On the spectral distribution of kinetic energy in large-scale atmospheric flow

International audienceA one-dimensional form of the equation of motion with forcing and dissipation is formulated in the spectral domain and used to make long term integrations from which the spectral distribution of the kinetic energy is determined The forcing in the wave number domain is determined in advance and kept constant for the duration of the time integrations. The dissipation is proportional to the second derivative of the velocity. The applied equation is made non-dimensional by selecting a length scale from which the time scale and the velocity scale may be determined. The resulting equation contains no parameters apart from the forcing. The integrations use a large number of spectral components and no approximation is made with respect to the non-linear interaction among the spectral components. Starting from an initial state in which all the velocity components are set to zero the equation is integrated for a long time to see if it reaches a steady state. The spectral distribution of the kinetic energy is determined in the steady state, and it is found that the distribution, in agreement with observational studies, may be approximated by a power law of the form n-3 within certain wave number regions. The wave numbers for which the -3 power law applies is found between the region of maximum forcing and the dissipation range. The intensity of the maximum forcing is varied to see how the resulting steady state varies. In addition, the maximum number of spectral components is varied. However, the available computing power sets an upper limit to the number of components

On the development of baroclinic waves influenced by friction and heating

The influence of surface skin friction and a specific type of heating on the stability of baroclinic waves in a two-level, quasi-geostrophic model is investigated. It is found that the effect of friction alone changes the neutral stability curve in such a way that a broader band of wavelengths are unstable for a given value of the vertical windshear. The neutral stability curve is independent of the intensity of friction in this case. The effect of heating is to make all waves longer than a certain critical wave length unstable, but the amplification rate is very small for large values of the wavelength. The combined effect of friction and heating will in general tend to stabilize the waves. The amplification rate is investigated in all cases.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43246/1/24_2004_Article_BF00874891.pd

On the maintenance of the axisymmetric part of the flow in the atmosphere

The maintenance of the axisymmetric component of the flow in the atmosphere is investigated by means of a steady-state, quasi-geostrophic formulation of the meteorological equations. It is shown that the meridional variations in the time-averaged axisymmetric variables can be expressed as the sum of three contributions, one being due to the eddy heat transport, another to the eddy momentum transport, and a third to the convective-radiative equilibrium temperature which enters the problem through the specification of a Newtonian form of diabatic heating. The contributions by the large scale eddies are evaluated through the use of observed values for the eddy heat and momentum transports.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43251/1/24_2004_Article_BF00878865.pd

A link between reduced Barents-Kara sea ice and cold winter extremes over northern continents

The recent overall Northern Hemisphere warming was accompanied by several severe northern continental winters, as for example, extremely cold winter 2005/2006 in Europe and northern Asia. Here we show that anomalous decrease of wintertime sea ice concentration in the Barents-Kara (B-K) Seas could bring about extreme cold events like winter 2005/2006. Our simulations with the ECHAM5 general circulation model demonstrate that lower-troposphere heating over the B-K Seas in the Eastern Arctic caused by the sea ice reduction may result in strong anti-cyclonic anomaly over the Polar Ocean and anomalous easterly advection over northern continents. This causes a continental-scale winter cooling reaching -1.5°C, with more than three times increased probability of cold winter extremes over large areas including Europe. Our results imply that several recent severe winters do not conflict the global warming picture but rather supplement it, being in qualitative agreement with the simulated large-scale atmospheric circulation realignment. Furthermore, our results suggest that high-latitude atmospheric circulation response to the B-K sea ice decrease is highly nonlinear and characterized by transition from anomalous cyclonic circulation to anticyclonic one and then again back to cyclonic type of circulation as the B-K sea ice concentration gradually reduces from 100% to ice free conditions. We present a conceptual model which may explain the nonlinear local atmospheric response in the B-K Seas region by counter play between convection over the surface heat source and baroclinic effect due to modified temperature gradients in the vicinity of the heating area

A note on multiple flow equilibria

A set of ordinary differential equations describing a mechanical system subject to forcing and dissipation is considered. A topological argument is employed to show that if all time-dependent solutions of the governing equations are bounded, the equations admit N steady solutions, where N is a positive odd integer and where at least ( N −1)/2 of the steady solutions are unstable. The results are discussed in the context of atmospheric flows, and it is shown that truncated forms of the quasigeostrophic equations of dynamic meteorology and of Budyko-Sellers climate models satisfy the hypotheses of the theorem.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43139/1/24_2004_Article_BF00881609.pd

Recent Developments in Understanding Two-dimensional Turbulence and the Nastrom-Gage Spectrum

Two-dimensional turbulence appears to be a more formidable problem than three-dimensional turbulence despite the numerical advantage of working with one less dimension. In the present paper we review recent numerical investigations of the phenomenology of two-dimensional turbulence as well as recent theoretical breakthroughs by various leading researchers. We also review efforts to reconcile the observed energy spectrum of the atmosphere (the spectrum) with the predictions of two-dimensional turbulence and quasi-geostrophic turbulence.Comment: Invited review; accepted by J. Low Temp. Phys.; Proceedings for Warwick Turbulence Symposium Workshop on Universal features in turbulence: from quantum to cosmological scales, 200