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Yoshiaki Toba

Abstract

It is shown that a simple relation, E * = 5.1 × 10−2 σ m *−3 for describing the conditions of growing wind waves, is supported by various available data, where E * = g 2 E/u * 4 is dimensionless energy. σ m * = u *σ m /g the dimensionless angular frequency at the maximum of the energy spectrum, g the acceleration of gravity and u * the friction velocity of the air. This expression is an alternative form of the relation between dimensionless wave height and period, H *T *3/2, which was previously proposed by the author (Toba, 1972) for energy-containing waves, and is extended to individual waves in the wind-wave field in a statistical sense. It is also shown, supported by various data, that the essential part of the one-dimensional energy spectra of growing wind waves should have the form g * u−4 for the high-frequency tail of the frequency spectrum, where g * is g expanded to include the surface tension. This is the form previously proposed by the author (Toba, 1973b) as the one-dimensional spectral form consistent with the above power law relationship, instead of the g 2σ−5 form proposed by Phillips (1958). By use of the power-law relationship for E *, it is shown that the proportion of that part of momentum which is retained as wave momentum to the total momentum transferred from the wind to the sea can be expressed by a function of σ m * , which has essentially the same physical meaning as C/U, the ratio between the phase velocity of the energy containing wave and the wind speed. The value of the proportion decreases from about 6% in the form of an error function of C/U. A prediction equation for the growth of wind waves by a single-parameter representation is proposed, in which the rate of change of E * is expressed by a formulation including the error function or by a simple stochastic form. The integration of the equation for the case of fetch-limited conditions is in excellent agreement with data compiled by Hasselmann et al. (1973). Reviewing results of recent wind-wave tunnel experiments, emphasis is given on the fact that wind waves are strongly nonlinear phenomena, especially for C/U ≪ 1. A discussion is presented from this standpoint as to the physical basis for the existence of the simple power law relationship. the spectral form of g * u−4 and the stochastic form of the growth equation, and a systematic derivation of these relationships and equations is attempted.

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Toshio Suga
,
Kimio Hanawa
, and
Yoshiaki Toba

Abstract

The subtropics mode water (STMW) in the North Pacific Ocean has been investigated based on the data of long-term observations along the 137°E meridian, which have been performed by the Japan Meteorological Agency since 1967 for winter and since 1972 for summer. STMW cores were identified as vertical potential vorticity minima, and examined by the use of apparent oxygen utilization as an indicator of the age of STMW.

The main results can be summarized as follows. 1) A major post of the STMW appearing in the summer (or the winter) sections is the water formed in the immediately previous winter, its age being half a year (or one year). 2) Within half a year after its formation the STMW can be advected to the 137°E section only as far south as about 26°N and as far as about 23°N within one year. 3) Typical potential temperature in summer was higher than in winter, with salinity higher and potential density lower. 4) Less STMW was observed during the period of the typical large meander of the Kuroshio in the later 1970s. 5) The salinity of STMW was relatively low before 1981; it increased considerably in the summer of 1981 and has since showed a slowly decreasing trend.

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Ian S. F. Jones
and
Yoshiaki Toba

Abstract

No abstract available

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Youichi Tanimoto
,
Kimio Hanawa
,
Yoshiaki Toba
, and
Naoto Iwasaka

Abstract

Temporal evolution and spectral structure of sea surface temperature (SST) anomalies in the North Pacific over the last 37 years are investigated on the three characteristic time scales: shorter than 24 months (HF), 24–60 months (ES), and longer than 60 months (DC). The leading empirical-orthogonal function (EOF) for the DC time scale is characterized by a zonally elongated monopole centered at around 40°N, 180°. The leading EOF for the HF time scale is somewhat similar to that for the DC time scale, although there are two centers of action with the same polarity at the mid and western Pacific. The leading EOF for the ES time scale, however, exhibits a different pattern whose center of action at the mid Pacific is located farther southeastward.

In the time evolution of the SST anomalies associated with the leading EOF of the DC time scale, several anomaly periods can be identified that last five years or longer. The transition from a persistent period to another with the opposite polarity is generally very brief, except for the one that lasts throughout the late 1960s.

The EOF analysis was repeated separately on these persistent anomaly periods and the long transition period. The spatial structure of the leading EOF of the SST variability with the ES time scale is found to be sensitive to the polarity of the decadal anomaly. These results are suggestive of the possible influence of the decadal SST variability upon the spatial structure of the variability with shorter time scales.

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Yoshiaki Toba
,
Kozo Okada
, and
Ian S. F. Jones

Abstract

Continuous time series of wind profiles and wind waves under growing conditions, recorded at Shirahama Oceanographic Tower Station and discussed by Kawai, Okada and Toba, have been reanalysed for this study of the response of one-dimensional wind-wave frequency spectra to unsteady rising winds. The factor α s , in the equilibrium-range spectral form ϕ(σ) = α s gu *σ−4 (g is gravity, σ is angular frequency and u * is the friction velocity) shows a remarkable fluctuation. It becomes smaller for increasing wind conditions (i.e., increasing friction velocity) and larger for decreasing wind conditions within a range of (5–9) × 10−2. The slope of the spectra is very close to σ−4 generally, but it has a tendency to be slightly steeper for decreasing winds. The peak of the spectra is broader for increasing winds, and narrower for decreasing winds, when fluctuations of several-minute duration of u * are considered. The time scale of the adjustment of the equilibrium-range spectra is on the order of ten minutes. This time scale is much faster than the time scale of growth of the total energy of the wind waves, and consequently the peak frequency shifts to higher frequencies for increasing u *, or vice versa. This response suggests that the processes of the adjustment of the wind-wave field involve both upward and downward cascading of the wave energy. Further evidence is presented in the form of ocean wave data recorded in Bass Strait, Australia, where the waves, although much larger, show similar trends.

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Yoshiaki Toba
,
Noriko Iida
,
Hiroshi Kawamura
,
Naoto Ebuchi
, and
Ian S. F. Jones

Abstract

Distribution of the wind stress over the oceans is usually estimated by using a bulk formula. It contains the squared 10-m wind speed multiplied by the drag coefficient, which has been assumed in many cases to be a weak function of the 10-m wind speed. Over land the important role of thermal stratification has been clearly recognized, but over the sea the influence of wind waves is less well documented. This paper presents evidence showing the likelihood that the influence of the wind waves can also be large. Charnock proposed an expression for the marine atmospheric boundary layer roughness parameter, z 0, which depended only on the wind friction velocity, u and the acceleration of gravity, g. Toba and Koga have recently proposed an alternative expression for flow over growing wind waves, which are in local equilibrium with the wind, given by a form including the wind-wave spectral peak frequency explicity. The criterion for local equilibrium of the wave field with the wind is its consistency with the 3/2power law between nondimensional wave height and wave period normalized by u and g. The differences between these expressions are significant. The two expressions are compared with a composite dataset which comprises some representative data from laboratories and tower stations together with data from storms at an oil producing platform in Bass Strait, Australia. In these storms strong winds up to 25 m s−1 and large wind waves up to 12 s in significant wave period, from a direction of long fetch, lasted for two or three days. The composite dataset shows that the drag coefficient C D depends also on the sea scale and that in storm conditions C D can be larger by a factor of two to three than the value that Charnock's expression usually predicts. Further experiments focussing on the examination of the effect of ocean waves on the wind stress are recommended.

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