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NASA NTRS1986

Baroclinic instability in the presence of barotropic jets

A formalism is developed for the calculation of baroclinic instability for barotropically stable jets. The formalism is applied to jet versions of both the Eady and Charney problems. It is found that jets act to confine instabilities meridionally, thus internally determining meridional wave scales. Once this internally determined meridional scale is taken into account, results correspond plausibly to classical results without a jet. Consideration of the effect of such instabilities on the mean flow shows that they act to concentrate the jet barotropically while simultaneously reducing baroclinicity.

Ioannou, Petros↗

NASA NTRS1972

Mars - The effects of topography on baroclinic instability.

The effects of a sloping lower boundary on the quasi-geostrophic baroclinic instability model of Eady are considered. Although the analytical model is too simplified for direct application to Martian conditions, the results should be useful in the interpretation of observations and numerical experiments. For slope orientations of most interest on Mars, the wavelength, growth rate and heat fluxes associated with the most unstable waves are decreased. As a result, the radiative-dynamical equilibrium state is closer to radiative equilibrium than one would calculate for a model with a horizontal lower boundary.

Blumsack, S. L.↗

NASA NTRS1993

On radiating baroclinic instability of zonally varying flow

A quasi-geostrophic, two-layer, beta-plane model is used to study the baroclinic instability characteristics of a zonally inhomogeneous flow. It is assumed that the disturbance varied slowly in the cross-stream direction, and the stability problem was formulated as a 1D initial value problem. Emphasis is placed on determining how the vertically averaged wind, local maximum in vertical wind shear, and length of the locally supercritical region combine to yield local instabilities. Analysis of the local disturbance energetics reveals that, for slowly varying basic states, the baroclinic energy conversion predominates within the locally unstable region. Using calculations of the basic state tendencies, it is shown that the net effect of the local instabilities is to redistribute energy from the baroclinic to the barotropic component of the basic state flow.

Finley, Catherine A.↗

NASA NTRS1983

Three-dimensional baroclinic instability of a Hadley cell for small Richardson number

For the case of a baroclinic flow whose Richardson number, Ri, is of order unity, a three-dimensional linear stability analysis is conducted on the basis of a model for a thin, horizontal, rotating fluid layer which is subjected to horizontal and vertical temperature gradients. The Hadley cell basic state and stability analysis are both based on the Navier-Stokes and energy equations, and perturbations possessing zonal, meridional, and vertical structures are considered. An attempt is made to extend the previous theoretical work on three-dimensional baroclinic instability for small Ri to a more realistic model involving the Prandtl and Ekman numbers, as well as to finite growth rates and a wider range of the zonal wavenumber. In general, it is found that the symmetric modes of maximum growth are not purely symmetric, but have a weak zonal structure.

Antar, B. N.↗

NASA NTRS1984

Linear baroclinic instability in the Martian atmosphere

A spherical quasi-geostrophic model is used in an examination of linear baroclinic instability in such zonal-mean flows as those of the Martian atmosphere in winter, under both relatively nondusty and very dusty conditions. These zonal flows, which possess both vertical and meridional shear, are characterized by baroclinically unstable modes whose growth rates and phase speeds are generally consistent with available observations. The structures of the spherical modes are similar to those obtained for terrestrial zonal flows, if similar zonal wavelengths are compared. Zonally symmetric topography, like that of Mars' northern hemisphere, reduces linear growth rates without changing the most unstable scale. It also increases phase speeds.

Barnes, J. R.↗

NASA NTRS1984

Baroclinic instability in the Venus atmosphere

A three-dimensional, spherical, primitive equation eigenvalue model is used to investigate the baroclinic stability properties of the wind and temperature fields in the Venus atmosphere as measured by Pioneer Venus. It is found that baroclinic instability occurs in the region of the middle cloud deck. The most unstable modes have growth times less than eight days and are vertically confined to the region near the middle cloud layer. The most unstable baroclinic mode at zonal wavenumber 2 has characteristics similar to those observed for the high latitude rotating dipole thermal feature. Certain planetary scale baroclinic modes can penetrate to relatively high altitudes under the right circumstances, and may therefore explain some of the wave features observed between 60 and 90 km. For example, thermal oscillations with periods between four and seven days occurring at middle latitudes have characteristics which appear to be consistent with computed properties of planetary scale baroclinic modes.

Young, R. E.↗

NASA NTRS1985

Three-dimensional baroclinic instability of a Hadley cell for small Richardson number

A three-dimensional, linear stability analysis of a baroclinic flow for Richardson number, Ri, of order unity is presented. The model considered is a thin horizontal, rotating fluid layer which is subjected to horizontal and vertical temperature gradients. The basic state is a Hadley cell which is a solution of the complete set of governing, nonlinear equations and contains both Ekman and thermal boundary layers adjacent to the rigid boundaries; it is given in a closed form. The stability analysis is also based on the complete set of equations; and perturbation possessing zonal, meridional, and vertical structures were considered. Numerical methods were developed for the stability problem which results in a stiff, eighth-order, ordinary differential eigenvalue problem. The previous work on three-dimensional baroclinic instability for small Ri was extended to a more realistic model involving the Prandtl number, sigma, and the Ekman number, E, and to finite growth rates and a wider range of the zonal wavenumber.

Antar, B. N.↗

NASA NTRS1981

A WKB asymptotic analysis of baroclinic instability

A modest extension of conventional WKB methods of solving second-order differential equations asymptotically is developed and applied to the problem of baroclinic instability. Accurate results are obtained for the Charney problem using simple expressions. More important, the present expressions can be used immediately for a wide variety of basic velocity profiles.

Lindzen, R. S.↗

NASA NTRS1982

The baroclinic instability of highly structured one-dimensional basic states

A frictionless, adiabatic, quasi-geostrophic model on a beta-plane was employed to examine the baroclinic instability of highly structured one-dimensional basic states. Definitions of the model eigenvalue equation, the boundary conditions, and the fluxes and energetics are provided, and highly structured average wind speed and temperature profiles were selected to represent a wide range of latitudes. Attention was given to the instability source, wavelength, growth rate, phase velocity, steering levels, and the vertical structure of their amplitude, phase, meridional entropy transport, and conversion of potential-to-kinetic energy. Green modes, Charney-Eady modes, and the modes defined in the paper are examined in connection with the highly structured profiles. The eigenvalue approach is shown to be superior to the numerical time integration approach and necessary conditions for instabilities are defined.

Fullmer, J. W. A.↗

DOE OSTI2023

Hydrostatic and Non‐Hydrostatic Baroclinic Instability in the Dynamical Core of the DOE Global Climate Model

Abstract The dynamical core of the Department of Energy global climate model is used to understand the role of non‐hydrostatic dynamics in the simulation of dry and moist baroclinic waves. To reduce computational cost, the Diabatic Acceleration and REscaling approach is adopted. Scale analysis and numerical simulations suggest that the model solution is not distorted by the change of spherical metric terms due to the change of Earth radius, neither are the inter‐scale interactions strongly altered as indicated by the analysis of spectral flux. Compared with hydrostatic simulations, the onset of baroclinic instability is delayed under non‐hydrostatic dynamics as the associated weaker vertical motions tend to increase the critical wavelength and narrow the range of waves that can be baroclinically unstable. During the development of baroclinic waves, non‐hydrostatic dynamics tends to induce vertical motions in the upper troposphere, accelerating the eastward propagation of upper‐level ridges through their impact on local vorticity tendency. These processes reduce the westward tilt of the vertical ridge axes and suppress the conversion of mean flow available potential energy to eddy kinetic energy, leading to weaker baroclinic eddies than in hydrostatic simulations. The contrasts between hydrostatic and non‐hydrostatic settings hold in supplemental experiments that vary the background flow Rossby number, the amount of water vapor content and vertical resolution. We also find that mesoscale and smaller‐scale activities can be considerably under‐represented when the vertical resolution is limited to that typically used in global climate models.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1994

Baroclinic instability in the interiors of the giant planets: A cooling history of Uranus?

We propose a quasigeostrophic, baroclinic model for heat transport within the interior of a stably stratified Jovian planet, based on motion in thin cylindrical annuli. Density decreases from the center outward and is zero at the surface of the planet. In the homogeneous case (no core), we find instability for the poles hotter than the equator, but not for the reverse. If the motion is bounded by an impenetrable core, instability occurs for both cases. Much of the behavior can be explained by analogy to conventional baroclinic instability theory. Motivated by our results, we explore a possible connection between the highly inclined rotation axis of Uranus and its anomalously low surface heat flux. We assume that the planets formed hot. Our conjecture is that heat was efficiently convected outwards by baroclinic instability in Uranus (with the poles hotter than the equator), but not in the other three Jovian planets. The surface temperature was higher for the stably stratified case (Uranus), leading to a higher rate of infrared emission and faster cooling. Therefore, we propose that Uranus lost its internal heat sooner than Neptune because baroclinic motions, permitted by its inclination to the sun, were able to extract its internal heat while the surface was still warm.

Holme, Richard↗

NASA NTRS1981

Shallow baroclinic instability in the tropical oceans

A linear quasi-geostrophic stability analysis was performed. The stability is dependent on the shears between the first and second layers and between the second layer and the abyss. By computing the maximum growth rate as a function of the shears, the possibility of a shallow baroclinic instability is discovered. This stability is largely dependent on the shear between layers 1 and 2, and quite independent of the speed in layer 2. The scaling of the shears shown is applicable to 4 deg latitude. As in Philander's study, the stability region increases strongly as the equator is approached. This probably explains the advance of the thermal front out to the 4 to 5 deg latitude zone without development of eddies and their rather sudden development at 80 days.

Schopf, P. S.↗

NASA NTRS1984

Laboratory studies of baroclinic instability at small Richardson number

As part of the support program for the Atmospheric General Circulation Experiment, laboratory studies of baroclinic and other convective instabilities were performed for a thin layer of fluid between thermally conducting horizontal discs. There were three types of modes identified. The first has a spiral-arm appearance, and exists for large enough horizontal thermal forcing, weak enough static stability, and large enough rotation. The source of this wave is shown to be the Eady mode of instability. The second mode is due to convective instability in the thermal boundary layers which exist due to the thermally conducting horizontal boundaries. Finally, for strong enough negative static stability, thermal convection of the Benard type appears. The most significant result is that the symmetric (Solberg) mode was not found, even though the infinite-plane theory predicts this mode under certain experimental conditions.

Miller, T. L.↗

NASA NTRS1986

Viscous nongeostrophic baroclinic instability

Calculations have been performed of the (linear) stability of a baroclinic flow to three-dimensional perturbations. Both the simple Eady basic state and the rotating Hadley cell of Antar and Fowlis are considered. The independent influences of the Richardson (Ri), thermal Rossby (baroclinicity), Ekman, and Prandtl numbers are examined, as well as the influences of the angle of orientation of the horizontal wave vector and the wavelength. It is shown that if the wavelength is allowed to vary freely, disturbances of the Eady type are preferred (i.e., have greatest growth rate) unless Ri and Ekman numbers are small enough and the thermal Rossby number is large enough. In the latter case, disturbances whose angles of orientation are almost symmetric and whose wavelengths are mesoscale are preferred. If, on the other hand, the wavelength is fixed at a mesoscale size, only the symmetric and almost symmetric modes have growth. By allowing the wave vector orientation to deviate from purely symmetric, it is noted that the region of instability (i.e., critical Ri) is increased, the extent of which is greater for longer wavelength. For Prandtl number = 1, permitting the angle to be nonsymmetric demonstrates the existence of two maxima in growth rate at opposite angles of orientation and with very different energetics. For Prandtl number far enough from one and for large enough dissipation, only one of these two modes has positive growth rates. Growing oscillatory modes were found for some cases.

Miller, T. L.↗

DOE OSTI2024

Numerical Mixing Suppresses Submesoscale Baroclinic Instabilities Over Sloping Bathymetry

Abstract The impacts of spurious numerical salinity mixing on the larger‐scale flow and tracer fields are characterized using idealized simulations. The idealized model is motivated by realistic simulations of the Texas‐Louisiana shelf and features oscillatory near‐inertial wind forcing. can exceed the physical mixing from the turbulence closure in frontal zones and within the mixed layer. This suggests that simulated mixing processes in frontal zones are driven largely by . Near‐inertial alongshore wind stress amplitude is varied to identify a base case that maximizes the ratio of to in simulations with no prescribed horizontal mixing. We then test the sensitivity of the base case with three tracer advection schemes (MPDATA, U3HC4, and HSIMT) and conduct ensemble runs with perturbed bathymetry. Instability growth is evaluated using the volume‐integrated eddy kinetic energy and available potential energy . While all schemes have similar total mixing, the HSIMT simulations have over double the volume‐integrated and 20% less relative to other schemes, which suppresses the release of and reduces the by roughly 25%. This results in reduced isohaline variability and steeper isopycnals, evidence that enhanced suppresses instability growth. Differences in and between the MPDATA and U3HC4 simulations are marginal. However, the U3HC4 simulations have 25% more . Experiments with variable horizontal viscosity and diffusivity coefficients show that small amounts of prescribed horizontal mixing improve the representation of the ocean state for all advection schemes by reducing the and increasing the .

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1978

The effects of curvature and viscosity on baroclinic instability: A two-layer model

A linear stability analysis of a baroclinic zonal current contained between two parallel rigid boundaries is presented. Curvature is included by performing the analysis on a beta b-plane and viscosity by allowing for the effects of Ekman layers on the rigid boundaries. A two-layer model is used. This calculation was carried out to assist in the design of a spherical model of the general circulation of the earth's atmosphere for Spacelab. In the low-gravity environment on an orbiting vehicle, a dominant radial dielectric body force, analogous to planetary gravity, can be achieved over a volume of liquid held between two concentric spheres. The results show the Eady short wavelength cutoff, and long wavelength cutoffs due to Ekman damping and curvature.

Fowlis, W. W.↗

NASA NTRS1987

Linear baroclinic instability in the presence of large scale topography

The effect of a planetary-scale, wavenumber 2 topography on baroclinically active disturbances is investigated for a channel domain in a two-layer, quasi-geostrophic context. When the lower-layer zonal velocity is nonzero, the topography influences the disturbances by forcing a stationary wave, and the topography and the forced wave influence the growth rates and the spatial structures of the time-dependent solutions. The case of zero zonal velocity in the lower layer was also investigated, for which no forced wave exists. Asymptotic forms of the equations, valid when the topographic effect (governed by the ratio of the nondimensional topographic height to the rotational Froude number) is small, are used to obtain both the stationary and time-dependent solutions. The latter are also obtained using a numerical approach, in which is determined the eigenvalues and eigenfunctions of a matrix representing the dynamical equations. Agreement is good between the two approaches. Recent laboratory experiments with a baroclinic annulus in which there is a false bottom with wavenumber 2 topography, are used to select governing parameters. The simultaneous presence of a stationary forced wave of wavenumber 2 and a time-dependent baroclinic wave of wavenumber 4, which has wavenumber 2 and 6 sidebands due to the topography, yields a flow field that exhibits some principal features of the laboratory experiments. The position of the forced wave and the location of an excursion in latitude of the storm track show qualitative resemblance to those features observed in the atmosphere.

Reynolds, Nathaniel Dunton↗

NASA NTRS1980

The applicability of the piecewise linear current profile in the baroclinic instability problem

The applicability of the piecewise linear function in place of a similar smoothly-varying current profile is examined in the baroclinic context. Within the framework of small-perturbation linearization, the behavior of the vertical velocity and the horizontal divergence is analyzed at the discontinuity of the current shear. In the conventional geostrophic-type instability regime, the discontinuity in the horizontal divergence at the shear discontinuity is suppressed, and, therefore, the piecewise linear profile leads to a useful approximation to the true solution. In the symmetric-type instability regime, however, due to the magnified discontinuity in the horizontal divergence at the shear discontinuity, the solution thus obtained will show a major distortion, rendering the piecewise linear profile inadequate for modeling the smoothly-varying current profile. Using exemplary current profiles, numerical results are presented to demonstrate the behavior of the horizontal divergence near the discontinuity of current shear.

Hyun, J. M.↗