I especially appreciate the support of the Johns Hopkins University Applied Physics Laboratory in awarding the Stewart S. Full citations of sources can be found in the bibliography at the end of the chapter indicated by the figure or table number.
Physical Oceanography: An Overview
The Evolution of Modern Physical Oceanography
These directions incorporated much of what was known about the physical oceanography of the time. By the last third of the 19th century, a new force had come into play in marine science: the transoceanic telegraph.
Gravitational and Rotational Forces
The fluid invariably acts to develop boundary layers in response to these—for example, the Ekman layer at the ocean surface, the benthic boundary layer at the bottom, and western and eastern boundary currents along the edge of the ocean near continents. The centripetal acceleration and simultaneous flattening of the earth due to the first of these motions results in a variation of the effective surface gravity by about 0.52% from pole to equator.
Radiative, Thermodynamic, and Related Forces
The projection of the Earth's disk toward the Sun receives an amount of solar energy, P,y, from. Since the total area of the Earth's surface is 4nR, the average absorbed energy flux per unit area is equal to 4nR.
Zonal and Meridional Variations
The north-south asymmetry is largely due to the eccentricity of the Earth's orbit, with perihelion occurring during summer in the Southern Hemisphere. In the Southern Hemisphere, the latitudinal center of the Ferrel cell falls above the infamous.
Wind Stress
Not only wind speed, but also heat, temperature and humidity profiles change significantly in the lower few hundred meters of the atmosphere. By definition, wind stress-induced currents constitute wind-driven ocean circulation.
The General Circulation of the Ocean
From Dietrich, G., General Oceanography (1963); originally due to G. 2.17 The general surface circulation of the ocean in schematic form. From their latitudinal positions, it is clear that the transoceanic arms of the gyres are closely related to the surface wind stress (actually to the stress curl, as will be shown in Chapter 6), where Coriolis effects play a role.
The Wind.Driven Oceanic Circulation
This balanced flow equation provides an important tool in the oceanographer's analytical toolkit. Intensification of flow along the western boundary is due to the overall eddy balance in the gyre.
Pressure Forcing
For example, corrections must be made to bottom-mounted pressure gauges that measure the depth-integrated density of the overlying water column to remove the effects of atmospheric pressure fluctuations.
The Thermohaline Circulation
Also, a large eastward flow at depth accompanies the surface portion of the Antarctic Circumpolar Current. Another less important but nevertheless interesting thermohaline flow occurs in the Atlantic Ocean at the mouth of the Mediterranean Sea.
The Sea Floor and Its Dynamics
The margin generally ends at the abyss, the flat, sediment-filled plain that occupies much of the ocean floor. The pressure in the Earth's interior is largely hydrostatic and the crust approaches.
Hydrodynamic Equations of the Sea
Introduction
However, as far as one can see, the predictive skill of the equations seems to exceed the computational skill of the manipulators of those equations, so that we can proceed with some tentative confidence toward our mathematical goal until proven otherwise.
The Convective Derivative and the Momentum Equation
Then any arbitrary property, y (eg temperature, entropy), of the fluid element can be considered as a continuously differentiable function of space and time or a smooth field:. This equation, when applied to the property y, gives the total rate of change of y following the motion and states that the total rate is the sum of an intrinsic local rate observed at a fixed point, plus the change due to advection of the quantity at speed u while moving with dx in time dt.
Gravitational Forces
Let p = p ( x , t ) be the density of the liquid; then the momentum equation is simply Newton's First Law applied to a small mass of fluid, d 3 m = p dx dy dz. Furthermore, the actual gravitational forces are not spherically symmetric, but vary in significant ways due to local mass concentrations and anomalies, with the largest departure from spherical symmetry coming from the flattening of the earth at the poles caused by its rotation. around its north. - south axis.
Effects of Spin
Clearly, the centripetal acceleration and ellipticity of the earth must be included in the specification of the equipotential surface that defines the marine geoid. This form, in which the time derivative contains four terms describing special physical effects, will be used henceforth in ocean fluid dynamics.
The Coriolis Force
O i for one revolution of the pan, thereby giving rise to the factor of 2 in the Coriolis acceleration. In the Southern Hemisphere cos 8 < 0 and the direction of the force is opposite: The circle of inertia rotates anti-clockwise.
More Gravity
A remarkable number of features are visible, including the large gravity lows in the Indian Ocean and eastern Pacific, and the high in the North Atlantic off Europe; these represent examples of the previously mentioned anomalies with extreme areas of approx. -100 to + 65 m. But not all bathymetric features have surface gravity expressions (eg East Pacific Rise off South America).
Tidal Forces
3.11 (a) Force diagram showing the tidal generating forces when the moon is 28.5" north of the equatorial plane. Only the horizontal component of the latter is effective in producing tidal currents.
Total Potential Caused by Gravity and Rotation
Internal Forces in a Viscous Fluid
The viscosity coefficient A, indicates that the stress due to this element is transferred in the z-direction. Similar reasoning can be applied to the residual term and indeed, all eight elements of the stress tensor. Hydrodynamic Equations of the Sea 97. net viscous force over all six planes in the x-direction is seen as given by the sum.
Conservation Equations for Mass and Salinity The Continuity Equation
An alternative form of the continuity equation can be derived using the convective derivative notation (Eq. 3.8). The diffusive flux, Jd, is usually found to be proportional to the concentration gradient, VC, in the lowest approximation, where the proportionality constant is the diffusion coefficient.
The Momentum Equation
Together they describe most of the known volume forces acting on a unit mass of the ocean. Despite their widespread use in geophysics, we have chosen not to write the salient equations in geographic coordinates, because of the confusion they can cause.
Fluctuations, Reynolds Stresses, and Eddy Coefficients
Nevertheless, carefully defined ensemble averaging is the preferred method to arrive at the best estimates of the field. In a statistical sense, the elements should be considered as the cross-correlation functions of the time-varying velocity components.
Boundary Conditions in Fluid Dynamics
Now the curvatures are approximately the second derivatives of the surface view, so that the pressure is just below the surface. The radius of curvature is R, which is negative if its center is below the surface of the liquid.
Introduction
In the liquid state, an intermediate state between gas and solid, its anomalous physical properties are most apparent. According to current liquid state theories, fluctuations in the environment lead to two types of microstates:
Effects of Temperature, Salinity, and Pressure
From this phenomenological explanation, it is clear that the density of seawater is a complicated function of the state variables, and that an equation of state is necessary for an orderly and more complete description of the system. We will find that there is a large element of empiricism present in the treatment because of the complications.
Thermodynamics of Seawater
In fluid dynamics, as we shall see, entropy is proportional to the amplitude of motion, among other quantities. Then consider the coefficient of two in Eq. Similarly, a comparison of the coefficients of ds with the halinometric coefficients gives
Heat Conduction Equation
The values of the scalar K~ for the molecular conductance in the sea are of the order of 0.596 W (m2 K m the corresponding eddy conductances are orders of magnitude larger (see Appendix Three). An equation of state of sufficient accuracy to be used in the calculation of the ocean density field (which is needed for the so-called dynamical method of determining large-scale ocean currents; see Chapter 6) is very complicated indeed.
Combined Hydrodynamics and Thermodynamics
In the deep ocean, the decay rate is generally negative, so the potential temperature is less than the in situ temperature. Since most of the water in the ocean is deep, the potential temperatures are low.
Energy Flow and Energy Equations
On the right is (1) the rate of action by or against gravity when fluid crosses equipotential surfaces, -p u. The rate at which work is done per unit volume, p D 9 / D t , is exactly the rate at which the geopotential acts on the fluid flow, - p u.
Total Energy Equations
The total system energy therefore varies due to fluxes across the boundary surface, plus dissipation and energy transformations within the volume. The water masses of the world ocean: some results from a fine-scale census,” in Evolution of Physical Oceanography, B.
Geophysical Fluid Dynamics I
Waves and Tides
Introduction
Quasi-Steady Motions
In the Southern Hemisphere, the Coriolis force and the sense of the gradients are reversed, but the dynamic balances remain the same. The quantity p'g/p is called the reduced gravity, g', and is usually g in the ocean due to the small size of the density perturbations.
Buoyancy and Stability
This process is called convective instability and is a major source of the vertical lifting of clouds discussed in Chapter 2. The drift frequency therefore measures the stability of the water column against small vertical disturbances.
Surface Waves
However, more recent work suggests that the slope of the high-frequency region may actually be -4 when analyzed differently (dashed lines). The free surface boundary conditions can be approximately satisfied if applied at z = 0 rather than at z = t, due to the small amplitude assumption.
- Dispersion Characteristics of Surface Waves
- Surface Gravity Waves
To continue, we need one of several forms of the Bernoulli equation to describe surface dynamics. It is worth noting that w / k and w / l are the projections of the phase velocity, w / k h , on the x and y axes, respectively, and because k,l 5 kh these projected velocities are greater than the actual phase velocity.