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- Author or Editor: T. R. Osborn x
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Abstract
Scaling of the turbulent energy equation suggests the balance of terms in the ocean is between turbulent production, dissipation and the loss to buoyancy. In this paper two models for the source of oceanic turbulence are considered; namely, production by the Reynolds stress working against a time variable mean shear, and the gravitational collapse of Kelvin-Helmholtz instabilities. Both of these shear instabilities are believed to be important in the ocean. Using values for the critical flux Richardson number and the measurements from studies of Kelvin-Helmholtz instabilities, the efficiency of turbulent mixing is shown to be comparable for the two models. Therefore, a general relationship between the dissipation rate and the buoyancy flux due to the small-scale turbulent velocity fluctuations is derived. The result is expressed as an upper bound on the value of the turbulent eddy coefficient for mass K ρ ⩽ 0.2ε/N 2. Values of K ρ are calculated from recent oceanic measurements of energy dissipation. Isopycnal advection and doubly diffusive phenomena are not included in the model.
Abstract
Scaling of the turbulent energy equation suggests the balance of terms in the ocean is between turbulent production, dissipation and the loss to buoyancy. In this paper two models for the source of oceanic turbulence are considered; namely, production by the Reynolds stress working against a time variable mean shear, and the gravitational collapse of Kelvin-Helmholtz instabilities. Both of these shear instabilities are believed to be important in the ocean. Using values for the critical flux Richardson number and the measurements from studies of Kelvin-Helmholtz instabilities, the efficiency of turbulent mixing is shown to be comparable for the two models. Therefore, a general relationship between the dissipation rate and the buoyancy flux due to the small-scale turbulent velocity fluctuations is derived. The result is expressed as an upper bound on the value of the turbulent eddy coefficient for mass K ρ ⩽ 0.2ε/N 2. Values of K ρ are calculated from recent oceanic measurements of energy dissipation. Isopycnal advection and doubly diffusive phenomena are not included in the model.
Abstract
Measurements of the vertical component of the temperature gradient in Powell Lake show phenomena similar to those observed in the ocean. The gradient is an irregular function of depth, with temperature inversions indicating static instability of the water column on the centimeter scale.
The lower portion of the lake contains old sea water. Doubly diffusive layers were found only near the very bottom of the lake and another form of thermohaline circulation may exist for 60 m above the layers.
Abstract
Measurements of the vertical component of the temperature gradient in Powell Lake show phenomena similar to those observed in the ocean. The gradient is an irregular function of depth, with temperature inversions indicating static instability of the water column on the centimeter scale.
The lower portion of the lake contains old sea water. Doubly diffusive layers were found only near the very bottom of the lake and another form of thermohaline circulation may exist for 60 m above the layers.
Abstract
Vertical profiles of temperature microstructure were collected at seven sites in the equatorial Atlantic between 24°W and 33°W, 2°N and 1°20′S. The use of three identical temperature microstructure profiles gives insight into the spatial and temporal variation of the temperature microstructure. Data on the velocity microstructure taken with a fourth instrument show a relationship between temperature and velocity microstructure.
Cox numbers show a relative minimum near the center of the core with largest values in the shear region between the South Equatorial Current and the Equatorial Undercurrent.
Abstract
Vertical profiles of temperature microstructure were collected at seven sites in the equatorial Atlantic between 24°W and 33°W, 2°N and 1°20′S. The use of three identical temperature microstructure profiles gives insight into the spatial and temporal variation of the temperature microstructure. Data on the velocity microstructure taken with a fourth instrument show a relationship between temperature and velocity microstructure.
Cox numbers show a relative minimum near the center of the core with largest values in the shear region between the South Equatorial Current and the Equatorial Undercurrent.
Abstract
A series of profiles of velocity microstructure along 152°E in the western North Pacific Ocean were collected in May–June 1982. Large, averaged turbulent dissipation rates, ε, found in the main thermocline (400 to 1000 m) were determined by a combination of large independent estimates of ε and a greater rate of occurrence of turbulent events in the main thermocline than elsewhere. Concurrently we find that averaged values of ε exhibit a positive dependence on the buoyancy frequency, N, and that form ε = aN γ is best fit by γ = 1 when only the data below 400 m are considered. Of the more than 5000 m of data collected below 1000 m depth, 12% showed measurable turbulence and dominated the depth averages. A deep ocean estimate of an upper bound to the eddy coefficient for vertical diffusion, K ρ, is 10−4 m2 s−1 and not significantly different from the value estimated by Munk. The inferred dependence of the mass flux with depth indicates the relative significance of vertical mixing in the main thermocline. Other processes must influence the maintenance of the more weakly stratified 15°–18°C water above.
Abstract
A series of profiles of velocity microstructure along 152°E in the western North Pacific Ocean were collected in May–June 1982. Large, averaged turbulent dissipation rates, ε, found in the main thermocline (400 to 1000 m) were determined by a combination of large independent estimates of ε and a greater rate of occurrence of turbulent events in the main thermocline than elsewhere. Concurrently we find that averaged values of ε exhibit a positive dependence on the buoyancy frequency, N, and that form ε = aN γ is best fit by γ = 1 when only the data below 400 m are considered. Of the more than 5000 m of data collected below 1000 m depth, 12% showed measurable turbulence and dominated the depth averages. A deep ocean estimate of an upper bound to the eddy coefficient for vertical diffusion, K ρ, is 10−4 m2 s−1 and not significantly different from the value estimated by Munk. The inferred dependence of the mass flux with depth indicates the relative significance of vertical mixing in the main thermocline. Other processes must influence the maintenance of the more weakly stratified 15°–18°C water above.
Abstract
Observations are described in an experiment undertaken to determine the response of a stratified inlet to changing conditions of wind, tide and runoff. Time series of conductivity profiles taken in Alberni Inlet, British Columbia, show marked fluctuations in surface layer thickness that appear to be related to strong winds. The effect of an up-inlet wind is to produce a rapid thickening of the fresh-water layer at the inlet head which may persist for several days. Strong winds were also associated with significant changes in the intensity of stratification.
Abstract
Observations are described in an experiment undertaken to determine the response of a stratified inlet to changing conditions of wind, tide and runoff. Time series of conductivity profiles taken in Alberni Inlet, British Columbia, show marked fluctuations in surface layer thickness that appear to be related to strong winds. The effect of an up-inlet wind is to produce a rapid thickening of the fresh-water layer at the inlet head which may persist for several days. Strong winds were also associated with significant changes in the intensity of stratification.
Abstract
Temperature ramps or microfronts are coherent tilted structures in the oceanic and atmospheric boundary layers at which there are small, but detectable, changes in mean temperature. Their presence contributes to a nonzero skewness, ST (θ), of the spatial derivatives of temperature, dT/dx, at constant depth within the ocean mixed layer. The skewness ST (θ) has a roughly sinusoidal variation with θ, the direction in which the derivatives are measured relative to the wind. The magnitude of the skewness, |ST (0)|, measured in a direction into the wind (θ = 0) is of order unity, and the sign of ST (0) depends on the heat flux from the air to the water through the sea surface, being positive if the heat flux is positive. Recent observations using an AUV, Autosub, have shown that the mean values of ε, the rate of dissipation of turbulent kinetic energy per unit mass, change as temperature ramps are crossed. This observation raises the questions: Is the skewness of the gradient of logε, S logε (θ), nonzero in the mixed layer even though ε is observed to be lognormal? If so, is S logε (θ) related to ST (θ)? The answer to both of the questions appears to be “yes,” although the magnitude of S logε (θ) is small, of order 5 × 10−2, and no clearly detectable variation with θ is found in the available data.
Abstract
Temperature ramps or microfronts are coherent tilted structures in the oceanic and atmospheric boundary layers at which there are small, but detectable, changes in mean temperature. Their presence contributes to a nonzero skewness, ST (θ), of the spatial derivatives of temperature, dT/dx, at constant depth within the ocean mixed layer. The skewness ST (θ) has a roughly sinusoidal variation with θ, the direction in which the derivatives are measured relative to the wind. The magnitude of the skewness, |ST (0)|, measured in a direction into the wind (θ = 0) is of order unity, and the sign of ST (0) depends on the heat flux from the air to the water through the sea surface, being positive if the heat flux is positive. Recent observations using an AUV, Autosub, have shown that the mean values of ε, the rate of dissipation of turbulent kinetic energy per unit mass, change as temperature ramps are crossed. This observation raises the questions: Is the skewness of the gradient of logε, S logε (θ), nonzero in the mixed layer even though ε is observed to be lognormal? If so, is S logε (θ) related to ST (θ)? The answer to both of the questions appears to be “yes,” although the magnitude of S logε (θ) is small, of order 5 × 10−2, and no clearly detectable variation with θ is found in the available data.
Abstract
High-resolution velocity shear, CTD, and microstructure measurements were made simultaneously from the research submarine Dolphin in Monterey Bay in October 1984. During three consecutive dives, the Dolphin cycled between the surface and 110 m along predetermined tracks 10 miles northwest of Monterey. Inside the seasonal thermocline, the vertical velocity shear appeared to be concentrated in layers 10 m thick extending several kilometers horizontally. The thickness of the shear layers is consistent with the typical size of turbulent patches encountered in the seasonal thermocline. In contrast, no large shear layers were observed below a 50 m depth. The depth levels at which the shear layers were observed were nearly constant throughout each dive, suggesting that the shear layers, with some unknown degree of intermittency, might extend horizontally over several square kilometers. The shear vector inside the seasonal themocline (at σ t = 25.5) rotated 360° over an inertial period, but did appear to propagate vertically over the 30-hour observation period. These observations suggest that the passage of a storm caused the upper thermocline to ring, creating a local jetlike flow below the mixed layer.
Abstract
High-resolution velocity shear, CTD, and microstructure measurements were made simultaneously from the research submarine Dolphin in Monterey Bay in October 1984. During three consecutive dives, the Dolphin cycled between the surface and 110 m along predetermined tracks 10 miles northwest of Monterey. Inside the seasonal thermocline, the vertical velocity shear appeared to be concentrated in layers 10 m thick extending several kilometers horizontally. The thickness of the shear layers is consistent with the typical size of turbulent patches encountered in the seasonal thermocline. In contrast, no large shear layers were observed below a 50 m depth. The depth levels at which the shear layers were observed were nearly constant throughout each dive, suggesting that the shear layers, with some unknown degree of intermittency, might extend horizontally over several square kilometers. The shear vector inside the seasonal themocline (at σ t = 25.5) rotated 360° over an inertial period, but did appear to propagate vertically over the 30-hour observation period. These observations suggest that the passage of a storm caused the upper thermocline to ring, creating a local jetlike flow below the mixed layer.
Abstract
Observations of turbulent energy dissipation rate ε in the deep surface mixed layer at a mid-Sargasso site are presented: two occupations of this site include a large range of local meteorological forcing. Two frontal passages and a large time interval between profiles during the first series of measurements preclude examination of the turbulent kinetic energy balance: qualitatively, a profile taken during the strongest wind-wave forcing of the observation set suggests that layer deepening was not being driven directly from the surface, but by a shear instability at the mixed layer base. A quantitative assessment of terms in the steady-state locally balanced model of the turbulent kinetic energy budget proposed by Niiler (1975) has been possible for two profiles having dissipation characteristics and surface meteorological conditions which allow us to argue for the absence of all but a few of the possible source/sink terms in the turbulent kinetic energy balance. In one case, a steady-state local balance is possible. In the other case, a local balance can be maintained by giving up the steady-state assumption. i.e., by including the time rate of decay of the turbulent kinetic energy. Other possible balances exist. The analysis of the surface mixed-layer turbulent kinetic energy balance highlights two major uncertainties-parameterization of the wind-wave forcing term and lack of reliable dissipation measurements in the upper 10–20 m of the water column.
Abstract
Observations of turbulent energy dissipation rate ε in the deep surface mixed layer at a mid-Sargasso site are presented: two occupations of this site include a large range of local meteorological forcing. Two frontal passages and a large time interval between profiles during the first series of measurements preclude examination of the turbulent kinetic energy balance: qualitatively, a profile taken during the strongest wind-wave forcing of the observation set suggests that layer deepening was not being driven directly from the surface, but by a shear instability at the mixed layer base. A quantitative assessment of terms in the steady-state locally balanced model of the turbulent kinetic energy budget proposed by Niiler (1975) has been possible for two profiles having dissipation characteristics and surface meteorological conditions which allow us to argue for the absence of all but a few of the possible source/sink terms in the turbulent kinetic energy balance. In one case, a steady-state local balance is possible. In the other case, a local balance can be maintained by giving up the steady-state assumption. i.e., by including the time rate of decay of the turbulent kinetic energy. Other possible balances exist. The analysis of the surface mixed-layer turbulent kinetic energy balance highlights two major uncertainties-parameterization of the wind-wave forcing term and lack of reliable dissipation measurements in the upper 10–20 m of the water column.
Abstract
Turbulence measurements from the central equatorial Pacific in February 1982 have been analyzed and compared to synoptic CTD and current velocity profiles and current meter data. These suggest considerably more time (if not space) variability than had previously been anticipated. Above 300 m at the equator the turbulence levels were greater but less than previous equatorial measurements, and turbulent patches occurred more frequently than elsewhere in the open ocean. Below 300 m the occurrence of turbulent patches was less frequent than in other regions of the ocean, except for the persistence of a patch at 500 m.
Abstract
Turbulence measurements from the central equatorial Pacific in February 1982 have been analyzed and compared to synoptic CTD and current velocity profiles and current meter data. These suggest considerably more time (if not space) variability than had previously been anticipated. Above 300 m at the equator the turbulence levels were greater but less than previous equatorial measurements, and turbulent patches occurred more frequently than elsewhere in the open ocean. Below 300 m the occurrence of turbulent patches was less frequent than in other regions of the ocean, except for the persistence of a patch at 500 m.
Abstract
A method is developed for estimating the uncertainty (standard error) of observed regional, hemispheric, and global-mean surface temperature series due to incomplete spatial sampling. Standard errors estimated at the grid-box level [SE2 = S 2(1 − r̄)/(1 + (n − 1)r̄)] depend upon three parameters: the number of site records (n) within each box, the average interrecord correlation (r̄) between these sites, and the temporal variability (S 2) of each grid-box temperature time series. For boxes without data (n = 0), estimates are made using values of S 2 interpolated from neighboring grid boxes. Due to spatial correlation, large-scale standard errors in a regional-mean time series are not simply the average of the grid-box standard errors, but depend upon the effective number of independent sites (N eff) over the region.
A number of assumptions must be made in estimating the various parameters, and these are tested with observational data and complementary results from multicentury control integrations of three coupled general circulation models (GCMs). The globally complete GCMs enable some assumptions to be tested in a situation where there are no missing data; comparison of parameters computed from the observed and model datasets are also useful for assessing the performance of GCMs. As most of the parameters are timescale dependent, the resulting errors are likewise timescale dependent and must be calculated for each timescale of interest. The length of the observed record enables uncertainties to be estimated on the interannual and interdecadal timescales, with the longer GCM runs providing inferences about longer timescales. For mean annual observed data on the interannual timescale, the 95% confidence interval for estimates of the global-mean surface temperature since 1951 is ±0.12°C. Prior to 1900, the confidence interval widens to ±0.18°C. Equivalent values on the decadal timescale are smaller: ±0.10°C (1951–95) and ±0.16°C (1851–1900).
Abstract
A method is developed for estimating the uncertainty (standard error) of observed regional, hemispheric, and global-mean surface temperature series due to incomplete spatial sampling. Standard errors estimated at the grid-box level [SE2 = S 2(1 − r̄)/(1 + (n − 1)r̄)] depend upon three parameters: the number of site records (n) within each box, the average interrecord correlation (r̄) between these sites, and the temporal variability (S 2) of each grid-box temperature time series. For boxes without data (n = 0), estimates are made using values of S 2 interpolated from neighboring grid boxes. Due to spatial correlation, large-scale standard errors in a regional-mean time series are not simply the average of the grid-box standard errors, but depend upon the effective number of independent sites (N eff) over the region.
A number of assumptions must be made in estimating the various parameters, and these are tested with observational data and complementary results from multicentury control integrations of three coupled general circulation models (GCMs). The globally complete GCMs enable some assumptions to be tested in a situation where there are no missing data; comparison of parameters computed from the observed and model datasets are also useful for assessing the performance of GCMs. As most of the parameters are timescale dependent, the resulting errors are likewise timescale dependent and must be calculated for each timescale of interest. The length of the observed record enables uncertainties to be estimated on the interannual and interdecadal timescales, with the longer GCM runs providing inferences about longer timescales. For mean annual observed data on the interannual timescale, the 95% confidence interval for estimates of the global-mean surface temperature since 1951 is ±0.12°C. Prior to 1900, the confidence interval widens to ±0.18°C. Equivalent values on the decadal timescale are smaller: ±0.10°C (1951–95) and ±0.16°C (1851–1900).
