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      Reply to comment on `A simple model for the short-time evolution of near-surface current and temperature profiles'

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          Abstract

          This is our response to a comment by Walter Eifler on our paper `A simple model for the short-time evolution of near-surface current and temperature profiles' (arXiv:physics/0503186, accepted for publication in Deep-Sea Research II). Although Eifler raises genuine issues regarding our model's validity and applicability, we are nevertheless of the opinion that it is of value for the short-term evolution of the upper-ocean profiles of current and temperature. The fact that the effective eddy viscosity tends to infinity for infinite time under a steady wind stress may not be surprising. It can be interpreted as a vertical shift of the eddy viscosity profile and an increase in the size of the dominant turbulent eddies under the assumed conditions of small stratification and infinite water depth.

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          A Realistic Model of the Wind-Induced Ekman Boundary Layer

          Ole Madsen (1977)
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            On the scaling of stress-driven entrainment experiments

            The entrainment experiments of Kato & Phillips (1969) and Kantha, Phillips & Azad (1977) (hereafter KP and KPA) are analysed to demonstrate a more general and effective scaling of the entrainment observations. The preferred scaling is \[ V^{-1} dh/dt = E(R_v), \] where h is the mixed-layer depth, V is the mean velocity of the mixed layer, R v = B/V 2 and B is the total mixed-layer buoyancy. This scaling effectively collapses entrainment data taken at various h/L, where L is the tank width, and in cases in which the interior is density stratified (KP) or homogeneous (KPA). The entrainment law E(R v ) is computed from the KP and KPA observations using the conservation equations for mean momentum and buoyancy. A side-wall drag term is included in the momentum conservation equation. In the range 0·5 < R v < 1·0, which includes nearly all of the KP, KPA data, E ≃ 5 × 10−4 R −4 v. This is very similar to the entrainment law followed by a surface half-jet (Ellison & Turner 1959) and by the wind-driven ocean surface mixed layer (Price, Mooers & Van Leer 1978). The analysis shows that, when forcing is steady, R v is quasi-steady and, provided that side-wall drag is not large, R v ≃ 0·6 over a wide range of R T = B/U 2 *, where U * is the friction velocity of the imposed stress. In the absence of side-wall drag (vanishing h/L) the conservation of momentum then leads to U −1 * dh/dt = n(0·6)½ R −½ T , where n = ½ or 1 if the interior is linearly stratified or homogeneous. The KP, KPA data show this dependence throughout the range 17 < R T < 160 where the effect of side-wall drag is negligible or can be removed by a linear extrapolation. This result, together with the form and magnitude of the observed side-wall effect, suggests that mean momentum conservation is a key constraint upon the entrainment rate in the KP, KPA experiments.
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              Author and article information

              Journal
              2005-03-23
              Article
              10.1016/j.dsr2.2005.03.003
              physics/0503187
              2ce89b05-3d37-469f-bfd3-67b71be8149e
              History
              Custom metadata
              4 pages. Accepted for publication in Deep-Sea Research II. Uses a modified form of elsart.cls
              physics.ao-ph physics.flu-dyn

              Atmospheric, Oceanic and Environmental physics
              Atmospheric, Oceanic and Environmental physics

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