Steve Piacsek

Numerical solutions and laser-Doppler measurements of spin-up

The spin-up flow in a cylinder of homogeneous fluid has been examined both experimentally and numerically. The primary motivation for this work was to check numerical solution schemes by comparing the numerical results with laboratory measurements obtained with a rotating laser-Doppler velocimeter. The laser-Doppler technique is capable of high accuracy with small space and time resolution, and disturbances of the flow are virtually negligible. A series of measurements was made of the zonal flow over a range of Ekman numbers (1·06 × 10 −3 ≤ E ≤ 3·30 × 10 −3 ) and Rossby numbers (0·10 [les ]|e| [les ] 0·33) at various locations in the interior of the flow. These measurements exceed previous ones in accuracy. The weak inertial modes excited by the impulsive start are detectable. The numerical simulations used the primitive equations in axisymmetric form and employed finite-difference techniques on both constant and variable grids. The number of grid points necessary to resolve the Ekman layers was determined. A thorough comparison of the simulations and the experimental measurements is made which includes the details of the amplitude and frequency of the inertial modes. Agreement to within the experimental tolerance is achieved. Analytical results for conditions identical to those in the experiments are not available but some similar linear and nonlinear theories are also compared with the experiments.

Sea surface temperature variability of the Iceland‐Faeroe front

Several advanced very high resolution radiometer (AVHRR) images with spatial resolution of 1.1–3.3 km, together with several concurrent aircraft-deployed expendable bathythermograph (AXBT) surveys and conductivity-temperature-depth (CTD) stations, from spring 1989 are used to describe the Iceland-Faeroe sea surface temperature (SST) front. In the AVHRR images, SST fronts are located by maximizing |∇SST|. Single, large gradient segments of the SST front do exist, with some exceeding 100 km in length, indicating a multiple frontal structure. These single frontal lines are also segments where |∇2SST| is small, and they can be followed uniquely by a single isotherm eastward from Iceland for a distance of 300 km. With a 35-km sampled AXBT survey, two small subsurface cold eddies were located south of the surface front in an area 170 km × 270 km east of Iceland. From a May 1987 AVHRR image on 1.1-km resolution, a population of seven such cold eddies are found between Iceland and the Faroes. They appear to be generated along the surface expression of the Iceland Faroes front and populate the northern slope of the Iceland-Faroes Ridge. Historical data from towed high-resolution instruments suggest that the cold eddies are ∼30–50 km in size and uplift the main thermocline by 150 m.

Studies of the Arctic ice cover and upper ocean with a coupled ice-ocean model

An ice-ocean model has been developed by coupling the Hibler ice model to a three-dimensional ocean model that consists of a turbulent mixed layer model and an inverse geostrophic model. The coupled model has a horizontal grid spacing of 127 km and has 17 vertical levels extending to the ocean bottom. The model is forced with 12-hourly general circulation model-derived atmospheric fluxes for the year 1986, for which good quality ice edge analyses and buoy tracks were available for comparisons. The results are presented for the fifth year of a repetitive simulation with the 1986 fluxes, at which time the system has reached a statistical equilibrium. The seasonal and geographical variations of the ice cover and the upper few hundred meters of the ocean have been examined, including the heat and salt budgets. The computed heat fluxes and mixed layer depths (MLDs) fall in the observed seasonal ranges, with winter heat fluxes ranging from 15 W m−2 in the central Arctic to about 500 W m−2 in the Barents Sea area, and summer fluxes from about 5 W m−2 under the ice to about 30 W m−2 in the various marginal ice zone (MIZ) edge areas. The corresponding winter MLDs are found to be about 25–75 m in the central Arctic to a deep 800 m in the Greenland Sea; typical summer MLDs are between 5 and 30 m. In all seasons, the MIZ was found to be the center of flux activity for both heat and salt, with the processes of advection, diffusion, atmospheric forcing, and vertical oceanic fluxes having their largest values here, and of comparable magnitudes. Values of the heat flux components in the MIZ exceed those found under the ice by an order of magnitude or more, and those in the open water region by a factor of 2. For salt, the situation is similar except in the summer (June through September), when a lot of salt flux activity takes place under the ice. Comparisons are made with Naval Polar Oceanography Center (NPOC) analyses for ice concentration and ice edge, and with observed Arctic buoy tracks, in the same 1986 time period. The computed ice edge positions have comparable accuracy to previous three-dimensional coupled ice-ocean studies, with too much ice growth during the winter in the Barents Sea and too little ice east of Greenland. The ice thickness distributions, however, are much better, with a monotonic increase of the ice thickness from the Siberian coast east toward the Canadian archipelago with maximum winter values of about 5–6 m.

Numerical experiments on stratified spin-up

Abstract Numerical experiments were performed for the spin-up of a stratified Boussinesq fluid in a right cylinder. The so-called “corner jet,” postulated in earlier analytical treatments by Walin, is found to have an inclination which oscillates between near-horizontal to near-vertical positions. The net effect is that some of the fluid spends more time in viscous boundary layers before entering the interior than if the jet were inclined at a steady angle to the vertical. This accounts for the shorter experimentally observed spin-up times and for the discrepancy between theory and experiments.

An investigation of the importance of third-order correlations and choice of length scale in mixed layer modelling

Abstract A study of the mixed-layer deepening is conducted with a one-dimensional, third-order closure turbulence model. An approximate model that retains second-order terms in ratios of characteristic turbulence to mean-field scales is also developed. Development of the mixed layer is initiated by applying a constant wind stress and heat flux to an ocean of linear initial stratification. Results show that inside the mixed layer, the contribution of the triple-correlation terms to the turbulent energy equation is negligible. In the entrainment zone, the triple-correlation terms are of the same order of magnitude as the other significant terms. The net effect of the triple-correlation terms is to deepen the mixed layer. Various length scale prescriptions have been considered and compared against each other. The entrainment rates are calculated for a chosen range of parameter space and compared against the experimental results of Kato and Phillips (1969).

Synoptic and Seasonal Variations of the Ice-Ocean Circulation in the Arctic: A Numerical Study

Abstract : The circulations of the Arctic ice cover and ocean are investigated using a coupled ice-ocean model. The coupling is strong and two-way for synoptic time scales, but is limited on seasonal time scales: the geostrophic ocean currents are not changed by the computed heat and salt fluxes. The ice-drift motion, Ekman transports and the wind-driven part of the barotropic circulation are examined for the months of February and August 1986, representing different atmospheric forcing, ice thickness and ice-strength regimes. Initial examination of the results revealed no significant seasonal dependence of ice-drift response on the synoptic time scale, other than larger velocities with larger wind stresses. Daily maximum ice-drift velocities range from 20-40 cm/s in February, and 15-30 cm/s in August. The corresponding mean monthly maximum drifts were 11 and 9 cm, respectively. The drag associated with the geostrophic currents plays a much bigger role in the summer because of the lighter atmospheric stresses. The well-known reversal of the normally clockwise Beaufort Gyre to a cyclonic system in August takes place in a few days and lasts well into September. In February, the Beaufort Gyre varies between a large, clockwise system covering all the Canadian Basin to a small, tight gyre centered over the southern Beaufort Sea, without any hint of reversal or disappearance. Large areas of strong divergence were found in the Ekman transport patterns, as well as the ice-divergence fields, indicating areas where ice thinning, openings and new ice formation might occur. In August this occurred in the Chukchi Sea, and in February just north of Novaya Zemlya.

Coupled ocean‐acoustics studies at Navy and NATO laboratories: The legacy of Ralph Goodman.

A brief history of collaborations between ocean and acoustic modelers is given under the directorships of Ralph Goodman at NORDA and SACLANT, and of continuing coupled modeling studies at NRL built on previous studies he sponsored. At NORDA the Numerical Modeling Division consisted of an acoustic and an ocean branch, one of the first known instances of such close‐knit administrative units for ocean and acoustic modelers. At SACLANT, close collaborations were strongly encouraged by Ralph Goodman and the respective group leaders. The results of these studies eventually appeared among the first published papers on the effects of mixed layer and Gulf Stream properties on surface‐duct propagation (Computational Acoustics: Ocean‐Acoustic Models and Supercomputing (North Holland Press, 1990); Oceanography and Acoustics: Prediction and Propagation Models (AIP Press, 1994). At NRL, these studies were restarted recently: evaluation of sonic layer depth relative to mixed layer depth [JGR 113 (2008)]; the acoustic im...

Acoustic hindcasts of array performance using a combination of submesoscale hydrodyamic and acoustic models.

It is well known that submesoscale ocean processes such as nonlinear internal gravity waves can have a significant effect on both the amplitude and the phase of an acoustic field propagating through this type of ocean environment. We report here on hindcasts computed with a numerical model combination consisting of a submesoscale hydrodynamic solver to compute a set of three‐dimensional (3‐D) environmental (sound speed) volumes evolving in time and a 3‐D wide‐angle parabolic equation code for acoustic field computation within each environmental volume. The data set was chosen from the ASIAEX 2001 experiment in the South China Sea, during a period of strong internal wave activity. A nonlinear wave packet was simulated propagating up the shelf and passing through both the acoustic source and receiver positions. The hindcasts computed the time evolving beam response on a horizontal array, located approximately 19 km from a 300 Hz low‐frequency modulat source. Comparison of experimental and modeled beamformed...

Surface cooled convection simulations with application to ice-covered seas

Some idealized numerical experiments were carried out to study certain basic aspects of convective motions likely to occur during cooling and ice formation in the Nordic seas. The studies were restricted to two-dimensional motions in shallow water up to 300m deep. The freezing point was not assumed to depend on salinity. Cooling rates of 200–500 W m-2 (mass flux rates of (4–10) X 10−5 kgm−2 s−1), and brine discharge rates of (4–8) X 10−5 kgm−2 s−1 were assumed, the latter corresponding roughly to a cm h−1 ice growth. The initial fluid state was assumed to be homogeneous, having been thoroughly stirred by the preceding strong wind events common to those regions. It was assumed that upon reaching the freezing temperature, all further cooling of the surface goes into ice formation, thus losing the buoyancy forcing owing to the cooling-associated mass flux. Under these conditions, the results showed that the occurrence of freezing regions and ice formation can either inhibit or enhance convection in the underlying water masses, depending on the ratio of the cooling-associated mass flux loss (owing to ice formation) to the brine release mass flux gain. Another important dependence was found on diffusivity, which can enhance (or diminish) the heat advected from the ambient ocean below. The augmentation of the upward heat flux by the higher diffusivity delayed both the onset of freezing and the growth of the freezing area, thus diminishing the loss of buoyancy forcing owing to the (higher) cooling-associated mass flux. For a cooling/brine mass flux ratio of five, the kinetic energy of the no-freezing system exceeded that of the freezing system by a factor of three. For cooling rates of 476W m-2 the maximum vertical velocities of the no-freeze simulation steadied at about 10 cm s−1, and for the case of cooling-freezing with a mass flux ratio of about five, at about 5 cm s−1 These values are within the range observed in penetrative ocean convection, or simulated by previous modelers in convection experiments. In the case of insufficient cooling (238 vs. 476 W m-2 the freezing point was reached only briefly, with brine injection lasting for a period of about 3 h. Then the heat transported from below by the convective cells (mainly driven by cooling-associated buoyancy) raised the surface temperature to above freezing conditions.

Sea surface temperature variability of the Iceland-Faeroe front: Correction

In a previous study by Niiler et al. (1992), advanced very high resolution radiometer (AVHRR) images were used for locating the Iceland-Faeroe front temperature distributions and gradients. In that study the satellite-sensed sea surface temperatures were found to contain an error after an atmospheric correction algorithm was applied. This was determined through a regression fit of AVHRR data against in situ aircraft-deployed expendable bathythermograph (AXBT) and conductivity-temperature-depth measurements. Recently, Minnett (1993) pointed out that an error occurred in that fit. As a result, we decided to repeat the comparisons of AVHRR sea surface temperature (SST) data against in situ measurements. After correcting several errors, we still find a shift of about 2°C in the scatter of AVHRR against AXBT SST data. The bias (mean difference) was 1.73°C, and the standard deviation was 0.3°C.