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- Author or Editor: Bruce R. Sutherland x
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Abstract
As upward-propagating anelastic internal gravity wave packets grow in amplitude, nonlinear effects develop as a result of interactions with the horizontal mean flow that they induce. This qualitatively alters the structure of the wave packet. The weakly nonlinear dynamics are well captured by the nonlinear Schrödinger equation, which is derived here for anelastic waves. In particular, this predicts that strongly nonhydrostatic waves are modulationally unstable and so the wave packet narrows and grows more rapidly in amplitude than the exponential anelastic growth rate. More hydrostatic waves are modulationally stable and so their amplitude grows less rapidly. The marginal case between stability and instability occurs for waves propagating at the fastest vertical group velocity. Extrapolating these results to waves propagating to higher altitudes (hence attaining larger amplitudes), it is anticipated that modulationally unstable waves should break at lower altitudes and modulationally stable waves should break at higher altitudes than predicted by linear theory. This prediction is borne out by fully nonlinear numerical simulations of the anelastic equations. A range of simulations is performed to quantify where overturning actually occurs.
Abstract
As upward-propagating anelastic internal gravity wave packets grow in amplitude, nonlinear effects develop as a result of interactions with the horizontal mean flow that they induce. This qualitatively alters the structure of the wave packet. The weakly nonlinear dynamics are well captured by the nonlinear Schrödinger equation, which is derived here for anelastic waves. In particular, this predicts that strongly nonhydrostatic waves are modulationally unstable and so the wave packet narrows and grows more rapidly in amplitude than the exponential anelastic growth rate. More hydrostatic waves are modulationally stable and so their amplitude grows less rapidly. The marginal case between stability and instability occurs for waves propagating at the fastest vertical group velocity. Extrapolating these results to waves propagating to higher altitudes (hence attaining larger amplitudes), it is anticipated that modulationally unstable waves should break at lower altitudes and modulationally stable waves should break at higher altitudes than predicted by linear theory. This prediction is borne out by fully nonlinear numerical simulations of the anelastic equations. A range of simulations is performed to quantify where overturning actually occurs.
Abstract
A new effect related to the evaluation of momentum deposition in conventional parameterizations of orographic gravity wave drag (GWD) is considered. The effect takes the form of an adjustment to the basic-state wind about which steady-state wave solutions are constructed. The adjustment is conservative and follows from wave–mean flow theory associated with wave transience at the leading edge of the wave train, which sets up the steady solution assumed in such parameterizations. This has been referred to as “self-acceleration” and it is shown to induce a systematic lowering of the elevation of momentum deposition, which depends quadratically on the amplitude of the wave. An expression for the leading-order impact of self-acceleration is derived in terms of a reduction of the critical inverse Froude number Fc , which determines the onset of wave breaking for upwardly propagating waves in orographic GWD schemes. In such schemes Fc is a central tuning parameter and typical values are generally smaller than anticipated from conventional wave theory. Here it is suggested that self-acceleration may provide some of the explanation for why such small values of Fc are required. The impact of Fc on present-day climate is illustrated by simulations of the Canadian Middle Atmosphere Model.
Abstract
A new effect related to the evaluation of momentum deposition in conventional parameterizations of orographic gravity wave drag (GWD) is considered. The effect takes the form of an adjustment to the basic-state wind about which steady-state wave solutions are constructed. The adjustment is conservative and follows from wave–mean flow theory associated with wave transience at the leading edge of the wave train, which sets up the steady solution assumed in such parameterizations. This has been referred to as “self-acceleration” and it is shown to induce a systematic lowering of the elevation of momentum deposition, which depends quadratically on the amplitude of the wave. An expression for the leading-order impact of self-acceleration is derived in terms of a reduction of the critical inverse Froude number Fc , which determines the onset of wave breaking for upwardly propagating waves in orographic GWD schemes. In such schemes Fc is a central tuning parameter and typical values are generally smaller than anticipated from conventional wave theory. Here it is suggested that self-acceleration may provide some of the explanation for why such small values of Fc are required. The impact of Fc on present-day climate is illustrated by simulations of the Canadian Middle Atmosphere Model.
Abstract
Some parameterizations of gravity wave mean flow forcing in global circulation models (GCMs) add realism by describing wave generation by tropospheric convection. Because the convection in GCMs is itself a parameterized process, these convectively generated wave parameterizations necessarily use many simplifying assumptions. In this work, the authors use a realistic simulation of wave generation by convection described in previous work, which was validated by observations from the Darwin Area Wave Experiment (DAWEX), to test these assumptions and to suggest some possible improvements to the parameterizations. In particular, the authors find that wave trapping in the troposphere significantly modifies the spectrum of vertically propagating waves entering the stratosphere above convective wave sources, and offer a linear method for computing wave transmission and reflection effects on the spectrum suitable for inclusion in the parameterizations. The wave fluxes originate from both a time-varying heating mechanism and an obstacle effect mechanism acting in the simulation. Methods for including both mechanisms in the parameterizations are described. Waves emanating from the obstacle effect remain very sensitive to the depth of penetration of latent heating cells into an overlying shear zone, which will continue to make it difficult to accurately parameterize in a GCM where the convective cells are not resolved.
Abstract
Some parameterizations of gravity wave mean flow forcing in global circulation models (GCMs) add realism by describing wave generation by tropospheric convection. Because the convection in GCMs is itself a parameterized process, these convectively generated wave parameterizations necessarily use many simplifying assumptions. In this work, the authors use a realistic simulation of wave generation by convection described in previous work, which was validated by observations from the Darwin Area Wave Experiment (DAWEX), to test these assumptions and to suggest some possible improvements to the parameterizations. In particular, the authors find that wave trapping in the troposphere significantly modifies the spectrum of vertically propagating waves entering the stratosphere above convective wave sources, and offer a linear method for computing wave transmission and reflection effects on the spectrum suitable for inclusion in the parameterizations. The wave fluxes originate from both a time-varying heating mechanism and an obstacle effect mechanism acting in the simulation. Methods for including both mechanisms in the parameterizations are described. Waves emanating from the obstacle effect remain very sensitive to the depth of penetration of latent heating cells into an overlying shear zone, which will continue to make it difficult to accurately parameterize in a GCM where the convective cells are not resolved.
Abstract
A theory is developed for the baroclinic destabilization of density-driven abyssal flows over topography in a rotating environment. The dominant instability mechanism being studied is the release of available potential energy caused by gradual downhill slumping of the abyssal current. The present model assumes a two-layer configuration and allows for intersections of the interface with the bottom (i.e., true fronts), as well as continuous stratification in the ambient fluid. The linear instability problem in a channel for a current with parabolic cross section is solved, and the perturbation growth rate and most unstable wavenumber are both shown to increase with current thickness. A similar trend is evident as the stratification number is increased or the current width is decreased. The instability manifests itself in the overlying ocean as an amplifying topographic Rossby wave. Alternating positive/negative pressure anomalies in the upper layer are accompanied by a wavelike deformation of the abyssal current that is most pronounced on the downslope side. Upper-layer vortical features have a distinct vertically tapered shape and are to be interpreted as bottom-intensified eddies. Long-term evolution of the flow is elucidated in a series of simulations employing the fully nonlinear governing equations. It is found that, even though the linear instability calculation relates to a periodic current, the instability characteristics are still valid to a good approximation for the case of a source flow. The abyssal current breaks up into a series of plumes that penetrate downslope into the deeper ocean, producing strong current fluctuations not unlike those observed in Denmark Strait overflow water. Furthermore, introduction of more realistic topography into the numerical simulation leads to the development of coherent baroclinic vortex pairs whose upper-layer component is strongly cyclonic.
Abstract
A theory is developed for the baroclinic destabilization of density-driven abyssal flows over topography in a rotating environment. The dominant instability mechanism being studied is the release of available potential energy caused by gradual downhill slumping of the abyssal current. The present model assumes a two-layer configuration and allows for intersections of the interface with the bottom (i.e., true fronts), as well as continuous stratification in the ambient fluid. The linear instability problem in a channel for a current with parabolic cross section is solved, and the perturbation growth rate and most unstable wavenumber are both shown to increase with current thickness. A similar trend is evident as the stratification number is increased or the current width is decreased. The instability manifests itself in the overlying ocean as an amplifying topographic Rossby wave. Alternating positive/negative pressure anomalies in the upper layer are accompanied by a wavelike deformation of the abyssal current that is most pronounced on the downslope side. Upper-layer vortical features have a distinct vertically tapered shape and are to be interpreted as bottom-intensified eddies. Long-term evolution of the flow is elucidated in a series of simulations employing the fully nonlinear governing equations. It is found that, even though the linear instability calculation relates to a periodic current, the instability characteristics are still valid to a good approximation for the case of a source flow. The abyssal current breaks up into a series of plumes that penetrate downslope into the deeper ocean, producing strong current fluctuations not unlike those observed in Denmark Strait overflow water. Furthermore, introduction of more realistic topography into the numerical simulation leads to the development of coherent baroclinic vortex pairs whose upper-layer component is strongly cyclonic.
Abstract
In Michigan in early 1977, an experiment was conducted to test the ability of silver iodide (AgI) ice nucleus curtains generated by vertical-fall pyrotechnics to produce clearings in supercooled stratus. A second objective of the experiment was to determine how well a clearing could be targeted over a preselected ground location. Previous stratus clearing tests had primarily involved curtains of dry ice particles or horizontal lines of AgI nuclei. Silver iodide pyrotechnics were chosen because of their logistical advantages over dry ice.
Results of the Michigan testing were favorable. Clearings were produced in cloud decks up to 1400 m thick and as warm as −8°C. In thicker cloud decks, glaciation occurred only to a depth equal to the fall distance of the pyrotechnics. There were indications of “overseeding” from the relatively poor visibility through the cleared area that likely was caused by high ice-crystal concentrations. Targeting was successful when accurate wind data were available.
Abstract
In Michigan in early 1977, an experiment was conducted to test the ability of silver iodide (AgI) ice nucleus curtains generated by vertical-fall pyrotechnics to produce clearings in supercooled stratus. A second objective of the experiment was to determine how well a clearing could be targeted over a preselected ground location. Previous stratus clearing tests had primarily involved curtains of dry ice particles or horizontal lines of AgI nuclei. Silver iodide pyrotechnics were chosen because of their logistical advantages over dry ice.
Results of the Michigan testing were favorable. Clearings were produced in cloud decks up to 1400 m thick and as warm as −8°C. In thicker cloud decks, glaciation occurred only to a depth equal to the fall distance of the pyrotechnics. There were indications of “overseeding” from the relatively poor visibility through the cleared area that likely was caused by high ice-crystal concentrations. Targeting was successful when accurate wind data were available.
Abstract
The weakly nonlinear evolution, stability, and overturning of horizontally and vertically localized internal gravity wave packets is examined for a nonrotating, anelastic atmosphere that is stationary in the absence of waves. The weakly nonlinear evolution is examined through the derivation of their wave-induced mean flow, which is used to formulate a nonlinear Schrödinger equation. The induced flow is manifest as a long, hydrostatic, bow wake-like disturbance, whose flow direction transitions from positive on the leading flank of the wave packet to negative on the trailing flank of the wave packet. As such, two-dimensional wave packets are always modulationally unstable. This instability results in enhanced amplitude growth confined to either the leading or trailing flank. Hence, when combined with anelastic growth predicted by linear theory, we anticipate two-dimensional waves will overturn either somewhat below or just above the heights predicted by linear theory. Numerical solutions of the Schrödinger equation are compared with the results of fully nonlinear simulations to establish the validity of the weakly nonlinear theory. Actual wave overturning heights are determined quantitatively from a range of fully nonlinear simulations.
Abstract
The weakly nonlinear evolution, stability, and overturning of horizontally and vertically localized internal gravity wave packets is examined for a nonrotating, anelastic atmosphere that is stationary in the absence of waves. The weakly nonlinear evolution is examined through the derivation of their wave-induced mean flow, which is used to formulate a nonlinear Schrödinger equation. The induced flow is manifest as a long, hydrostatic, bow wake-like disturbance, whose flow direction transitions from positive on the leading flank of the wave packet to negative on the trailing flank of the wave packet. As such, two-dimensional wave packets are always modulationally unstable. This instability results in enhanced amplitude growth confined to either the leading or trailing flank. Hence, when combined with anelastic growth predicted by linear theory, we anticipate two-dimensional waves will overturn either somewhat below or just above the heights predicted by linear theory. Numerical solutions of the Schrödinger equation are compared with the results of fully nonlinear simulations to establish the validity of the weakly nonlinear theory. Actual wave overturning heights are determined quantitatively from a range of fully nonlinear simulations.
