Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
HYDROSTATIC EQUILIBRIUM The pressure in the ocean is partially affected by the movement of the water. However, the ocean currents are very slow, and the vertical movements even slower. Thus, for most of the purposes the pressure in depth is taken as the hydrostatic pressure. The hydrostatic pressure is the weight of the water column per unit of area at a depth z. Considering ρ=constant, the hydrostatic pressure at depth z is given by the Hydrostatic Equation, p = − ρgz. In the real ocean, ρ changes with depth. We can consider the water column as an infinite number of layers of infinitesimal thickness dz, that contributes with an infinitesimal pressure dp to the total hydrostatic pressure at the depth z. Thus, the hydrostatic pressure at the depth z is given by: dp = − ρgdz. The pressure at the depth z is the summation (well....the integral....) of all the individual contributions dp of the several layers. HYDROSTATIC EQUILIBRIUM Variation of the hydrostatic pressure with depth: (a) in the real case, where the density varies with depth; (b) in the case the density is assumed as constant. GEOSTROPHIC CURRENTS Horizontal Pressure Gradient Geostrophic Adjustment isobaric sea surface ⇒ geostrophic equilibrium situation: The pressure gradient force and the Coriolis force are in balance, thus the movement has constant velocity – geostrophic velocity (Law of Inertia). Coastal boundaries and the heterogeneity of the wind field originate slopes in the sea surface, that induces variations of the hydrostatic pressure on horizontal surfaces at depth ⇒ horizontal pressure gradient. Horizontal pressure gradient force per unit of mass: 1 dp = g tan θ ρ dx Initial situation: there is an accelerated motion, “descending” the pressure gradient. The water tends to move in order to eliminate the horizontal differences in the pressure field. The force that originates this motion is known as the horizontal pressure gradient force. If the Coriolis force, that acts on the moving water, is balanced by the horizontal pressure gradient force, the current is in geostrophic equilibrium and is called geostrophic current. BAROTROPIC AND BAROCLINIC CONDITIONS Barotropic Conditions : • In real conditions, if the ocean is homogeneous, the density increases in depth due to the compression caused by the weight of the overlaying water; the isobaric surfaces are parallel to the sea surface and to the isopycnic surfaces ⇒ we are in Barotropic Conditions. • In barotropic conditions, the pressure variation on a horizontal surface, at a given depth, is determined only by the sea surface slope, because the the isobars are parallel to the sea surface. Baroclinic Conditions: • Any variation of the density will affect the weight of the overlaying water and, consequently, will affect the pressure that acts on a given horizontal surface. When lateral density variations occur, the isobaric surfaces are not parallel to the sea surface; the isobars intersect the isopycnics, with opposing slopes. The tilt of the isobars relatively to the isopycnics characterize the Baroclinic Conditions. BAROTROPIC AND BAROCLINIC CONDITIONS In barotropic flow the isopycnic and isobaric surfaces are parallel and their slopes in relation to the horizontal remain constant with depth. Thus, since the slope of the isobars is constant with depth, the horizontal pressure gradient from B to A, and in consequence the geostrophic current, is constant with depth. In a baroclinic flow the isopycnic surfaces intersect the isobaric surfaces. At shallow depths, the isobaric surfaces are parallel to the sea surface, but with the increasing depth their slope becomes smaller, because the average density of a column of water at A is higher than that of a column of water at B (in barotropic conditions the average density these two columns is the same). As the isobaric surfaces become increasingly near horizontal, so the horizontal pressure gradient decreases and so does the geostrophic current, until at some depth the isobaric surfaces are horizontal and the geostrophic current is zero. BAROTROPIC AND BAROCLINIC CONDITIONS The relationship between isobaric and isopycnic surfaces: (a) barotropic conditions – the desnsity distribution, indicted by the intensity of blue shading, does not influence the shape of isobaric surfaces. (b) baroclinic conditions – lateral variations of density do affect the shape of isobaric surfaces. (a) Barotropic conditions: the slope of the isobars is constant with depth. Geostrophic velocity is the same at all depths: u = g tan θ (u: geost. veloc.) f (b) Baroclinic conditions: the slope of the isobars varies with depth. At the reference level, z0, the isobar corresponding to pressure p0 is assumed to be constant. In this case, geostrophic velocity decreases with depth. Anyway, different behaviors may occur. Profiles of geostrophic current velocity: (a) Baroclinic (b) Combination of baroclinic and barotropic components. In this case the reference level is not a level of no motion.