m in the horizontal directions and 50m in the vertical direction. At the upper boundary rigid-lid approximation is adopted, and the lateral boundary is periodic. No momentum flux is given at the upper and lower boundaries.
In a numerical experiments, the plume scale depend on diffusivities. We set diffusion coefficients as isotropic constants in the present model. The value is 0.3m2s-1=l, and the plume scale is about 1km, the model can resolve the plume. Coriolis parameter is l0-4s-1=l. The initial condition is neutral to which small random density perturbation is added.
3 FORCINC AREAS AND INTENSITY
The positive density flux is given in the upper 50m(only the upper most grid). In the first three experiments, the total of forcing areas and the intensity of the density flux are kept unchanged.
Thus, the total density flux over the domain is unchanged. However, we change the distribution of forcing areas. These areas are as follows (See also Figure 1).
experiment A Large single disk, the diameter of which is 4km.
experiment B 16 disks clustered near the Center of the domain with diameters of 1km.
experiment C 16 disks distributed uniformly with diameters of 1km.
Density flux is 10-5kgm-2s-1. It corresponds to rejecting brine with 4cm ice forming per day.
In the fourth experiments(experiment D), we set large forcing disk whose diameter is 8km. We set the density flux at 2.5 × 10-6kgm-2s-1. Hence, which is one forth of the other three cases. The total density flux over the domain is same as the first three experiments. The forcing disk of experiment D is almost same as the area of the square in which small forcing disks are clustered in experiment B.
4 RESULTS
After 2 days forcing, in experiment A, some plume develops (Figure 2a). Here, a plume is de-fined as a group of upward and downward movements within an area with about a 1km diameters. In experiment A we find four plumes. In experiment B and C, no clear plume structure develops; each convected area is smaller than a plume(Figure 2b,2c).
Figure 3 is a density histogram at Day 2 : i.e., an effective density anomaly ( = density deviation from the initial neutral volume multiplied by its
*Corresponding author address. Naosuke Okada, Division of Oceanic and Atmospheric Science, Graduate school of Environmental Earth science, Hokkaido University, N10W5, Sapporo, 060-0810, Japan; E-mail: okada@ees. hokudai.ac.jp
