Form-drag instability in a barotropic and a baroclinic atmosphere

We discuss the form-drag instability for a quasi-geostrophic channel flow. We first study the characteristics of this instability in a barotropic flow, considering in detail the influence of the meridional scale and discussing which structure of the perturbation zonal flow must be chosen in order to describe properly this instability.We then consider a continuous quasi-geostrophic channel model in which the topography enters only through the bottom boundary condition, and we discuss how in this case the effects of the form-drag are felt by the mean zonal flow through the ageostrophic mean meridional circulation. Because the meridional structure of the perturbation zonal flow cannot simply be extended from the barotropic to the continuous case, we show how to modify it properly.We then study the baroclinic model in the particular case of constant (in the vertical) basic-state zonal flow and show how this case closely resembles the barotropic, demonstrating the barotropic nature of the form-drag instability.Symbols _t is the partial derivative with respect tot. - _x is the partial derivative with respect tox. - _y is the partial derivative with respect toy. - represents the geostrophic stream function. - u is the eastward component of the geostrophic wind. - v is the northward component of the geostrophic wind. - u _a is the eastward component of the ageostrophic wind. - v _a is the northward component of the ageostrophic wind. - w is the vertical component of the wind. - f is the Coriolis parameter=2 sin f _o+y. - f _o is the Coriolis parameter evaluated at mid-latitude. - N is the Brunt-Vaisala frequency. - [A] is the zonal (x) average ofA at constantp andy. - <A> is the horizontal (x andy) average ofA at constantp     

Rossby-Haurwitz's equation for the conservation of vertical vorticity component in the baroclinic atmosphere

Summary It is shown that the conservation equation of potential vorticity in the barotropic atmosphere holds good, even in the baroclinic atmosphere, if it is permissible to introduce the isentropic and mass-conservation approximations.     

Interaction of two baroclinic waves as a result of the daily variation of the stability of the atmosphere

Summary A schematic theoretical explanation of one type of cyclogenesis, described in detail in [1], is presented. From a theoretical point of view, a parameteric instability of a system of two baroclinic waves (a synoptic trough and a sub-synoptic, locally conditioned wave), associated with the daily variation of the vertical stratification of the atmosphere, is involved. The theoretical possibility of explaining the interaction of the waves itself, based on the outflow of cold air from the region of the trough towards the sub-synoptic wave (the so-called jump of the cold front), is investigated.     

Some laboratory model experiments on the mechanism of two-dimensional momentum transfer in the atmosphere

Summary Investigating the jetstream formation in the upper troposphere, it becomes evident that two-dimensional transfer processes are, to a high degree, responsible for the accumulation of kinetic energy and momentum in those upper tropospheric regions. To shed light on these processes a series of barotropic model experiments has been carried out using a special dynamic procedure for vortex generation. In a large, rotating, cylindrical vessel (filled with water, rotation rate ₀) three smaller cylinders have been fitted eccentrically. Their rotation relative to the vessel (rotation rate _i ,i=1, 2, 3) produces a sharply limited narrow region around each of them, where a nearly two-dimensional relative motion can be observed. Beyond this region — we call it friction zone — there is no motion. Now if we impose some perturbation on this steady mean flow (e.g. by setting _i = 0) the zonal current breaks down into a definite number of vortices which show a random distribution. The dynamic behaviour of these nearly two-dimensional vortices can then be studied.The main results are: I) After the sudden breakdown of the friction zones the most intensive eddies, which are cyclonic, drift more or less directly towards the centre to be organized there into a larger vortex. This development is strongly influenced by the -effect and the ratio = _i /₀, which controls the supply of rotational energy. II) If there exists a steady zonal basic current, the vortices will be more and more deformed when approaching and penetrating the zonal flow until they are wholly incorporated.     

Barotropic model of the atmosphere and seasonal changes of the lod

Summary The spherical barotropic model in combination with angular momentum conservation in the Earth-atmosphere system is used to calculate the difference in the LOD between winter and summer.     

Cosmic ray-induced ionization in the atmosphere: spatial and temporal changes

Detailed calculations of the time-variable spatial distribution of cosmic ray-induced ionization of the lower atmosphere are presented using a physical model. Using the differential energy spectrum of cosmic rays obtained from the worldwide neutron monitor network since 1951 and taking into account also the slow changes in the geomagnetic dipole, we have calculated the corresponding 3D (geographical coordinates and altitude) equilibrium ion concentration in the lower atmosphere as a function of time for the period 1951–2000. A comparison to the results of measurements validates the calculation method, as the calculated cosmic ray-induced ionization reproduces in general the observed altitudinal and latitudinal profiles of the ion concentration. The results of the present work provide a basis for a quantitative study of the solar–terrestrial relationships on long time scales.     

Diffusive destabilisation of the baroclinic circular vortex

Abstract

It is shown that, even for vanishingly small diffusivities of momentum and heat, a rotating stratified zonal shear flow is more unstable to zonally symmetric disturbances than would be indicated by the classical inviscid adiabatic criterion, unless σ, the Prandtl number, = 1. Both monotonic instability, and growing oscillations ("overstability") are involved, the former determining the stability criterion and having the higher growth rates. The more σ differs from 1, the larger the region in parameter space for which the flow is stable by the classical criterion, but actually unstable.

If the baroclinity is sufficiently great for the classical criterion also to indicate instability, the corresponding inviscid adiabatic modes usually have the numerically highest growth rates. An exception is the case of small isotherm slope and small σ.

A single normal mode of the linearized theory is also, formally, a finite amplitude solution; however, no theoretical attempt is made to assess the effect of finite amplitude in general. But, in a following paper, viscous overturning (the mechanism giving rise to the sub‐classical monotonic instability when σ > 1) is shown to play an important role at finite amplitude in certain examples of nonlinear steady thermally‐driven axisymmetric flow of water in a rotating annulus. Irrespective of whether analogous mechanisms turn out to be identifiable and important in large‐scale nature, it appears then that a Prandtl‐type parameter should enter the discussion of any attempt to make laboratory or numerical models of zonally‐symmetric baroclinic geophysical or astrophysical flows.     

Mid-latitude summer response of the middle atmosphere to short-term solar UV changes

Temperature and wind data obtained with Rayleigh lidar since 1979 and Russian rockets since 1964 are analyzed to deduce the summer response of the middle atmosphere to short-term solar UV changes. The equivalent width of the 1083 nm He I line is used as a proxy to monitor the short-term UV flux changes. Spectral analyses are performed on 108-day windows to extract the 27-day component from temperature, wind and solar data sets. Linear regressions between these spectral harmonics show some significant correlations around 45 km at mid-latitudes. For large 27-day solar cycles, amplitudes of 2 K and 6 m s⁻¹ are calculated for temperature data series over the south of France (44°N), and on wind data series over Volgograd (49°N), respectively. Cross-spectrum analyses have indicated correlations between these atmospheric parameters and the solar proxy with a phase lag of less than 2 days. These statistically correlative results, which provide good qualitative agreement with numerical simulations, are both obtained at mid-latitude. However, the observed amplitudes are larger than expected, with numerical models suggesting that dynamical processes such as equatorial or gravity waves may be responsible.     

Transverse baroclinic oscillations in Lake Überlingen

An episode of velocity measurements in the epilimnion at a midlake station in Lake Überlingen and taken from the campaign in October 1972 discloses a uni-nodal Poincaré-type baroclinic mode response with a 4 h period. We discuss the data and interpret it in terms of a two-layered linear wave model on the rotating Earth.

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Wave-induced topographic formstress in baroclinic channel flow

Large-scale zonal flow driven across submarine topography establishes standing Rossby waves. In the presence of stratification, the wave pattern can be represented by barotropic and baroclinic Rossby waves of mixed planetary topographic nature, which are locked to the topography. In the balance of momentum, the wave pattern manifests itself as topographic formstress. This wave-induced formstress has the net effect of braking the flow and reducing the zonal transport. Locally, it may lead to acceleration, and the parts induced by the barotropic and baroclinic waves may have opposing effects. This flow regime occurs in the circumpolar flow around Antarctica. The different roles that the wave-induced formstress plays in homogeneous and stratified flows through a zonal channel are analyzed with the BARBI (BARotropic-Baroclinic-Interaction ocean model, Olbers and Eden, J Phys Oceanogr 33:2719–2737, 2003) model. It is used in complete form and in a low-order version to clarify the different regimes. It is shown that the barotropic formstress arises by topographic locking due to viscous friction and the baroclinic one due to eddy-induced density advection. For the sinusoidal topography used in this study, the transport obeys a law in which friction and wave-induced formstress act as additive resistances, and windstress, the effect of Ekman pumping on the density stratification, and the buoyancy forcing (diapycnal mixing of the stratified water column) of the potential energy stored in the stratification act as additive forcing functions. The dependence of the resistance on the system parameters (lateral viscosity ε, lateral diffusivity κ of eddy density advection, Rossby radius λ, and topography height δ) as well as the dependence of transport on the forcing functions are determined. While the current intensity in a channel with homogeneous density decreases from the viscous flat bottom case in an inverse quadratic law ~δ ^–2 with increasing topography height and always depends on ε, a stratified system runs into a saturated state in which the transport becomes independent of δ and ε and is determined by the density diffusivity κ rather than the viscosity: κ/λ ² acts as a vertical eddy viscosity, and the transport is λ ²/κ times the applied forcing. Critical values for the topographic heights in these regimes are identified.     

Solar cycle changes to planetary wave propagation and their influence on the middle atmosphere circulation

Recent observations suggest that there may be a causal relationship between solar activity and the strength of the winter Northern Hemisphere circulation in the stratosphere. A three-dimensional model of the atmosphere between 10–140 km was developed to assess the influence of solar minimum and solar maximum conditions on the propagation of planetary waves and the subsequent changes to the circulation of the stratosphere. Ultraviolet heating in the middle atmosphere was kept constant in order to emphasise the importance of non-linear dynamical coupling. A realistic thermo-sphere was achieved by relaxing the upper layers to the MSIS-90 empirical temperature model. In the summer hemisphere, strong radiative damping prevents significant dynamical coupling from taking place. Within the dynamically controlled winter hemisphere, small perturbations are reinforced over long periods of time, resulting in systematic changes to the stratospheric circulation. The winter vortex was significantly weakened during solar maximum and western phase of the quasi-biennial oscillation, in accordance with reported 30 mb geopotential height and total ozone measurements.     

Variability of baroclinic tidal currents on the Mackenzie Shelf,the Southeastern Beaufort Sea

Semidiurnal tidal currents on the outer shelf of the Mackenzie Shelf in the Beaufort Sea were found to be strongly influenced by the locally generated baroclinic tide. Two primary factors are involved in this process: (1) the sharp shelf break along the northeastern Mackenzie Shelf, promoting the generation of vigorous internal tidal waves; and (2) the proximity to critical latitudes for M₂ and N₂ motions locking these waves and preventing them from leaving the source region. As a result, internal tides are resonantly trapped between the shelf and critical latitudes. The physical properties and temporal variations of tidal motions were examined using current meter measurements obtained from 1987–1988 at four sites (SS1, SS2, SS3, and SS4) offshore of the shelf break at depths of ∼200 m. Each mooring had Aanderaa RCM4s positioned at ∼35 m below the surface and ∼50 m above the bottom. Complex demodulation was used to compute the envelopes (amplitude modulation) of these components. A striking difference in the variability of clockwise (CW) and counterclockwise (CCW) tidal currents was found. The CW tides are highly variable, have greater amplitude, exhibit a burst-like character associated with wind events and contain about 80% of the total energy of the semidiurnal tidal currents. In contrast, the CCW components have a more regular temporal regime with distinct monthly, fortnightly and 10-day modulation at astronomical periodicities associated with frequency differences M₂–N₂ (0.03629 cpd), S₂–M₂ (0.06773 cpd), and S₂–N₂ (0.10402 cpd). Significant horizontal correlation of the CW current envelopes was found only between stations near the northeast Mackenzie Shelf, indicating this to be the main area of baroclinic internal wave generation.     

Effects of surface drag on low-level frontogenesis within baroclinic waves

Using a three-dimensional nonhydrostatic mesoscale numerical model (MM5), the evolution and structures of baroclinic waves with and without surface drag in case of dry and moist atmosphere are simulated, with special emphases on the effects of surface drag on the low-level frontal structure and frontogenesis. There are two different effects of surface drag on the low-level frontogenesis in the dry case. On one hand, the surface drag weakens the low-level frontogenesis and less inclined to develop the baroclinic wave due to the dissipation. But on the other hand, the surface drag induces a strong ageostrophic flow, which prolongs the low-level frontogenesis and finally leads to the enhancement of cold front. Compared with the no surface drag case, the surface drag increases the frontal slope espe- cially in the boundary layer, where the front is almost vertical to the surface, and then enhances the prefrontal vertical motion. All these conclusions expanded the analytical theory of Tan and Wu (1990). In the moist atmosphere, the influence of surface drag on frontal rainbands is also obvious. The surface drag weakens the convection, and reduces the energy dissipation near the surface when the initial relative humidity is relatively weak. At this time, the confluence induced post-frontal updrafts moves across the cold front and reinforces the prefrontal convection, which is beneficial to the maintenance of the rainband in cold sector. Given the enhancement of relative humidity, the moist convection domi- nates the low-level frontogenesis while the retardation of surface drag on energy dissipation is not obvious, therefore the effects of surface drag on the low-level frontogenesis and precipitation are re- duced.     

A note on the deflection of a baroclinic current by a continental shelf

The deflection, at a step-shelf fronted coast, of a constant potential vorticity current in a reduced-gravity, inviscid model ocean is studied theoretically. The step shelf, with a depth smaller than the reservoir depth, forces the uplifting of the approaching current and causes water column foreshortening, leading to relative vorticity generation that enhances current deflection to the right (facing the coast). As a consequence, in comparison to the case of a vertical wall coast, the proportion of the transport to the right is increased. For normal incidence for a shelf-depth/reservoir-depth ratio of 0.3 and shelf width to deformation radius ratio of 1.5, more than 90% of the approaching current transport goes to the right and less than 10% to the left. In addition, the (barotropic) dynamic pressure at the coast is low to the right and high to the left (with the highest pressure at the stagnation point). In the vertical wall case, the wall pressures on the flank are equal. For oblique incidence from the left, the deflection to the left is drastically reduced. In fact, there is practically no steady-state flow diverted to the left (less than 2%) when the approach angle is greater than 60° to the left of normal. In the vertical wall case, the same angle would have to be 90° for the flow to the left to vanish, namely only when the approach current is parallel to the coast to the right.     

Terrestrial transect study on driving mechanism of vegetation changes

In terms of Chinese climate-vegetation model based on the classification of plant functional types, to- gether with climatic data from 1951 to 1980 and two future climatic scenarios (SRES-A2 and SRES-B2) in China from the highest and the lowest emission scenarios of greenhouse gases, the distribution patterns of vegetation types and their changes along the Northeast China Transect (NECT) and the North-South Transect of Eastern China (NSTEC) were simulated in order to understand the driving mechanisms of vegetation changes under climatic change. The results indicated that the vegetation distribution patterns would change significantly under future climate, and the major factors driving the vegetation changes were water and heat. However, the responses of various vegetation types to the changes in water and heat factors were obviously different. The vegetation changes were more sensi- tive to heat factors than to water factors. Thus, in the future climate warming will significantly affect vegetation distribution patterns.     

A note on the necessary condition for baroclinic instability of monsoon zonal current

Analytic expressions are derived for the minimum easterly and westerly jet strengths necessary for baroclinic instability, in terms of their half-widths and location. For this purpose the necessary condition for an internal jet is utilized and the jets and static stability are represented by simple mathematical functions. Dependency of the minimum jet strengths to their half-width and location are discussed.     

Ocean and atmosphere changes in the Caribbean Sea during the twenty-first century using CMIP5 models

Ocean Dynamics - Coastal communities around the Caribbean Sea are vulnerable to global warming impacts, partly because of constraints on their adaptive capacity. We use three climate models...     

Laboratory experiments in a baroclinic annulus with heating and cooling on the horizontal boundaries

Abstract

Experiments have been performed in a cylindrical annulus with horizontal temperature gradients imposed upon the horizontal boundaries and in which the vertical depth was smaller than the width of the annulus. Qualitative observations were made by the use of small, suspended, reflective flakes in the liquid (water).

Four basic regimes of flow were observed: (1) axisymmetric flow, (2) deep cellular convection, (3) boundary layer convective rolls, and (4) baroclinic waves. In some cases there was a mix of baroclinic and convective instabilities present. As a “mean” interior Richardson number was decreased from a value greater than unity to one less than zero, axisymmetric baroclinic instability of the Solberg type was never observed. Rather, the transition was from non-axisymmetric baroclinic waves, to a mix of baroclinic and convective instability, to irregular cellular convection.