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Miles G. McPhee

Abstract

Smoothed records of ice drift, surface wind and upper ocean currents at four manned stations of the 1975–76 AIDJEX experiment in the central Arctic have been analyzed to provide a statistical relationship between stress at the ice-ocean interface and ice-drift velocity during a 60-day period when the ice, was too weak to support internal forces. Using interfacial stress calculated from a balance with air stress and Coriolis force on the ice column for times longer than the inertial period, logarithmic linear regression of the stress-velocity samples provided the relation τ = 0.010V 1.78, where τ is the magnitude of interfacial stress and V the ice speed relative to the geostrophic current in the ocean. This result is statistically indistinguishable from predictions of a numerical model adapted from Businger and Arya (1974) with surface roughness Z 0 = 10 cm. Essential features of the model are dynamic scaling by u *, u * 2 and u */f for velocity, kinematic stress and length, with exponential attenuation of a linear dimensionless eddy viscosity, viz., K * = −kξe ε1ξ, where ξ = fz/u * and k is von Kaa's constant. Currents measured 2 m below the ice confirmed the shape of the τ vs V curve and provided an estimate of the angle between surface stress and velocity. The model was used to qualitatively estimate the effect of a pycnocline at 25 m on surface characteristics. The observed behavior when stratification at that level was most pronounced tended toward slightly higher drag at higher speeds, which is qualitatively consistent with the model results.

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Miles G. McPhee

Abstract

The hypothesis is tested that, for the planetary boundary layer, turbulent vertical velocity (w) spectral density, normalized by u2/k (u2 is Reynolds stress magnitude and k is wavenumber: 2π times frequency divided by mean flow speed), is a “universal” function of nondimensional wavenumber k/k max, where k max is the wavenumber at the peak in the area-preserving log–log w spectrum. Data from clusters of turbulence-measuring instruments deployed through the ocean boundary layer beneath pack ice during the yearlong Surface Heat Budget of the Arctic (SHEBA) project were analyzed by averaging spectra in 3-h bins, then nondimensionalizing weighted w spectral density by directly measured Reynolds stress magnitude and wavenumber by k max. In the outer boundary layer, normalized spectra were remarkably uniform, suggesting that (i) the fundamental turbulence scale is inversely proportional to k max and (ii) the w wavenumber spectrum by itself may be used to estimate local stress magnitude and eddy viscosity. The arguments are extended to a scalar variable (temperature) using a combination of the w and scalar spectra, in a way somewhat analogous to the inertial dissipation method used for the atmospheric surface layer. Spectral estimates of turbulent heat flux agreed reasonably well with direct covariance estimates. The structure of the vertical velocity spectrum in the outer boundary layer implies that, in a neutrally stratified, homogeneous flow, production of turbulent kinetic energy (TKE) exceeds dissipation by a significant factor, with the balance provided mainly by vertical TKE turbulent flux divergence.

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Miles G. McPhee

Abstract

Measurements of surface drift and near-surface currents taken during August 1975, at drifting ice stations of the AIDJEX experiment in the central Arctic, are used to infer the response of the upper ocean to the passage of two frontlike wind events. As an aid in interpretation, a multilevel, time-dependent, dynamical boundary-layer model commensurate with earlier investigations of PBL turbulence and ice drift versus surface wind statistics is developed and shown to reproduce the main features observed, including energetic inertial oscillation of the ice cover and mixed layer, relatively small currents at 30 m (∼5 m into the pycnocline), and little inertial-period shear between the ice and currents measured at 2 m. The model employs an eddy viscosity dependent on the surface friction velocity (u *) and the nondimensional depth (fz/u *) in the well-mixed layer, and on the product of the local stress and the local Obukhov length in the upper pycnocline. When the dominant horizontal length scale (related to the Coriolis parameter and the propagation speed of the atmospheric system) is of the order 750.km, the phase and amplitude of the inertial motions across the 190 km span of the station array are observed to be more coherent than predicted by the locally driven (i.e., horizontally homogeneous) model. It is suggested that a small pressure term due to Ekman convergence could account for the discrepancy.

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Miles G. Mcphee

Abstract

Turbulence measurements from under drifting pack ice illustrate the distribution of turbulent mixing length in the well-mixed layer of the upper ocean. Mixing length (λ ≡ K/u *, where K and u * are the local eddy viscosity and square root of Reynolds stress, respectively) is found to vary inversely with wavenumber at the peak in the weighted vertical velocity variance spectrum: λ = c λ/k max. This relation provides an empirical tool for making local estimates of eddy viscosity if the Reynolds stress is known, or alternatively, deriving fluxes via the inertial-dissipation method in the outer part of the rotational boundary layer. The vertical structure of λ is described for conditions of (i) neutral stratification (negligible surface buoyancy flux) under thick ice. (ii) stable stratification under rapidly melting ice, and (iii) statically unstable conditions from intense freezing. The last example, obtained during the 1992 Lead Experiment, included dime measurements of turbulent salinity flux, 〈wS′〉. As an analog to Monin-Obukhov similarity for the atmospheric surface layer, a simple algorithm is developed for calculating λ in the mixed layer in term of displacement from the interface, z; boundary values of friction velocity, u *0, and buoyancy flux, 〈wb′〉0; the planetary length scale, u *0/|f r| (for neutral and stable conditions); and mixed layer depth, |z ml (unstable conditions). A simple numerical model demonstrates the algorithm by simulating a hypothetical example of intense wind stirring in the wintertime Weddell Sea.

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Miles G. McPhee

Abstract

Temperature (T) and salinity (S) profiles from the central Weddell Sea near the Maud Rise seamount measured during the 1994 Antarctic Zone Flux Experiment (ANZFLUX) have been analyzed for stability with respect to the thermobaricity, that is, the pressure dependence of thermal expansion rate. For many T–S profiles in the region Δρ, the difference between actual density (including the pressure contribution) and density of a water column with uniform temperature and salinity equal to that of the mixed layer, exhibits a maximum in the upper ocean within tens of meters of the mixed layer–pycnocline interface. Following work by K. Akitomo, if the mixed layer were to deepen and increase in density so that the Δρ maximum coincided with the base of the mixed layer, the system would be thermobarically unstable and would overturn catastrophically. Thermobaric convection differs from convection driven by surface buoyancy flux (cooling and/or freezing) because once started, the production of turbulent mixing energy is derived from the water column instead of the surface, an important distinction in ice-covered oceans. A stability criterion is developed that considers the total sensible heat and latent heat of freezing required to drive a given T–S profile to thermobaric instability, and is mapped in the Maud Rise region. A simple upper-ocean model, combined with enthalpy conservation at the ice–water interface and driven by surface stress and ice heat conduction observed with a drifting buoy cluster left in place after the ANZFLUX manned drift stations, is used to assess the susceptibility of observed profiles to thermobaric instability as the winter advanced. In the model, roughly one quarter of the profiles become unstable by the end of August, and it is argued that this may account for extensive polynya-like features that appeared in satellite microwave imagery over Maud Rise in August 1994, shortly after completion of the ANZFLUX Maud Rise drift.

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Miles G. McPhee

Abstract

Continuous sampling of upper-ocean hydrographic data in the Canada Basin from various sources spanning from 2003 through 2011 provides an unprecedented opportunity to observe changes occurring in a major feature of the Arctic Ocean. In a 112-km-radius circle situated near the center of the traditional Beaufort Gyre, geopotential height referenced to 400 dbar increased by about 0.3 gpm from 2003 to 2011, and by the end of the period had increased by about 65% from the climatological value. Near the edges of the domain considered, the anomalies in dynamic height are much smaller, indicating steeper gradients. A rough dynamic topography constructed from profiles collected between 2008 and 2011 shows the center of the gyre to have shifted south by about 2° in latitude, along the 150°W meridian. Geostrophic currents are much stronger on the periphery of the gyre, reaching amplitudes 5–6 times higher than climatological values at grid points just offshore from the Beaufort and Chukchi shelf slopes. Estimates of residual buoy drift velocity after removing the expected wind-driven component are consistent with surface geostrophic currents calculated from hydrographic data. A three-decade time series of integrated ocean surface stress curl during late summer near the center of the Beaufort Gyre shows a large increase in downward Ekman pumping on decadal scales, emphasizing the importance of atmospheric forcing in the recent accumulation of freshwater in the Canada Basin. Geostrophic current intensification appears to have played a significant role in the recent disappearance of old ice in the Canada Basin.

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Miles G. McPhee and J. Dungan Smith

Abstract

The mean and turbulent flow structure under pack ice was measured during the 1972 AIDJEK pilot study with small mechanical current meter triplets at eight levels in the planetary boundary layer. CTD profiles showed a well-mixed layer of nearly neutral stability to about 35 m, bounded below by a strong pycnocline. The skin friction velocity u * was determined by measuring the Reynolds stress at 2 and 4 m below the ice (beyond the surface layer) and from consideration of other terms in the mean momentum equation. Local pressure gradients and advective acceleration due to topography could not be ignored; when an estimate of the effect was included, u * was 1.0±0.1 cm s−1 when the ice velocity relative to the ocean was 24 cm s−1.

With the proper coordinate transformation, the planetary boundary layer of the ocean resembles that of the atmosphere. Composite averages of non-dimensional Reynolds stress and mean flow in the ocean, when compared with recent models of a neutrally buoyant, horizontally homogeneous atmosphere, fit the model predictions fairly well. However, the lateral component (perpendicular to surface stress) departed markedly from those predictions, indicating that form drag associated with pressure ridge keels is important.

Peaks in spectra of vertical velocity were used to estimate eddy viscosity proportional to mixing length at eight levels in the outer layer. Results agreed well with the models, but this eddy viscosity did not provide a simple relation between Reynolds stress and mean flow shear.

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George L. Mellor, Miles G. McPhee, and Michael Steele

Abstract

A second-moment, turbulence closure model is applied to the problem of the dynamic and thermodynamic interaction of sea ice and the ocean surface mixed layer. In the case of ice moving over a warm, ocean surface layer, melting is intrinsically a transient process; that is, melting is rapid when warm surface water initially contacts the ice. Then the process slows when surface water is insulated from deeper water due to the stabilizing effect of the melt water, and the thermal energy stored in the surface layer is depleted. Effectively, the same process prevails when ocean surface water flows under stationary ice in which case, after an initial rapid increase, the melting process decreases with downstream distance. Accompanying the stabilizing effect of the melt water is a reduction in the ice-seawater interfacial shear stress. This process and model simulators are used to explain field observations wherein ice near the marginal ice zone diverges from the main pack.

When the surface ice layer is made to grow by imposing heat conduction through the ice, the surface ocean layer is destabilized by brine rejection and mixing in the water column is enhanced. The heat flux into the water column is a small percentage of the heat conduction through the ice.

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Michael Steele, George L. Mellor, and Miles G. Mcphee

Abstract

In an earlier paper, a second-moment turbulence closure model was applied to the problem of the dynamic and thermodynamic interaction of sea ice and the ocean surface mixed layer. An overly simplistic parameterization of the molecular sublayers of temperature and salinity within the mixed layer was used. This paper investigates the use of a more recent parameterization by Yaglom and Kader which is supported by laboratory data. A relatively low melt rate results in the case where ice overlays warm water. This agrees with some recent observations in the interior of the marginal ice zone.

A surface heat sink drives the freezing case which, due to the large difference in heat and salt molecular diffusivities, produces a strong supercooling effect. This is converted into an estimate of frazil ice production through a simple scheme. The model results provide an explanation for high frazil ice concentrations observed in the Arctic and Antarctic.

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Miles G. McPhee, Christoph Kottmeier, and James H. Morison

Abstract

Seasonal sea ice, which plays a pivotal role in air–sea interaction in the Weddell Sea (a region of large deep-water formation with potential impact on climate), depends critically on heat flux from the deep ocean. During the austral winter of 1994, an intensive process-oriented field program named the Antarctic Zone Flux Experiment measured upper-ocean turbulent fluxes during two short manned ice-drift station experiments near the Maud Rise seamount region of the Weddell Sea. Unmanned data buoys left at the site of the first manned drift provided a season-long time series of ice motion, mixed layer temperature and salinity, plus a (truncated) high-resolution record of temperature within the ice column. Direct turbulence flux measurements made in the ocean boundary layer during the manned drift stations were extended to the ice–ocean interface with a “mixing length” model and were used to evaluate parameters in bulk expressions for interfacial stress (a “Rossby similarity” drag law) and ocean-to-ice heat flux (proportional to the product of friction velocity and mixed layer temperature elevation above freezing). The Rossby parameters and dimensionless heat transfer coefficient agree closely with previous studies from perennial pack ice in the Arctic, despite a large disparity in undersurface roughness. For the manned drifts, ocean heat flux averaged 52 W m−2 west of Maud Rise and 23 W m−2 over Maud Rise. Unmanned buoy heat flux averaged 27 W m−2 over a 76-day drift. Although short-term differences were large, average conductive heat flux in the ice was nearly identical to ocean heat flux over the 44-day ice thermistor record.

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