Physical Oceanography: An Overview
2.6 Wind Stress
28 Principles of Ocean Physics
'080 70 60 50 40 30 20 10 0
South North
Latitude, A (deg)
10 20 30 40 50 60 70 80
Fig. 2.12 Cross sections of (a) zonal wind component, (u), and (b) meridional wind component, ( v ) , in m s - 1 , as averaged over the year and zonally around the globe.
(c) Mass transport in 1010 kg s - 1 . Jet stream axes are near 250 rnbar in both hemispheres. [From Piexoto, J. P., and A. H. Oort, Rev. Mod. Phys. (1984).]
tioned by atmospheric radiation, wind stress, temperature, pressure, and rain- fall, although its response times are much longer than those of the atmosphere. The ocean thus is the flywheel or the inertia on the global heat engine and serves to smooth out the high-frequency fluctuations of the at- mosphere. The two fluids are strongly coupled, having both positive and nega- tive feedback loops and greatly differing time constants.
(bl
Longitude, Q (deg)
East West
Longitude, Q (deg)
East
Fig. 2.13 (a) Global distribution of averaged surface pressure, p a , reduced to sea level; units are p a - 1000 mbar. Also shown are arrows indicating average velocity of wind, with each barb on tail representing a speed of 5 m s - l . (b) Surface stream- lines and wind barbs. [From Oort, A. H., Global Atmospheric Circulation Statistics (1982).]
30 O E Principles of Ocean Physics
Fig. 2.15 (a) Surface wind stress for the tropical Pacific, proportional to the square of the wind velocity, for the month of September, 1978. Dominant features are the north- east and southeast trades, and the strong coastal winds along South America. [From Legler, D. M., and J. J. O’Brien, Atlas of Tropical Pacific Wind-Stress Climatology 7977-7980 (1984).] (b) Surface wind velocity obtained from radar scatterometer on the Seasat spacecraft for September 6-7, 1978. Large Southern Hemisphere storm sys- tems are major features. [Courtesy of P. M. Woiceshyn and G. F. Cunningham, Jet Propulsion Laboratory (1986).]
(proportional to the square of wind speed) over the Tropical Pacific as aver- aged over September 1978, this month being one of both well-developed trade winds and cyclonic storm activity. However, the winds due to the latter have been smoothed out because of the movement of storms. On an even shorter time scale, Fig. 2.15b is a “snapshot” of surface wind velocity for most of
the Pacific for a two-day period in September 1978 that shows several large cyclonic systems. The data were obtained by a satellite radar scatterometer.
It is these winds that dominate the transfer of horizontal momentum t o the ocean and which produce the wind-driven ocean currents, these represent- ing the most energetic component of the oceanic circulation.
The elevation at which the measurement of the “surface” wind is made is an important quantity to specify, since near the surface of land, water, or ice, the winds vary sharply in speed and direction throughout the near- surface planetary boundary layer or the so-called atmospheric Ekman layer (named after the Swedish meteorologist/oceanographer, V. W . Ekman). The usual meteorological heights for specifying winds at sea are either 10 m or 19.5 m, set chiefly by the mast height of vessels. At a solid boundary, the wind speed must be zero just at the surface; for water, wind-induced motion means that the wind and water velocities must match just at the boundary.
Thus the transition regime in the vertical, i.e., the turbulent boundary layer, is one in which the windshear, or vertical derivative of velocity, is large and its direction variable; because of the latter effect, the wind is said to “veer aloft.’’ The mean wind speed profile in the lower few hundred meters of atmospheric height is approximately logarithmic in the vertical coordinate,
z.
In Fig. 2.15a, the stress, 7 , is approximately quadratically dependent on wind velocity. The stress is the aerodynamic force per unit area exerted by the wind on the sea surface and may be written as
(2.10) where u, is the wind velocity; p a , the density of air; and cd is a dimension- less quantity called the aerodynamic drag coefficient. The latter is itself a function of wind speed, being approximately constant at low speeds, but in- creasing linearly above some 10 m s - ’ . The stress directly induces surface waves and horizontal momentum, i.e., horizontal currents. Because of the more-than-quadratic dependence of the stress on u,, it seems likely that much momentum is conveyed to the ocean during brief intense storms (i.e., is episodic); thus, the type of data in Fig. 2.15b becomes highly relevant.
However, storms are usually separated by long intervals of lower winds that can do work on the ocean for extended times and which are therefore effec- tive in driving currents. Thus for an accurate description of wind-induced currents, it is necessary to know both the storm and the steady winds.
Not only the wind velocity but also the heat, temperature, and humidity profiles vary sharply in the lower few hundred meters of the atmosphere.
The turbulence in the lowest 10 m or so is largely driven by wind shear; at slightly higher levels, heat and moisture are carried upward by interchanges of warm, moist lower air with cooler, drier upper air, and depend on buoyan-
32 Principles of Ocean Physics
cy differences as well. It is these interchanges that bring about the turbu- lence in the planetary boundary layer; many of the properties of the layer depend on the sign of the air-sea temperature difference, To - T,, which, when negative (colder air over warmer water), leads to strong interchange, considerable turbulence, and roughened seas.
By definition, the currents induced by the wind stress make up the wind- driven circulation of the ocean. While the direct effects of the stress are felt close to the ocean surface (mainly within the so-called oceanic Ekman layer extending over the upper 10 to 100 m), it is the deeper components of circu- lation brought about by the surface motions that bring into play a signifi- cant volume of the waters of the sea. Furthermore, it is not only the stress itself, but also its curl, divergence, and gradient that drive the circulation;
the division of the wind effects into various portions is based partly on mathe- matical convenience and partly on physical response; this will be discussed in more detail in Chapters 3 and 6.