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- Author or Editor: Kurt L. Polzin x
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Abstract
The issue of internal wave–mesoscale eddy interactions is revisited. Previous observational work identified the mesoscale eddy field as a possible source of internal wave energy. Characterization of the coupling as a viscous process provides a smaller horizontal transfer coefficient than previously obtained, with vh ≅ 50 m2 s−1 in contrast to νh ≅ 200–400 m2 s−1, and a vertical transfer coefficient bounded away from zero, with νυ + ( f 2/N 2)Kh ≅ 2.5 ± 0.3 × 10−3 m2 s−1 in contrast to νυ + ( f 2/N 2)Kh = 0 ± 2 × 10−2 m2 s−1. Current meter data from the Local Dynamics Experiment of the PolyMode field program indicate mesoscale eddy–internal wave coupling through horizontal interactions (i) is a significant sink of eddy energy and (ii) plays an O(1) role in the energy budget of the internal wave field.
Abstract
The issue of internal wave–mesoscale eddy interactions is revisited. Previous observational work identified the mesoscale eddy field as a possible source of internal wave energy. Characterization of the coupling as a viscous process provides a smaller horizontal transfer coefficient than previously obtained, with vh ≅ 50 m2 s−1 in contrast to νh ≅ 200–400 m2 s−1, and a vertical transfer coefficient bounded away from zero, with νυ + ( f 2/N 2)Kh ≅ 2.5 ± 0.3 × 10−3 m2 s−1 in contrast to νυ + ( f 2/N 2)Kh = 0 ± 2 × 10−2 m2 s−1. Current meter data from the Local Dynamics Experiment of the PolyMode field program indicate mesoscale eddy–internal wave coupling through horizontal interactions (i) is a significant sink of eddy energy and (ii) plays an O(1) role in the energy budget of the internal wave field.
Abstract
Vertical profiles of horizontal velocity obtained during the Mid-Ocean Dynamics Experiment (MODE) provided the first published estimates of the high vertical wavenumber structure of horizontal velocity. The data were interpreted as being representative of the background internal wave field, and thus, despite some evidence of excess downward energy propagation associated with coherent near-inertial features that was interpreted in terms of atmospheric generation, these data provided the basis for a revision to the Garrett and Munk spectral model.
These data are reinterpreted through the lens of 30 years of research. Rather than representing the background wave field, atmospheric generation, or even near-inertial wave trapping, the coherent high wavenumber features are characteristic of internal wave capture in a mesoscale strain field. Wave capture represents a generalization of critical layer events for flows lacking the spatial symmetry inherent in a parallel shear flow or isolated vortex.
Abstract
Vertical profiles of horizontal velocity obtained during the Mid-Ocean Dynamics Experiment (MODE) provided the first published estimates of the high vertical wavenumber structure of horizontal velocity. The data were interpreted as being representative of the background internal wave field, and thus, despite some evidence of excess downward energy propagation associated with coherent near-inertial features that was interpreted in terms of atmospheric generation, these data provided the basis for a revision to the Garrett and Munk spectral model.
These data are reinterpreted through the lens of 30 years of research. Rather than representing the background wave field, atmospheric generation, or even near-inertial wave trapping, the coherent high wavenumber features are characteristic of internal wave capture in a mesoscale strain field. Wave capture represents a generalization of critical layer events for flows lacking the spatial symmetry inherent in a parallel shear flow or isolated vortex.
Abstract
This study presents novel observational estimates of turbulent dissipation and mixing in a standing meander between the Southeast Indian Ridge and the Macquarie Ridge in the Southern Ocean. By applying a finescale parameterization on the temperature, salinity, and velocity profiles collected from Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats in the upper 1600 m, we estimated the intensity and spatial distribution of dissipation rate and diapycnal mixing along the float tracks and investigated the sources. The indirect estimates indicate strong spatial and temporal variability of turbulent mixing varying from O(10−6) to O(10−3) m2 s−1 in the upper 1600 m. Elevated turbulent mixing is mostly associated with the Subantarctic Front (SAF) and mesoscale eddies. In the upper 500 m, enhanced mixing is associated with downward-propagating wind-generated near-inertial waves as well as the interaction between cyclonic eddies and upward-propagating internal waves. In the study region, the local topography does not play a role in turbulent mixing in the upper part of the water column, which has similar values in profiles over rough and smooth topography. However, both remotely generated internal tides and lee waves could contribute to the upward-propagating energy. Our results point strongly to the generation of turbulent mixing through the interaction of internal waves and the intense mesoscale eddy field.
Abstract
This study presents novel observational estimates of turbulent dissipation and mixing in a standing meander between the Southeast Indian Ridge and the Macquarie Ridge in the Southern Ocean. By applying a finescale parameterization on the temperature, salinity, and velocity profiles collected from Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats in the upper 1600 m, we estimated the intensity and spatial distribution of dissipation rate and diapycnal mixing along the float tracks and investigated the sources. The indirect estimates indicate strong spatial and temporal variability of turbulent mixing varying from O(10−6) to O(10−3) m2 s−1 in the upper 1600 m. Elevated turbulent mixing is mostly associated with the Subantarctic Front (SAF) and mesoscale eddies. In the upper 500 m, enhanced mixing is associated with downward-propagating wind-generated near-inertial waves as well as the interaction between cyclonic eddies and upward-propagating internal waves. In the study region, the local topography does not play a role in turbulent mixing in the upper part of the water column, which has similar values in profiles over rough and smooth topography. However, both remotely generated internal tides and lee waves could contribute to the upward-propagating energy. Our results point strongly to the generation of turbulent mixing through the interaction of internal waves and the intense mesoscale eddy field.
Abstract
Fine- and microstructure data from a free fall profiler are analysed to test models that relate the turbulent dissipation rate (ε) to characteristics of the internal wave field. The data were obtained from several distinct internal wave environments, yielding considerably more range in stratification and wave properties than has been previously available. Observations from the ocean interior with negligible large-scale flow were examined to address the buoyancy scaling of ε. These data exhibited a factor of 140 range in squared buoyancy frequency (N 2) with depth and uniform internal wave characteristics, consistent with the Garrettt–Munk spectrum. The magnitude of ε and its variation with N(ε ∼ N 2) was best described by the dynamical model of Henyey et al. A second dynamical model, by McComas and Muller, predicted an appropriate buoyancy scaling but overestimated the observed dissipation rates. Two kinematical dissipation parameterizations predicted buoyancy scalings of N 3/2; these are shown to be inconsistent with the observations.
Data from wave fields that depart from the canonical GM description are also examined and interpreted with reference to the dynamical models. The measurements came from a warm core ring dominated by strong near-inertial shears, a region of steep topography exhibiting high-frequency internal wave characteristics, and a midocean regime dominated al large wavelengths by an internal tide. Of the dissipation predictions examined, those of the Henyey et al. model in which εN −2 scales as E 2, where E is the nondimensional spectral shear level, were most consistent with observations. Nevertheless, the predictions for these cases exhibited departures from the observations by more than an order of magnitude. For the present data, these discrepancies appeared most sensitive to the distribution of internal wave frequency, inferred here from the ratio of shear spectral level to that for strain. Application of a frequency-based correction to the Henyey et al. model returned dissipation values consistent with observed estimates to within a factor of 2.
These results indicate that the kinetic energy dissipation rate (and attendant turbulent mixing) is small for the background Garrett and Munk internal wave conditions (0.25εN −2∼0.7 × 10−5 m2 s−1). Dissipation and mixing become large when wave shear spectral levels are elevated, particularly by high-frequency waves. Thus, internal wave reflection/generation at sleep topographic features appear promising candidates for achieving enhanced dissipation and strong diapycnal mixing in the deep ocean that appears required by box models and advection–diffusion balances.
Abstract
Fine- and microstructure data from a free fall profiler are analysed to test models that relate the turbulent dissipation rate (ε) to characteristics of the internal wave field. The data were obtained from several distinct internal wave environments, yielding considerably more range in stratification and wave properties than has been previously available. Observations from the ocean interior with negligible large-scale flow were examined to address the buoyancy scaling of ε. These data exhibited a factor of 140 range in squared buoyancy frequency (N 2) with depth and uniform internal wave characteristics, consistent with the Garrettt–Munk spectrum. The magnitude of ε and its variation with N(ε ∼ N 2) was best described by the dynamical model of Henyey et al. A second dynamical model, by McComas and Muller, predicted an appropriate buoyancy scaling but overestimated the observed dissipation rates. Two kinematical dissipation parameterizations predicted buoyancy scalings of N 3/2; these are shown to be inconsistent with the observations.
Data from wave fields that depart from the canonical GM description are also examined and interpreted with reference to the dynamical models. The measurements came from a warm core ring dominated by strong near-inertial shears, a region of steep topography exhibiting high-frequency internal wave characteristics, and a midocean regime dominated al large wavelengths by an internal tide. Of the dissipation predictions examined, those of the Henyey et al. model in which εN −2 scales as E 2, where E is the nondimensional spectral shear level, were most consistent with observations. Nevertheless, the predictions for these cases exhibited departures from the observations by more than an order of magnitude. For the present data, these discrepancies appeared most sensitive to the distribution of internal wave frequency, inferred here from the ratio of shear spectral level to that for strain. Application of a frequency-based correction to the Henyey et al. model returned dissipation values consistent with observed estimates to within a factor of 2.
These results indicate that the kinetic energy dissipation rate (and attendant turbulent mixing) is small for the background Garrett and Munk internal wave conditions (0.25εN −2∼0.7 × 10−5 m2 s−1). Dissipation and mixing become large when wave shear spectral levels are elevated, particularly by high-frequency waves. Thus, internal wave reflection/generation at sleep topographic features appear promising candidates for achieving enhanced dissipation and strong diapycnal mixing in the deep ocean that appears required by box models and advection–diffusion balances.
Abstract
The spectral energy density of the internal waves in the open ocean is considered. The Garrett and Munk spectrum and the resonant kinetic equation are used as the main tools of the study. Evaluations of a resonant kinetic equation that suggest the slow time evolution of the Garrett and Munk spectrum is not in fact slow are reported. Instead, nonlinear transfers lead to evolution time scales that are smaller than one wave period at high vertical wavenumber. Such values of the transfer rates are inconsistent with the viewpoint expressed in papers by C. H. McComas and P. Müller, and by P. Müller et al., which regards the Garrett and Munk spectrum as an approximate stationary state of the resonant kinetic equation. It also puts the self-consistency of a resonant kinetic equation at a serious risk. The possible reasons for and resolutions of this paradox are explored. Inclusion of near-resonant interactions decreases the rate at which the spectrum evolves. Consequently, this inclusion shows a tendency of improving of self-consistency of the kinetic equation approach.
Abstract
The spectral energy density of the internal waves in the open ocean is considered. The Garrett and Munk spectrum and the resonant kinetic equation are used as the main tools of the study. Evaluations of a resonant kinetic equation that suggest the slow time evolution of the Garrett and Munk spectrum is not in fact slow are reported. Instead, nonlinear transfers lead to evolution time scales that are smaller than one wave period at high vertical wavenumber. Such values of the transfer rates are inconsistent with the viewpoint expressed in papers by C. H. McComas and P. Müller, and by P. Müller et al., which regards the Garrett and Munk spectrum as an approximate stationary state of the resonant kinetic equation. It also puts the self-consistency of a resonant kinetic equation at a serious risk. The possible reasons for and resolutions of this paradox are explored. Inclusion of near-resonant interactions decreases the rate at which the spectrum evolves. Consequently, this inclusion shows a tendency of improving of self-consistency of the kinetic equation approach.
Abstract
This study reports on observations of turbulent dissipation and internal wave-scale flow properties in a standing meander of the Antarctic Circumpolar Current (ACC) north of the Kerguelen Plateau. The authors characterize the intensity and spatial distribution of the observed turbulent dissipation and the derived turbulent mixing, and consider underpinning mechanisms in the context of the internal wave field and the processes governing the waves’ generation and evolution.
The turbulent dissipation rate and the derived diapycnal diffusivity are highly variable with systematic depth dependence. The dissipation rate is generally enhanced in the upper 1000–1500 m of the water column, and both the dissipation rate and diapycnal diffusivity are enhanced in some places near the seafloor, commonly in regions of rough topography and in the vicinity of strong bottom flows associated with the ACC jets. Turbulent dissipation is high in regions where internal wave energy is high, consistent with the idea that interior dissipation is related to a breaking internal wave field. Elevated turbulence occurs in association with downward-propagating near-inertial waves within 1–2 km of the surface, as well as with upward-propagating, relatively high-frequency waves within 1–2 km of the seafloor. While an interpretation of these near-bottom waves as lee waves generated by ACC jets flowing over small-scale topographic roughness is supported by the qualitative match between the spatial patterns in predicted lee wave radiation and observed near-bottom dissipation, the observed dissipation is found to be only a small percentage of the energy flux predicted by theory. The mismatch suggests an alternative fate to local dissipation for a significant fraction of the radiated energy.
Abstract
This study reports on observations of turbulent dissipation and internal wave-scale flow properties in a standing meander of the Antarctic Circumpolar Current (ACC) north of the Kerguelen Plateau. The authors characterize the intensity and spatial distribution of the observed turbulent dissipation and the derived turbulent mixing, and consider underpinning mechanisms in the context of the internal wave field and the processes governing the waves’ generation and evolution.
The turbulent dissipation rate and the derived diapycnal diffusivity are highly variable with systematic depth dependence. The dissipation rate is generally enhanced in the upper 1000–1500 m of the water column, and both the dissipation rate and diapycnal diffusivity are enhanced in some places near the seafloor, commonly in regions of rough topography and in the vicinity of strong bottom flows associated with the ACC jets. Turbulent dissipation is high in regions where internal wave energy is high, consistent with the idea that interior dissipation is related to a breaking internal wave field. Elevated turbulence occurs in association with downward-propagating near-inertial waves within 1–2 km of the surface, as well as with upward-propagating, relatively high-frequency waves within 1–2 km of the seafloor. While an interpretation of these near-bottom waves as lee waves generated by ACC jets flowing over small-scale topographic roughness is supported by the qualitative match between the spatial patterns in predicted lee wave radiation and observed near-bottom dissipation, the observed dissipation is found to be only a small percentage of the energy flux predicted by theory. The mismatch suggests an alternative fate to local dissipation for a significant fraction of the radiated energy.
Abstract
A key remaining challenge in oceanography is the understanding and parameterization of small-scale mixing. Evidence suggests that topographic features play a significant role in enhancing mixing in the Southern Ocean. This study uses 914 high-resolution hydrographic profiles from novel EM-APEX profiling floats to investigate turbulent mixing north of the Kerguelen Plateau, a major topographic feature in the Southern Ocean. A shear–strain finescale parameterization is applied to estimate diapycnal diffusivity in the upper 1600 m of the ocean. The indirect estimates of mixing match direct microstructure profiler observations made simultaneously. It is found that mixing intensities have strong spatial and temporal variability, ranging from O(10−6) to O(10−3) m2 s−1. This study identifies topographic roughness, current speed, and wind speed as the main factors controlling mixing intensity. Additionally, the authors find strong regional variability in mixing dynamics and enhanced mixing in the Antarctic Circumpolar Current frontal region. This enhanced mixing is attributed to dissipating internal waves generated by the interaction of the Antarctic Circumpolar Current and the topography of the Kerguelen Plateau. Extending the mixing observations from the Kerguelen region to the entire Southern Ocean, this study infers a large water mass transformation rate of 17 Sverdrups (Sv; 1 Sv ≡ 106 m3 s−1) across the boundary of Antarctic Intermediate Water and Upper Circumpolar Deep Water in the Antarctic Circumpolar Current. This work suggests that the contribution of mixing to the Southern Ocean overturning circulation budget is particularly significant in fronts.
Abstract
A key remaining challenge in oceanography is the understanding and parameterization of small-scale mixing. Evidence suggests that topographic features play a significant role in enhancing mixing in the Southern Ocean. This study uses 914 high-resolution hydrographic profiles from novel EM-APEX profiling floats to investigate turbulent mixing north of the Kerguelen Plateau, a major topographic feature in the Southern Ocean. A shear–strain finescale parameterization is applied to estimate diapycnal diffusivity in the upper 1600 m of the ocean. The indirect estimates of mixing match direct microstructure profiler observations made simultaneously. It is found that mixing intensities have strong spatial and temporal variability, ranging from O(10−6) to O(10−3) m2 s−1. This study identifies topographic roughness, current speed, and wind speed as the main factors controlling mixing intensity. Additionally, the authors find strong regional variability in mixing dynamics and enhanced mixing in the Antarctic Circumpolar Current frontal region. This enhanced mixing is attributed to dissipating internal waves generated by the interaction of the Antarctic Circumpolar Current and the topography of the Kerguelen Plateau. Extending the mixing observations from the Kerguelen region to the entire Southern Ocean, this study infers a large water mass transformation rate of 17 Sverdrups (Sv; 1 Sv ≡ 106 m3 s−1) across the boundary of Antarctic Intermediate Water and Upper Circumpolar Deep Water in the Antarctic Circumpolar Current. This work suggests that the contribution of mixing to the Southern Ocean overturning circulation budget is particularly significant in fronts.
Abstract
Simultaneous full-depth microstructure measurements of turbulence and finestructure measurements of velocity and density are analyzed to investigate the relationship between turbulence and the internal wave field in the Antarctic Circumpolar Current. These data reveal a systematic near-bottom overprediction of the turbulent kinetic energy dissipation rate by finescale parameterization methods in select locations. Sites of near-bottom overprediction are typically characterized by large near-bottom flow speeds and elevated topographic roughness. Further, lower-than-average shear-to-strain ratios indicative of a less near-inertial wave field, rotary spectra suggesting a predominance of upward internal wave energy propagation, and enhanced narrowband variance at vertical wavelengths on the order of 100 m are found at these locations. Finally, finescale overprediction is typically associated with elevated Froude numbers based on the near-bottom shear of the background flow, and a background flow with a systematic backing tendency. Agreement of microstructure- and finestructure-based estimates within the expected uncertainty of the parameterization away from these special sites, the reproducibility of the overprediction signal across various parameterization implementations, and an absence of indications of atypical instrument noise at sites of parameterization overprediction, all suggest that physics not encapsulated by the parameterization play a role in the fate of bottom-generated waves at these locations. Several plausible underpinning mechanisms based on the limited available evidence are discussed that offer guidance for future studies.
Abstract
Simultaneous full-depth microstructure measurements of turbulence and finestructure measurements of velocity and density are analyzed to investigate the relationship between turbulence and the internal wave field in the Antarctic Circumpolar Current. These data reveal a systematic near-bottom overprediction of the turbulent kinetic energy dissipation rate by finescale parameterization methods in select locations. Sites of near-bottom overprediction are typically characterized by large near-bottom flow speeds and elevated topographic roughness. Further, lower-than-average shear-to-strain ratios indicative of a less near-inertial wave field, rotary spectra suggesting a predominance of upward internal wave energy propagation, and enhanced narrowband variance at vertical wavelengths on the order of 100 m are found at these locations. Finally, finescale overprediction is typically associated with elevated Froude numbers based on the near-bottom shear of the background flow, and a background flow with a systematic backing tendency. Agreement of microstructure- and finestructure-based estimates within the expected uncertainty of the parameterization away from these special sites, the reproducibility of the overprediction signal across various parameterization implementations, and an absence of indications of atypical instrument noise at sites of parameterization overprediction, all suggest that physics not encapsulated by the parameterization play a role in the fate of bottom-generated waves at these locations. Several plausible underpinning mechanisms based on the limited available evidence are discussed that offer guidance for future studies.
Abstract
In the stratified ocean, turbulent mixing is primarily attributed to the breaking of internal waves. As such, internal waves provide a link between large-scale forcing and small-scale mixing. The internal wave field north of the Kerguelen Plateau is characterized using 914 high-resolution hydrographic profiles from novel Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats. Altogether, 46 coherent features are identified in the EM-APEX velocity profiles and interpreted in terms of internal wave kinematics. The large number of internal waves analyzed provides a quantitative framework for characterizing spatial variations in the internal wave field and for resolving generation versus propagation dynamics. Internal waves observed near the Kerguelen Plateau have a mean vertical wavelength of 200 m, a mean horizontal wavelength of 15 km, a mean period of 16 h, and a mean horizontal group velocity of 3 cm s−1. The internal wave characteristics are dependent on regional dynamics, suggesting that different generation mechanisms of internal waves dominate in different dynamical zones. The wave fields in the Subantarctic/Subtropical Front and the Polar Front Zone are influenced by the local small-scale topography and flow strength. The eddy-wave field is influenced by the large-scale flow structure, while the internal wave field in the Subantarctic Zone is controlled by atmospheric forcing. More importantly, the local generation of internal waves not only drives large-scale dissipation in the frontal region but also downstream from the plateau. Some internal waves in the frontal region are advected away from the plateau, contributing to mixing and stratification budgets elsewhere.
Abstract
In the stratified ocean, turbulent mixing is primarily attributed to the breaking of internal waves. As such, internal waves provide a link between large-scale forcing and small-scale mixing. The internal wave field north of the Kerguelen Plateau is characterized using 914 high-resolution hydrographic profiles from novel Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats. Altogether, 46 coherent features are identified in the EM-APEX velocity profiles and interpreted in terms of internal wave kinematics. The large number of internal waves analyzed provides a quantitative framework for characterizing spatial variations in the internal wave field and for resolving generation versus propagation dynamics. Internal waves observed near the Kerguelen Plateau have a mean vertical wavelength of 200 m, a mean horizontal wavelength of 15 km, a mean period of 16 h, and a mean horizontal group velocity of 3 cm s−1. The internal wave characteristics are dependent on regional dynamics, suggesting that different generation mechanisms of internal waves dominate in different dynamical zones. The wave fields in the Subantarctic/Subtropical Front and the Polar Front Zone are influenced by the local small-scale topography and flow strength. The eddy-wave field is influenced by the large-scale flow structure, while the internal wave field in the Subantarctic Zone is controlled by atmospheric forcing. More importantly, the local generation of internal waves not only drives large-scale dissipation in the frontal region but also downstream from the plateau. Some internal waves in the frontal region are advected away from the plateau, contributing to mixing and stratification budgets elsewhere.
Abstract
Steady scale-invariant solutions of a kinetic equation describing the statistics of oceanic internal gravity waves based on wave turbulence theory are investigated. It is shown in the nonrotating scale-invariant limit that the collision integral in the kinetic equation diverges for almost all spectral power-law exponents. These divergences come from resonant interactions with the smallest horizontal wavenumbers and/or the largest horizontal wavenumbers with extreme scale separations.
A small domain is identified in which the scale-invariant collision integral converges and numerically find a convergent power-law solution. This numerical solution is close to the Garrett–Munk spectrum. Power-law exponents that potentially permit a balance between the infrared and ultraviolet divergences are investigated. The balanced exponents are generalizations of an exact solution of the scale-invariant kinetic equation, the Pelinovsky–Raevsky spectrum. A small but finite Coriolis parameter representing the effects of rotation is introduced into the kinetic equation to determine solutions over the divergent part of the domain using rigorous asymptotic arguments. This gives rise to the induced diffusion regime.
The derivation of the kinetic equation is based on an assumption of weak nonlinearity. Dominance of the nonlocal interactions puts the self-consistency of the kinetic equation at risk. However, these weakly nonlinear stationary states are consistent with much of the observational evidence.
Abstract
Steady scale-invariant solutions of a kinetic equation describing the statistics of oceanic internal gravity waves based on wave turbulence theory are investigated. It is shown in the nonrotating scale-invariant limit that the collision integral in the kinetic equation diverges for almost all spectral power-law exponents. These divergences come from resonant interactions with the smallest horizontal wavenumbers and/or the largest horizontal wavenumbers with extreme scale separations.
A small domain is identified in which the scale-invariant collision integral converges and numerically find a convergent power-law solution. This numerical solution is close to the Garrett–Munk spectrum. Power-law exponents that potentially permit a balance between the infrared and ultraviolet divergences are investigated. The balanced exponents are generalizations of an exact solution of the scale-invariant kinetic equation, the Pelinovsky–Raevsky spectrum. A small but finite Coriolis parameter representing the effects of rotation is introduced into the kinetic equation to determine solutions over the divergent part of the domain using rigorous asymptotic arguments. This gives rise to the induced diffusion regime.
The derivation of the kinetic equation is based on an assumption of weak nonlinearity. Dominance of the nonlocal interactions puts the self-consistency of the kinetic equation at risk. However, these weakly nonlinear stationary states are consistent with much of the observational evidence.
