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On the use of an annulus to study mixed-layer entrainment

Published online by Cambridge University Press:  20 April 2006

J. W. Deardorff  and
S.-C. Yoon
J. W. Deardorff
Affiliation:
Department of Atmospheric Sciences, Oregon State University, Corvallis, Oregon 97331
S.-C. Yoon
Affiliation:
Department of Atmospheric Sciences, Oregon State University, Corvallis, Oregon 97331
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Abstract

An annulus covered by a rotating screen (or surface) which imparts stress and turbulence to the upper of two fluid layers has been shown by Scranton & Lindberg (1983) and Jones & Mulhearn (1983) to produce mixed-layer entrainment that is dependent on annulus curvature and geometry. This general result is confirmed here, where photographs of the mixed-layer interface indicate that turbulent entrainment rapidly diminishes away from the outer wall. The problem is explained as a damping of the turbulence within the bulk of the mixed layer by inertial stability associated with angular momentum increasing rapidly with radius except very close to the outer wall. Through hot-film-anemometer measurements, a shallow turbulent Ekman layer is found to exist immediately underneath the rotating screen, having a depth of order $ 0.4u_{*}r/\overline{v}$, where u* is the friction velocity, $\overline{v}$ is the mean circumferential flow speed within the layer and r is the radius. For r of order 1 m, this depth is typically only a small fraction of the mixed-layer depth determined from the density profile.

When the stress input is placed near the inner wall, the mean-flow radial profile is much more nearly irrotational and the turbulence-damping problem becomes minimal. The entrainment is then much more uniform with radius, and local interfacial scaling can be used to relate the entrainment rate to one or more local Richardson numbers containing a turbulent velocity scale rather than u* or $\Delta\overline{v}$, where Δ signifies the change across the interface. Although u* and $\Delta\overline{v}$ are proper ‘external’ scales for entrainment in a horizontally homogeneous mixed layer that is turbulent throughout, a local internal turbulent velocity scale can alternatively be used. Entrainment rates thus scaled are presented and compared with Turner's (1973) locally scaled entrainment.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 142 , May 1984 , pp. 97 - 120
Copyright
© 1984 Cambridge University Press

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References

Brown, R. A. 1970 A secondary flow model for the planetary boundary layer. J. Atmos. Sci. 27, 742–757.Google Scholar
Comte-Bellot, G. 1965 Écoulement turbulent entre deux parois parallèles. Publ. Sci. Tech. Min. de l'Air, no. 419.Google Scholar
Deardorff, J. W. 1972 Numerical investigation of neutral and unstable planetary boundary layers. J. Atmos. Sci. 29, 91–115.Google Scholar
Deardorff, J. W. 1980 Stratocumulus-capped mixed layers derived from a three-dimensional model. Boundary-Layer Met. 18, 495–527.Google Scholar
Deardorff, J. W. & Willis, G. E. 1982 Dependence of mixed-layer entrainment on shear stress and velocity jump. J. Fluid Mech. 115, 123–149.Google Scholar
Denman, K. L. & Miyake, M. 1973 Upper layer modification of ocean station Papa: observations and simulation. J. Phys. Oceanog. 3, 185–196.Google Scholar
Eliassen, A. 1957 Dynamic meteorology. In Handbuch der Physik, Band 48, Geophysik II (ed. S. Flugge). Springer.
Ellison, T. H. & Turner, J. S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 6, 423–448.Google Scholar
Faller, A. J. 1971 Oceanic turbulence and the Langmuir circulations. Ann. Rev. Ecol. & Syst. 2, 201–236.Google Scholar
Gibson, M. M. & Rodi, W. 1981 A Reynolds-stress closure model of turbulence applied to the calculation of a highly curved mixing layer. J. Fluid Mech. 103, 161–182.Google Scholar
Jones, I. S. F. & Mulhearn, P. J. 1983 The influence of external turbulence on sheared interfaces. Geophys. Astrophys. Fluid Dyn. 24, 49–62.Google Scholar
Kantha, L. H. 1978 On surface-stress induced entrainment at a buoyancy interface. The Johns Hopkins Univ. GFDL TR 78–1.Google Scholar
Kantha, L. H., Phillips, O. M. & Azad, R. S. 1977 On turbulent entrainment at a stable density interface. J. Fluid Mech. 79, 753–768.Google Scholar
Kato, H. & Phillips, O. M. 1969 On the penetration of a turbulent layer into stratified fluid. J. Fluid Mech. 37, 643–655.Google Scholar
Kundu, P. K. 1980 A numerical investigation of mixed-layer dynamics. J. Phys. Oceanogr. 10, 220–236.Google Scholar
LeMone, M. A. 1973 The structure and dynamics of horizontal roll vortices in the planetary boundary layer. J. Atmos. Sci. 30, 1077–1091.Google Scholar
Lofquist, K. 1960 Flow and stress near an interface between stratified fluids. Phys. Fluids 3, 158–175.Google Scholar
Lumley, J. L. & Panofsky, H. A. 1964 The Structure of Atmospheric Turbulence. Interscience.
Moore, M. J. & Long, R. R. 1971 An experimental investigation of turbulent stratified shearing flow. J. Fluid Mech. 49, 635–655.Google Scholar
Niiler, P. P. & Kraus, E. B. 1977 One-dimensional models of the upper ocean. In Modelling and Prediction of the Upper Layers of the Ocean (ed. E. B. Kraus), pp. 143–172. Pergamon.
Price, J. F. 1979 On the scaling of stress-driven entrainment experiments. J. Fluid Mech. 90, 509–529.Google Scholar
Scranton, D. R. & Lindberg, W. R. 1983 An experimental study of entraining, stress-driven, stratified flow in an annulus. Phys. Fluids 26, 1198–1205.Google Scholar
Taylor, G. I. 1923 Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. Lond. A 223, 289–343.Google Scholar
Thompson, R. O. R. Y. 1979 A re-examination of the entrainment process in some laboratory flows. Dyn. Atmos. Oceans 4, 45–55.Google Scholar
Thompson, S. M. & Turner, J. S. 1975 Mixing across an interface due to turbulence generated by a grid. J. Fluid Mech. 67, 349–368.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
Veronis, G. 1970 The analogy between rotating and stratified fluids. Ann. Rev. Fluid Mech. 2, 37–66.Google Scholar
Yoon, S.-C. 1983 The structure of turbulent entraining flow in an annulus with a rotating screen. Ph.D. thesis, Dept Atmos. Sci., Oregon State Univ., Corvallis.