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- Author or Editor: Barry Saltzman x
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Abstract
A general solution is obtained for forced, stationary, quasi-geostrophic perturbations in an atmosphere having the main zonal-average characteristics of the winter troposphere and stratosphere. Special solutions along 45° N. latitude are obtained for idealized representations of forcing due to internal sources and sinks of heat and due to lower boundary airflow over topography. The results show how the solutions depend on the spatial scale of the disturbances. For example, on the long-wave side of a critical vector wave number corresponding to quasi-resonance, the disturbances forced by internal heating tilt eastward with height thereby transporting heat southward, and tend to increase in amplitude above the tropopause into the high stratosphere. The reverse is true for waves smaller than critical. Comparisons with observations suggest that the real atmospheric mean waves are combinations of modes from the two regimes. The energetics of the solutions are discussed.
Abstract
A general solution is obtained for forced, stationary, quasi-geostrophic perturbations in an atmosphere having the main zonal-average characteristics of the winter troposphere and stratosphere. Special solutions along 45° N. latitude are obtained for idealized representations of forcing due to internal sources and sinks of heat and due to lower boundary airflow over topography. The results show how the solutions depend on the spatial scale of the disturbances. For example, on the long-wave side of a critical vector wave number corresponding to quasi-resonance, the disturbances forced by internal heating tilt eastward with height thereby transporting heat southward, and tend to increase in amplitude above the tropopause into the high stratosphere. The reverse is true for waves smaller than critical. Comparisons with observations suggest that the real atmospheric mean waves are combinations of modes from the two regimes. The energetics of the solutions are discussed.
Abstract
The Oberbeck-Boussinesq equations are reduced to a two-dimensional form governing “roll” convection between two free surfaces maintained at a constant temperature difference. These equations are then transformed to a set of ordinary differential equations governing the time variations of the double-Fourier coefficients for the motion and temperature fields. Non-linear transfer processes are retained and appear as quadratic interactions between the Fourier coefficients. Energy and heat transfer relations appropriate to this Fourier resolution, and a numerical method for solution from arbitrary initial conditions are given. As examples of the method, numerical solutions for a highly truncated Fourier representation are presented. These solutions, which are for a fixed Prandtl number and variable Rayleigh numbers, show the transient growth of convection from small perturbations, and in all cases studied approach steady states. The steady states obtained agree favorably with steady-state solutions obtained by previous investigators.
Abstract
The Oberbeck-Boussinesq equations are reduced to a two-dimensional form governing “roll” convection between two free surfaces maintained at a constant temperature difference. These equations are then transformed to a set of ordinary differential equations governing the time variations of the double-Fourier coefficients for the motion and temperature fields. Non-linear transfer processes are retained and appear as quadratic interactions between the Fourier coefficients. Energy and heat transfer relations appropriate to this Fourier resolution, and a numerical method for solution from arbitrary initial conditions are given. As examples of the method, numerical solutions for a highly truncated Fourier representation are presented. These solutions, which are for a fixed Prandtl number and variable Rayleigh numbers, show the transient growth of convection from small perturbations, and in all cases studied approach steady states. The steady states obtained agree favorably with steady-state solutions obtained by previous investigators.
Abstract
A solution is given, in the form of influence functions, for the forced geostrophic response of the atmosphere to the combined effects of zonal asymmetries in (i) the lower boundary orography and (ii) the mean, geographically-fixed source field of heat and momentum originating from all causes including transient eddy transports. As such, the solution represents a generalization of the work of Smagorinsky, and Charney and Eliassen. No attempt is made to improve upon either the “β-plane” approximation or the quasi-geostrophic approximation.
As an example, calculations for two harmonic components of the complete Fourier representation are made, based on idealized distributions of the forcing functions suggested by observations. It is shown that a variety of modes of response are possible, all of which can contribute to a greater or lesser extent in accounting for the observed mean state.
Suggestions are made for improving the formalism and extending it into a more satisfactory theory of the observed normal state of the atmosphere.
Abstract
A solution is given, in the form of influence functions, for the forced geostrophic response of the atmosphere to the combined effects of zonal asymmetries in (i) the lower boundary orography and (ii) the mean, geographically-fixed source field of heat and momentum originating from all causes including transient eddy transports. As such, the solution represents a generalization of the work of Smagorinsky, and Charney and Eliassen. No attempt is made to improve upon either the “β-plane” approximation or the quasi-geostrophic approximation.
As an example, calculations for two harmonic components of the complete Fourier representation are made, based on idealized distributions of the forcing functions suggested by observations. It is shown that a variety of modes of response are possible, all of which can contribute to a greater or lesser extent in accounting for the observed mean state.
Suggestions are made for improving the formalism and extending it into a more satisfactory theory of the observed normal state of the atmosphere.
Abstract
The results of computations of the spectrum of the eddy kinetic energy, the angular momentum transport, and the transfer of kinetic energy between the eddies and the mean motion, for the month of January 1949, are presented. The calculations are based on geostrophic winds measured at the 500-mb level. Of greatest interest is the finding that, for the month, disturbances of wave-number three were of singular importance as a source of the energy of the mean zonal motion.
Abstract
The results of computations of the spectrum of the eddy kinetic energy, the angular momentum transport, and the transfer of kinetic energy between the eddies and the mean motion, for the month of January 1949, are presented. The calculations are based on geostrophic winds measured at the 500-mb level. Of greatest interest is the finding that, for the month, disturbances of wave-number three were of singular importance as a source of the energy of the mean zonal motion.
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Cross sections of the mean meridional wind for winter and summer along five latitudes (15°, 30°, 45°, 60° and 75°N) are presented, and their salient features described.
Abstract
Cross sections of the mean meridional wind for winter and summer along five latitudes (15°, 30°, 45°, 60° and 75°N) are presented, and their salient features described.
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Abstract
A simplified version of a previously described dynamical model governing global ice mass, atmospheric carbon dioxide, and mean ocean temperature (that may also be a proxy for some other CO2–controlling oceanic variable, e.g., nutrient supply) is shown to possess solutions, in a realistic parameter range, that can replicate the main features of the climatic variations implied by the full, two million years, Quarternary δ18O record. These variations include a major “transition” between a low-ice (δ18O, low variance mode before roughly 900 kyr BP to a high-ice (near 100 kyr period) variance mode after that time to the present. The model contains only three free parameters in this simplified form. No external earth-orbital forcing is prescribed; i.e., the model represents only internal dynamics. From the previous studies it seems clear that additional variance representing such features as the “rapid” deglaciation and the phase of the major Quaternary oscillation can be largely explained with no more than four additional parameters representing an internal asymmetry and the external periodic forcing. The present results, therefore, constitute a first-order account for the existence of the “ice age” fluctuations over the last two million years, including the concomitant variations of atmospheric CO2. The variations of mean ocean temperature (or a related VO2–controlling proxy variable) are also deduced and represent a side prediction of the model.
Abstract
A simplified version of a previously described dynamical model governing global ice mass, atmospheric carbon dioxide, and mean ocean temperature (that may also be a proxy for some other CO2–controlling oceanic variable, e.g., nutrient supply) is shown to possess solutions, in a realistic parameter range, that can replicate the main features of the climatic variations implied by the full, two million years, Quarternary δ18O record. These variations include a major “transition” between a low-ice (δ18O, low variance mode before roughly 900 kyr BP to a high-ice (near 100 kyr period) variance mode after that time to the present. The model contains only three free parameters in this simplified form. No external earth-orbital forcing is prescribed; i.e., the model represents only internal dynamics. From the previous studies it seems clear that additional variance representing such features as the “rapid” deglaciation and the phase of the major Quaternary oscillation can be largely explained with no more than four additional parameters representing an internal asymmetry and the external periodic forcing. The present results, therefore, constitute a first-order account for the existence of the “ice age” fluctuations over the last two million years, including the concomitant variations of atmospheric CO2. The variations of mean ocean temperature (or a related VO2–controlling proxy variable) are also deduced and represent a side prediction of the model.
Abstract
Because of the small net rates of energy flow involved in very long-term changes in ice mass (10−1 W m−2) it will be impossible to proceed in a purely deductive manner to develop a theory for these changes. An inductive approach will be necessary-perhaps beg formulated in terms of multi-component stochastic-dynamical systems of equations governing the variables and feedbacks thought to be relevant from qualitative physical reasoning (e.g., “conceptual models”). The output of such models should be required to conform as closely as possible to all lines of observational evidence on climatic change, have a predictive quality in the search for new observational evidence, and satisfy the general conservation laws and all the results of physical measurement of the fast response (high energy flux) processes that generally lead to diagnostic relationships.
A prototype of such an inductive model is described. This model is formulated as a nonlinear dynamical system governing three components: continental ice mass marine ice mass, and bulk ocean temperature. The solution is shown to have several properties in common with geological evidence for the variations of these quantities.
Abstract
Because of the small net rates of energy flow involved in very long-term changes in ice mass (10−1 W m−2) it will be impossible to proceed in a purely deductive manner to develop a theory for these changes. An inductive approach will be necessary-perhaps beg formulated in terms of multi-component stochastic-dynamical systems of equations governing the variables and feedbacks thought to be relevant from qualitative physical reasoning (e.g., “conceptual models”). The output of such models should be required to conform as closely as possible to all lines of observational evidence on climatic change, have a predictive quality in the search for new observational evidence, and satisfy the general conservation laws and all the results of physical measurement of the fast response (high energy flux) processes that generally lead to diagnostic relationships.
A prototype of such an inductive model is described. This model is formulated as a nonlinear dynamical system governing three components: continental ice mass marine ice mass, and bulk ocean temperature. The solution is shown to have several properties in common with geological evidence for the variations of these quantities.
