Forces and accelerations in a fluid: (a) acceleration, (b) advection, (c) pressure gradient force, (d) gravity, and (e) acceleration associated with viscosity υ.

Observed diapycnal diffusivity (m²/s²) along 32°S in the Indian Ocean, which is representative of other ocean transects of diffusivity. See Figure S7.4 for diffusivity profiles. This figure can also be found in the color insert. ©American Meteorological Society. Reprinted with permission. Source: From Kunze et al. (2006).

Mixed layer development. (a, b) An initially stratified layer mixed by turbulence created by wind stress; (c, d, e) an initial mixed layer subjected to heat loss at the surface which deepens the mixed layer; (f, g, h) an initial mixed layer subjected to heat gain and then to turbulent mixing presumably by the wind, resulting in a thinner mixed layer; (i, j) an initially stratified profile subjected to internal mixing, which creates a stepped profile. Notation: τ is wind stress, Q is heat (buoyancy).

Observations of near-inertial currents. Surface drifter tracks during and after a storm. ©American Meteorological Society. Reprinted with permission. Source: From d'Asaro et al. (1995). See Figure S7.8 for schematics of inertial currents and Ekman's (1905) original hodograph.

Ekman layer velocities (Northern Hemisphere). Water velocity as a function of depth (upper projection) and Ekman spiral (lower projection). The large open arrow shows the direction of the total Ekman transport, which is perpendicular to the wind.

(a) Ekman transport divergence near the equator driven by easterly Trade Winds. (b) The effect of equatorial Ekman transport divergence on the surface height, thermocline, and surface temperature. (c) Coastal upwelling system due to an alongshore wind with offshore Ekman transport (Northern Hemisphere).

Observations of an Ekman-like response in the California Current region. Observed mean velocities (left) and two theoretical Ekman spirals (offset) using different eddy diffusivities (274 and 1011 cm²/s). The numbers on the arrows are depths. The large arrow is the mean wind. See Figure S7.14 for the progressive vector diagram. Source: From Chereskin (1995).

Ekman response. Average wind vectors (red) and average ageostrophic current at 15 m depth (blue). The current is calculated from 7 years of surface drifters drogued at 15 m, with the geostrophic current based on average density data from Levitus et al. (1994a) removed. (No arrows were plotted within 5 degrees of the equator because the Coriolis force is small there.) This figure can also be found in the color insert. ©American Meteorological Society. Reprinted with permission. Source: From Ralph and Niiler (1999).

Geostrophic balance: horizontal forces and velocity. PGF = pressure gradient force. CF = Coriolis force. v = velocity (into and out of page). See also Figure S7.17.

Geostrophic flow and thermal wind balance: schematic of change in pressure gradient force (PGF) with depth. The horizontal geostrophic velocity v is into the page for this direction of PGF and is strongest at the top, weakening with depth, as indicated by the circle sizes. Density (dash-dot) increases with depth, and isopycnals are tilted. With the sea surface at B higher than at A, the PGF at the sea surface (h₁) is to the left. The PGF decreases with increasing depth, as indicated by the flattening of the isobars p₂ and p₃.

Geostrophic flow using observations. (a) Potential density section across the Gulf Stream (66°W in 1997). (b) Specific volume anomaly δ (×10⁻⁸ m³/kg) at stations A and B. (c) Dynamic height (dyn m) profiles at stations A and B, integrated from 3000 m depth. (d) Eastward geostrophic velocity (cm/sec), assuming zero velocity at 3000 m. This figure is described in detail in Section S7.6.2 of the online supplement.

Vorticity. (a) Positive and (b) negative vorticity. The (right) hand shows the direction of the vorticity by the direction of the thumb (upward for positive, downward for negative).

Sverdrup balance circulation (Northern Hemisphere). Westerly and trade winds force Ekman transport, creating Ekman pumping and suction and hence Sverdrup transport. See also Figure S7.12.

(a) Vorticity balance at a western boundary, with sidewall friction (Munk's model). (b) Hypothetical eastern boundary vorticity balance, showing that only western boundaries can input the positive relative vorticity required for the flow to move northward.

Subduction schematic (Northern Hemisphere). See Figure S7.35 for additional schematics, including obduction.

Global abyssal circulation model, assuming two deep water sources near Greenland and Antarctica (filled circles), filling a single abyssal layer. (These sources are actually at different densities.) Source: From Stommel (1958).