WAVES AND SEAAIR FLUXES. CALM CONDITIONS

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WAVES AND SEA-AIR FLUXES. CALM CONDITIONS

• Surface waves are the most obvious feature of the
  ocean. They result from the density discontinuity
  (we have discontinuity of about 8001 at the
  surface). When the discontinuity is perturbed,
  two forces act to return the sea surface to the
  static equilibrium
• Gravity body force
• Surface tension elastic force

Dispertion relation

d is depth, ?w is surface tension of the water,
normalized with ?
Phase velocity
group velocity
Velocity of the energy propagation
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Main measures of surface wind waves
Basic measures The zero-upcrossing period is
the time between two successive upcrossings of
the mean level by surface elevation. The
zero-upcrossing wave height is the difference
between the maximum and minimum values of the
surface elevation between adjacent upcrossings of
the mean level. The crest period is the time
between two successive crests. The
crest-to-tough wave height is the difference in
height between a crest and the following
tough. Statistical measure Significant wave
height is defined in terms of spectral moments as
where m0 is the zeroth moment of the spectrum
which is equal to the sea surface variance.
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WAVES GROWTH AND PROPAGATION

• Waves are generated by wind and have right after
  generation the phase velocities, smaller than
  wind has. They are short in wave length and small
  in amplitude. Their spectrum is represented by a
  smooth peak in the high frequency range. If wind
  acts for a certain time, waves start to propagate
  faster, become longer and higher. In general they
  tend to increase their speed up to the wind
  speed. When their speed achieves the values of
  the wind speed, they become no more dependent on
  wind and start to propagate as free waves.
• Surface waves, traveling slower than wind (i.e.
  waves still under
• the wind influence) are called wind sea
  (sea).
• Wind sea traveling at wind speed is a fully
  developed sea.
• Waves, traveling faster than wind are swell.

Estimation of SWH from sea and swell heights
Swell height
Sea height
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Propagation measures
Wave age a CP / Vef , where CP is the deep
water wave phase speed at spectral peak, derived
from an estimate of the wave period pw CP
(g/2?) pw ,

where g is the gravitational acceleration, and
Vef is component of the wind in the wave
direction Vef V10 cos? ,

where ? is the angle between wave
and wind directions and V10 is the wind speed at
10-m anemometer height and neutral stability.
It is suggested, that for a lt 1 wave can be
regarded as sea, while for a gt 1, they should
be considered as swell.
Wave length ? CP ? pw wave slope
? h/?

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Mechanics of wind-wave interaction normal stress
induced by waves
Wind, not disturbed by waves
Wind stream functions

Normal stress
Tangential stress

• Through the normal stress wind works to push
  waves ahead, providing
• Acceleration of wave motion
• Transferring kinetic energy

(17)
If wind acts over a longer distance (fetch) or
during a longer time (duration), waves tend to
grow up, become longer and travel faster.
Thus, wind stress over waves should be expressed
as
Tangential stress
Normal stress


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How to parameterize the normal stress induced by
waves?
Key parameter wave age
Donelan (1982) Lake Ontario
where ? is rms wave height
Smith (1991)
Toba et al. (1990)  laboratory experiment 
Alternative wave age scaling with friction
velocity. However, wind speed is a much easier
available parameter, than u. Estimates of a
vary within the range from 4-5 (very young sea)
to 30-40 (fully developed sea).

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Geernaert et al. (1987) MARSEN experiment
Taylor and Yelland, 2001 consideration of the
relationship between the wave height and wave
length
where Hs is significant wave height, Ls is the
peak wavelength.

• Summary of sea-state-dependent wind stress
• In general it should exist due to normal
  pressure components
• The effect ranges from nearly 0 to 30,
  reasonable estimate is
• of about 10
• The role of swell is uncertain, up-to-date
  concern no effect of swell.

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Estimates of the effect of wave-induced
stress (Gulev and Hasse 1998, JPO)
Smith 1988 Traditional estimate
Smith 1991 Wave-age- based stress
Ratio Sea-state dependent vs traditional
JAN
JUL
Major effect Midlatitudes, Winter
season, Up to 20
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The other impacts of waves on sea-air
exchange Surface albedo There are two major
mechanisms through which labedo can be affected
by the wind waves
1. Multiply scattering of the SW from the rough
surface generally should act to decrease
albedo. The main role belongs to capillary waves
and not to developed seas.
Theoretical results of Presendorfer and Mobley
(1986)

• Albedo decreases with windspeed by
• approximately 10-20 within the range
• 0-20 m/s
• Clear sky albedo decreases strongly than
• that under the cloudy sky

2. However, this effect seems to be not the
largest. Under strong storms foam patches work to
increase albedo. Thus, the total effect is the
slight increase of the albedo. Decreasing with
surface roughness albedo has been observed only
under small solar declinations and nearly
complete cloud cover.
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Observational results, based on 32000 direct
measurements worldwide
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Impact of the wave breaking on evapration
(non-turbulent mechanisms of the water transfer
from the ocean to the atmosphere)
Wave breaking results in the generation of foam,
which is normally represented by the so-called
white caps at sea surface. Moreover, wave
breaking results into generation of water drops,
spread in the surface atmospheric layer. These
drops are characterized by different from the sea
surface characteristics (temperature, heat
capacity, surface tension). Thus, the conditions
of evaporation of these drops are quite different
from the evaporation from the surface. Normally,
they evaporate easier. Which part of the sea
surface is covered by the white caps
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Monahan et al (1982)
Measurements based on photos
W()3.84?10-6u3.4
Normally drops do not jump too high (10-15 cm)
their further evaporation depends on how long
they live in the surface layer before they are
dumping back. How do the drops behave? How long
they are living in the surface layer?

Lagrangian simulation of droplets at 12 cm
height Wind is 5-12 m/s. Life time up to
1 sec
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• How to account for what is going on with the
  droplet,
• while it is flying in air?
• Typical approach modeling of the thermodynamics
  of droplets with field observations and
  laboratory experiments.
• Architecture of a typical model (Bortkovsky 1982
  Sea-air exchange in storm conditions)
• System of equations of the droplet
  thermodynamics
• Derivation of the droplet coordinates (2D) at
  every step from the droplet size
• and wind conditions
• Estimation of the droplet freshening and
  surface tension
• Estimation of the droplet temperature and heat
  capacity
• Estimation of the droplet size
• Computation of the heat and moisture loss by
  the droplet.

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Calm conditions
Paradox of bulk formulae
What happens if U0, even if temperature and
humidity gradients are quite high? 0
Q 0 ???!!!
Where we are with respect to the TKE?

Production of TKE by buoyancy (/-) (reversible)
Mechanical production of TKE (normally positive)
When u approaches zero, the buoyancy flux does
not!
?0
These are the called free convection
conditions, where the heat and mass transfer is
fully driven by the buoyant production. This case
can be easily studied in laboratory experiments.
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• Design of special experiment (Golitcyn and
  Grachov 1984)
• Fully dark room 4x4x3 m
• Tank of water, d30 cm, h1m,
• One open surface, the walls are inconductive for
  heat
• Temperature is measured at many levels
• Air temperature is measured
• The level of water is measured.

Temperature parameter
Tw(0) initial temperature, ? - scaling constant
for time
Field measurements under Vlt3 m/s
? is the thermal expansion of air, ??0.61 is the
analog of humid contraction, ? is kinematic
viscosity of air, g is gravitational
acceleration, A0.144, B0.159 are empirical
constants.
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Surface cool skin
Under calm and low winds absorption of the solar
radiation occurs on a larger scale (wave length)
than sensible and latent heat transfer (molecular
scale). This leads to the fact that very thin
upper layer of the water is in a lesser degree
affected by SW, but, nevertheless is cooled by
sensible a latent heat. This is surface cold skin
layer. Its temperature has to be taken for
estimation of fluxes and not the bulk temperature.
Hasse, 1971 experimental measurements in the
surface layer during day time and night time
dependence of the SST skin-bulk deviation from
heat flux and wind speed.

Variations of empirical coefficients with the
reference depth
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/helios/u2/gulev/handout gra.for - Golitcyn
and Grachov free convection scheme
(1984) SST10C, Ta8C, ez9mb, SST10C, Ta12C,
ez11mb,