Search Results

You are looking at 1 - 10 of 37 items for :

  • Author or Editor: Peter H. Stone x
  • Journal of the Atmospheric Sciences x
  • Refine by Access: All Content x
Clear All Modify Search
Peter H. Stone

Abstract

Bergeron first suggested that atmospheric frontogenesis is caused by horizontal wind deformation fields acting on pre-existing horizontal temperature gradients. A three-dimensional time-dependent mathematical model of the atmosphere which incorporates this process through the initial conditions and boundary conditions is formulated. Dissipative processes are neglected and the equations are approximated by assuming that the Richardson number is initially large. The resulting equations are then solved analytically. The solution shows, under certain conditions, fronts developing with properties similar to many atmospheric fronts, thereby giving support to Bergeron's hypothesis.

Full access
Peter H. Stone

Abstract

The solutions of Eady's 1949 model of baroclinic stability are extended numerically to include the non-geostrophic perturbations which wore not covered by the analysis in Part I. It is found that the largest growth rates are never associated with these new perturbations, so the tentative conclusions of Part I are verified. The more exact numerical solutions lead only to slight quantitative modifications of the results of Part I. If we let Ri be the Richardson number, then the largest growth rates are associated with “geostrophic” baroclinic instability if Ri>0.950; with symmetric instability if ¼<Ri<0.950; and with Kelvin-Helmholtz instability if 0<Ri<¼. Geostrophic baroclinic instability and symmetric instability can exist simultaneously if 0.84<Ri<1, and symmetric instability and Kelvin-Helmholtz instability can exist simultaneously if 0<Ri<¼

Full access
Peter H. Stone

Abstract

No abstract available.

Full access
Peter H. Stone

Abstract

The results of Parts I and II are used to calculate the transports of heat and momentum that accompany growing baroclinic instabilities in Eady's model. The transports are calculated for both the conventional (“geostrophic”) kind of baroclinic instability and for symmetric instability, without any restriction on the stratification, as measured by the Richardson number. The transports are calculated consistently to second order in the amplitude expansion of stability theory, so that the transports are the sum of an eddy transport term and a mean transport term.

The results show that both kinds of instability always transport heat upward and poleward, and always transport zonal momentum downward. Under geostrophic conditions the horizontal transport of zonal momentum depends on the horizontal shear of the basic flow. This shear is neglected in Eady's model so the horizontal momentum transports calculated here only contain the non-geostrophic contribution to the transport. The results show that this non-geostrophic transport is always equatorward for geostrophic instability, but for symmetric instability it may be either equatorward or poleward depending on the value of the Richardson number. It is suggested that the equatorward transport of zonal momentum by geostrophic instability is a more likely mechanism for Jupiter's equatorial acceleration than the transport by symmetric instability.

Full access
Peter H. Stone

Abstract

It is suggested that the apparent lag of Jupiter's mean rotation rate in extratropical latitudes (System II) behind the rotation rate of Jupiter's radio emissions (System III) is caused by the difference between phase speeds and true speeds in extratropical latitudes. An estimate of the difference based on the formula for the phase speed of Rossby waves agrees with the difference calculated from the two rotation rates.

Full access
Peter H. Stone

Abstract

A parameterization for the fluxes of sensible heat by large-scale eddies developed in an earlier paper is incorporated into a model for the mean temperature structure of an atmosphere including only these fluxes and the radiative fluxes. The climatic changes in this simple model are then studied in order to assess the strength of the dynamical feedback and to gain insight into how dynamical parameters may change in more sophisticated climatic models. The model shows the following qualitative changes: 1) an increase in the solar constant leads to increased static stability, decreased dynamic stability, and stronger horizontal and vertical winds; 2) an increase in the amount of atmospheric absorption leads to decreased static and dynamic stability, and stronger horizontal and vertical winds; and 3) an increase in rotation rate leads to greater static and dynamic stability, weaker horizontal winds, and stronger vertical winds. The quantitative results provide support for the common assumption that the static stability remains constant during climatic changes. Twenty-five percent changes in the external parameters cause changes in the static stability of the order of only a few tenths of a degree per kilometer. The results also show that the assumption that the horizontal eddy flux can be represented by a diffusion law with a constant eddy coefficient is a bad one, because of the strong negative feedback in the eddy fluxes.

Full access
Peter H. Stone

Abstract

No abstract available.

Full access
Peter H. Stone

Abstract

Two-layer models of baroclinic instability predict that there is a critical temperature gradient separating conditions which are stable from those which are baroclinically unstable. In continuous models this critical gradient corresponds to a transition from conditions where the dominant baroclinic instabilities are inefficient at transporting heat to conditions where they are efficient. Zonal mean meridional temperature gradients in the atmosphere are compared with this critical gradient. For averages over periods longer than a few months the observed mid and mean tropospheric gradients never appreciably exceed the critical gradient. In fact they coincide remarkably closely with it in mid and high latitudes in all seasons in spite of strong seasonal changes in the forcing. This behavior shows that a very rapid transition must exist between conditions where eddy fluxes are inefficient to conditions where they are highly efficient. Thus, the primary effect of baroclinic eddies on the meridional temperature structure is to limit the gradients from becoming appreciably supercritical. This behavior allows one to take into account quite accurately the effect of the eddy fluxes on temperature structure without calculating the eddy fluxes explicitly, simply by adjusting the temperature gradients so that they never exceed the critical value. This baroclinic adjustment process is illustrated by incorporating it into a one-dimensional energy balance climate model. The results show that the process enhances the stability of the current climate to changes in the solar constant.

Full access
Peter H. Stone

Abstract

The problem of the steady symmetric motion of a Boussinesq fluid is considered for a system with small aspect ratio. It is assumed that the motion is driven by applying a periodic heat flux to the horizontal boundaries. Solutions are first found for a non-rotating system in which nonlinear effects are small, but not zero. The solutions show that if the fluid is heated from above, the meridional circulation tends to be concentrated near the upper boundary at the point where the cooling is a maximum; when the fluid is heated from below the meridional circulation tends to be concentrated near the lower boundary at the paint where the heating is a maximum.

Then, it is shown for a non-rotating system that when nonlinear effects are dominant, vertical boundary layers must form. These vertical boundary layers form at points where the horizontal velocity is zero, and are characterized by small horizontal velocities and temperature gradients, but large vertical velocities and horizontal diffusion. By means of scaling analysis, the scales and magnitudes of the variables are determined for both the internal boundary layers and the boundary layers along the horizontal boundaries, when nonlinear effects are dominant.

Next, the effect of rotation is considered, and it shown that exactly the same sorts of vertical boundary layers will form in a rotating system. Scaling analysis is again used to show that in this case the horizontal boundary layers near the internal boundary layers are of the same kind as in the non-rotating case, but far enough away from the internal boundary layers they merge into a nonlinear Ekman layer.

Finally, some possible geophysical applications are considered. The model of the atmospheric circulations on Venus proposed by Goody and Robinson is found to agree qualitatively with the results presented here, but the quantitative results for the internal boundary layer, or mixing region, are found to differ considerably. Also, estimates are made for the internal boundary layer which would accompany a Hadley cell similar to that found in the earth's tropical region. It is found that the rising motions will occur over a region about 200 km in width. This result suggests that the nonlinear process which produces these internal boundary layers may be one of the important processes in determining the structure of the Intertropical Convergence Zone. Finally, the identification of the narrow sinking regions as another example of the kind of internal boundary layer studied here is considered, but in this case the magnitudes and scales are not plausible.

Full access
Peter H. Stone

Abstract

The hypothesis that the zonal motions in the Jovian atmosphere are thermal winds and that the latitudinal cloud bands are caused by baroclinic instabilities under nongeostrophic conditions is investigated. The stability theory is modified to take into account deep atmosphere effects. Comparison with observations indicates that the hypothesis is feasible, although very speculative in view of our present ignorance of Jovian conditions. In order to cheek the hypothesis, “dishpan” experiments at small values of the Richardson number and a better knowledge of the temperature distribution in the cloud layer and of the widths of the cloud bands at high resolutions would he particularly useful.

Full access