The term 〈 υ′ w′〉 in (1)–(4) is ignored on the assumption that it is unimportant or insignificant relative to 〈 u′ w′〉. In most analyses to date, the direction of the stress vector is generally assumed to be aligned with the wind. In (5), both the wind speed and drag coefficient are representative of 10-m height above the surface. The stress of the ocean on the atmosphere is directed opposite to τ according to Newton's third law. Note that the stress vector defined above is that of the atmosphere on the ocean, that is, exerted by the wind on the surface. The following sign convention for stress is used: τ x > 0 if the longitudinal stress component is facing in the wind direction, and vice versa, and τ y is positive (negative) if the lateral stress component is directed to the right (left) on the wind vector. Thus, the longitudinal stress component τ x = − ρ 〈 u′ w′〉 i ≡ τ x i is the downstream stress, and the lateral stress component τ y = − ρ 〈 υ′ w′〉 j ≡ τ y j is the cross-wind stress. In this paper, we will hold the latter position that is, in the general case, i is a function of z. In general, ( x, y, z) is a fixed reference frame, although it is a common practice to align the x axis with wind direction at a reference height z. Where ρ is air density i and j represent the longitudinal ( x axis) and lateral ( y axis) unit vectors 〈 〉 is a time and/or spatial averaging operator u, υ, and w are the longitudinal, lateral, and vertical ( z axis) velocity components, respectively and a prime denotes fluctuations about a mean value (e.g., u = 〈 u〉 + u′). As a result, the stress vector may deviate widely from the mean wind flow, including cases in which stress is directed across or even opposite to the wind. The direction of the wind-wave-induced stress and the swell-induced stress components may coincide with, or be opposite to, the direction of wave propagation (pure wind waves and swell, respectively). In general, the wind stress is a vector sum of the 1) pure shear stress (turbulent and viscous) aligned with the mean wind shear, 2) wind-wave-induced stress aligned with the direction of the pure wind-sea waves, and 3) swell-induced stress aligned with the swell direction. Results based on measurements made during three field campaigns onboard the R/P Floating Instrument Platform ( FLIP) in the Pacific are discussed. In this paper, the focus is on the study of the stress vector direction relative to the mean wind and surface-wave directions. However, the stress vector is often aligned with a direction different from that of the mean wind flow. Previous investigations of the wind stress in the marine surface layer have primarily focused on determining the stress magnitude (momentum flux) and other scalar variables (e.g., friction velocity, drag coefficient, roughness length).
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