Instability of planetary waves in a high vertical resolution model

Abstract

A high vertical resolution model is used to examine the instability of a baroclinic zonal flow and a finite amplitude topographically forced wave. Two families of unstable modes are found, consisting of zonally propagating most unstable modes, and stationary unstable modes. The former have time scale and spatial structure similar to baroclinic synoptic disturbances, but are localized in space due to interaction with the zonally asymmetric forcing. These modes transport heat efficiently in both the zonal and meridional directions. The second family of stationary unstable modes has characteristics of modes of low frequency variability of the atmosphere. They have time scales of 10 days and longer, and are of planetary scale with an equivalent barotropic vertical structure. The horizontal structure resembles blocking flows. They are maintained by available potential energy of the basic wave, and have large zonal heat fluxes. The results for both families of modes are interpreted in terms of an interaction between forcing and baroclinic instability to create favoured regions for eddy development. Applications to baroclinic planetary waves are also considered.     

The generation of baroclinic Rossby waves by stationary and and translating currents part 1. Stationary current forcing

Abstract

This paper investigates the generation of linear, baroclinic Rossby waves by an imposed current distribution, in a reduced gravity ocean, both with and without an eastern coast. A zonal current is impulsively applied and maintained along the northern edge of the domain of solution. Using Green's function techniques, analytical solutions are found, and these are evaluated for small times. Numerical solutions are obtained for larger times. The upper layer depth field consists of a transient response, due to the sudden application of the current. Maintenance of the current causes a response which is singular along the line of imposed non-zero h _y. The interior field decays with time (this is shown asymptotically). The parameters used are appropriate for the mid-latitude North Pacific, and the results are relevant to sudden transport changes in the North Pacific Current.     

Effects of wave-wave and wave-mean flow interactions on the evolution of a baroclinic wave

Abstract

The weakly nonlinear evolution of a free baroclinic wave in the presence of slightly supercritical, vertically sheared zonal flow and a forced stationary wave field that consists of a single zonal scale and an arbitrary number of meridional harmonics is examined within the context of the conventional two-layer model. The presence of the (planetary-scale) stationary wave introduces zonal variations in the supercriticality and is shown to alter the growth rate and asymptotic equilibrium of the (synoptic-scale) baroclinic wave via two distinct mechanisms: The first is due to the direct interaction of the stationary wave with the shorter synoptic wave (wave-wave mechanism), and the second is due to the interaction of the synoptic wave with that portion of the mean field that is corrected by the zonally rectified stationary wave fluxes (wave-mean mechanism). These mechanisms can oppose or augment each other depending on the amplitude and spatial structure of the stationary wave field. If the stationary wave field is confined primarily to the upper (lower) layer and consists of only the gravest cross-stream mode, conditions are favorable (unfavorable) for nonzero equilibrium of the free wave.

In addition to the time dependent heat flux generated by baroclinic growth of the free wave, its interaction with a stationary wave field consisting of two or more meridional harmonics generates time dependent heat fluxes that vary with period of the free wave. However, if the stationary wave field contains several meridional harmonics of sufficiently large amplitude, the free baroclinic wave is destroyed.     

The nonlinear stabilization of a zonal shear flow instability

Abstract

The development of initially small perturbations in a weakly supercritical zonal shear flow on a β-plane is studied. Two different scenarios of evolution are possible. If the supercriticality is sufficiently small, the growth of a perturbation is stopped in the viscous critical layer regime; for this case the evolution equation (corrected by the inclusion of a quintic nonlinearity) is derived. At greater supercriticality the nonlinearity cannot stop the growth of the perturbation in a linear (viscous or unsteady) critical layer regime, and the evolution is more complicated. Transition to a nonlinear critical layer regime leads to a reduction in the growth rate and to a slowing (but not a stopping) of the increase in amplitude, A. These are connected to the formation of a plateau (S=constant) of width L=O(A ^½) in the profile of absolute vorticity, S. Careful analysis reveals that the growth in amplitude ceases only when the whole instability domain (where the slope of unperturbed S-profile is positive) becomes covered again by the plateau.     

Symmetric baroclinic instability for small ekman numbers

Abstract

The stability of a zonal shear flow to symmetric baroclinic perturbations is examined when the Ekman number, E, is asymptotically small. It is assumed, following Antar and Fowlis (1982), that the zonal Row is generated by imposing a constant horizontal temperature gradient γ* at the horizontal boundaries, and by maintaining a constant temperature difference δT* between them. The boundaries are at rest relative to a rotating frame.

Features of the neutral stability curve are determined for several ranges of values of δT/E ^1/3, where δT = δT*/Hγ* and H is the depth of the fluid layer, and all values of the Prandtl number, [sgrave]. In some cases it is possible to determine the whole curve analytically. The most important feature of the results is that the neutral stability curve is closed.

The results are compared to the numerical integrations of Antar and Fowlis (1982). The qualitative features of the solutions are in accord and the quantitative results are, in most cases, as good as can be expected for E only as small as ～ 10^?4. The implications of the results for experimental observations of symmetric baroclinic instability are explored.     

Zonal shear flows with a free surface: Hamiltonian formulation and linear and nonlinear stability

General theoretical results via a Hamiltonian formulation are developed for zonal shear flows with the inclusion of the vortex stretching effect of the deformed free surface (equivalent barotropic model). These results include a generalization of the Flierl–Stern–Whitehead zero angular momentum theorem for localized nonlinear structures (whether or not on a β-plane), and sufficient conditions for linear and nonlinear stability in the Liapunov sense–the latter are given as estimates in terms of an L ²-type perturbation norm which are global in time and are derived via bounds on the equilibrium potential vorticity gradient.     

A case study of storm commencement and recovery plasmaspheric electric fields near L=2.5 at equinox

Data from the VLF Doppler experiment at Faraday, Antarctica (65○ S, 64○ W) are used to study the penetration of the high-latitude convection electric field to lower latitudes during severely disturbed conditions. Alterations of the electric field at L-values within the range 2.0 - 2.7 are studied for two cases at equinox (10 - 12 September 1986 and 1 - 3 May 1986). The recovery of the electric field is found to be approximately an exponential function of time. Values for the equatorial meridional E×B drift velocity, inferred from the data, are used as inputs to a model of the plasmasphere and ionosphere. The model and experimental results are used to investigate the post-storm alteration of ionospheric coupling processes. The magnitude of the effect of ionosphere-plasmasphere coupling fluxes on N_mF2 values and the O⁺-H⁺ transition height is dependent on the local time of storm commencement, and on the orientation of the electric field. The coupling fluxes appear to have a maximum influence on ionospheric content during the main phase of geomagnetic activity that produces outward motion of plasmaspheric whistler ducts.     

The zonal E×B plasma drift effects on the low latitude ionosphere electron density at solar minimum near equinox

The F2-layer peak density, NmF2, and peak altitude, hmF2, which were observed by 12 ionospheric sounders during the 20 September 1964 geomagnetically quiet time period at solar minimum are compared with those calculated by the three-dimensional time-dependent theoretical model of the Earth's low and middle latitude ionosphere and plasmasphere. The modeled NmF2 are also compared with those measured during the geomagnetically quiet time periods of 12–15, 18–21, and 26 September 1964 to take into account observed day-to-day ionospheric variability. Major features of the data are reproduced by the model if the corrected HWM90 neutral wind is used. The changes in NmF2 due to the zonal E×B plasma drift are found to be less than 20% in the daytime low latitude ionosphere. The model, which does not take into account the zonal E×B plasma drift, underestimates night-time NmF2 up to the maximum factor of 2 at low geomagnetic latitudes. The night-time increase of NmF2 caused by the zonal E×B plasma drift is less pronounced at −20° and 20° geomagnetic latitudes in comparison with that between −10° and 10° geomagnetic latitude. The longitude dependence of the calculated night-time low latitude influence of the zonal E×B plasma drift on NmF2 is explained in terms of the longitudinal asymmetry in B (the eccentric magnetic dipole is displaced from the Earth's center and the Earth's eccentric tilted magnetic dipole moment is inclined with respect to the Earth's rotational axis), and the variations of the wind induced plasma drift and the meridional E×B plasma drift in geomagnetic longitude. The difference between the hmF2 values calculated by including the effect of zonal E×B drift and that obtained when it is excluded does not exceed 19 km in the low latitude ionosphere. Over the geomagnetic equator the zonal E×B plasma drift produces the maximum increase in the electron density by a factor of 1.06–1.48 and 1.05–1.30 at 700 and 1000 km altitude, respectively, and this increase is not significant above about 1500 km. Changes in the vertical electron content, VEC, caused by the zonal E×B plasma do not exceed 16% during the day, while the value of the night-time VEC is increased up to a factor of 1.4 due to this drift. The maximum effects of the zonal E×B plasma drift on the night-time electron density derived from the model results corresponding to solar minimum and maximum are quite comparable.     

Solitary and cnoidal planetary waves

Abstract

A class of long planetary waves in a zonal channel analogous to the solitary and cnoidal waves of surface and internal gravity wave theory is discussed. On a mid-latitude β-plane, such waves exist as the result of divergence, non-uniform zonal velocity fields or bottom topography. In all cases studied the wave profile along the channel was found to satisfy the Korteweg-de Vries equation.     

Transitions to chaotic thermal convection in a rapidly rotating spherical fluid shell

Abstract

Numerical simulations of thermal convection in a rapidly rotating spherical fluid shell heated from below and within have been carried out with a nonlinear, three-dimensional, time-dependent pseudospectral code. The investigated phenomena include the sequence of transitions to chaos and the differential mean zonal rotation. At the fixed Taylor number T _a =10⁶ and Prandtl number Pr=1 and with increasing Rayleigh number R, convection undergoes a series of bifurcations from onset of steadily propagating motions SP at R=R _c = 13050, to a periodic state P, and thence to a quasi-periodic state QP and a non-periodic or chaotic state NP. Examples of SP, P, QP, and NP solutions are obtained at R = 1.3R _c , R = 1.7 R _c , R = 2R _c , and R = 5 R _c , respectively. In the SP state, convection rolls propagate at a constant longitudinal phase velocity that is slower than that obtained from the linear calculation at the onset of instability. The P state, characterized by a single frequency and its harmonics, has a two-layer cellular structure in radius. Convection rolls near the upper and lower surfaces of the spherical shell both propagate in a prograde sense with respect to the rotation of the reference frame. The outer convection rolls propagate faster than those near the inner shell. The physical mechanism responsible for the time-periodic oscillations is the differential shear of the convection cells due to the mean zonal flow. Meridional transport of zonal momentum by the convection cells in turn supports the mean zonal differential rotation. In the QP state, the longitudinal wave number m of the convection pattern oscillates among m = 3,4,5, and 6; the convection pattern near the outer shell has larger m than that near the inner shell. Radial motions are very weak in the polar regions. The convection pattern also shifts in m for the NP state at R = 5R _c , whose power spectrum is characterized by broadened peaks and broadband background noise. The convection pattern near the outer shell propagates prograde, while the pattern near the inner shell propagates retrograde with respect to the basic rotation. Convection cells exist in polar regions. There is a large variation in the vigor of individual convection cells. An example of a more vigorously convecting chaotic state is obtained at R = 50R _c . At this Rayleigh number some of the convection rolls have axes perpendicular to the axis of the basic rotation, indicating a partial relaxation of the rotational constraint. There are strong convective motions in the polar regions. The longitudinally averaged mean zonal flow has an equatorial superrotation and a high latitude subrotation for all cases except R = 50R _c , at this highest Rayleigh number, the mean zonal flow pattern is completely reversed, opposite to the solar differential rotation pattern.     

The structure of the natural stratosphere and the impact of chlorofluoromethanes on the ozone layer investigated in a 2-D time dependent model

two-dimensional time dependent model of the stratosphere incorporating the major interactions between radiative-photochemical and dynamical processes is described. The main prognostic equations considered are the thermodynamic equation and the general conservation equation for the minor chemical constituents representing the odd oxygen (O _x =O+('D)+O₃), odd hydrogen (HO _x =HO+HO₂), N₂O, odd nitrogen (NO _x =NO+NO₂+HNO₃), CF₂Cl₂, CFCl₃ and odd chlorine (Cl _x =Cl+ClO+HCl). The zonal wind and mean meridional circulations are determined diagnostically by the integration of the thermal wind equation and the stream function equation in the meridional plane espectively. The large scale eddy processes are parameterized in terms of zonal mean quantities using the generalized diffusion formulation on a sloping surface. The radiative heating and cooling and the hotochemical sources and sinks are incorporated in a form which allows for the major interactions among the minor trace constituents, temperature and mean circulation.Two integrations consisting of natural stratosphere and a stratosphere contaminated by the chlorofluoromethanes through lower boundary fluxes are carried out for 23 model years by changing the declination of the sun every day and using 6-hour time step. The model simulations of temperature, mean circulation, ozone, HO _x , N₂O and NO _x in the meridional plane for the normal stratosphere, show satisfactory agreement with the available observations. Based on the results of second integration it is found that the injection of chlorofluoromethanes in the atmosphere at the estimated current production rates can lead to significant changes in the meridional distribution of ozone, temperature and NO _x in the middle and upper stratosphere. The results also indicate that the percentage total ozone depletion increases from tropics to high latitudes and from summer to winter high latitudes. Also discussed are the results of additional experiments incorporating the reaction of HO₂ with NO and the reactions involving ClNO₃.     

A Reynolds-averaged turbulence modelling approach to the maintenance of the Venus superrotation

Abstract

A maintenance mechanism of an approximately linear velocity profile of the Venus zonal flow or superrotation is explored, with the aid of a Reynolds-averaged turbulence modelling approach. The basic framework is similar to that of Gierasch (Meridional circulation and maintenance of the Venus atmospheric rotation. J. Atmos. Sci. 1975, 32, 1038–1044) in the sense that the mechanism is examined under a given meridional circulation. The profile mimicking the observations of the flow is initially assumed, and its maintenance mechanism in the presence of turbulence effects is investigated from a viewpoint of the suppression of energy cascade. In the present work, the turbulent viscosity is regarded as an indicator of the intensity of the cascade. A novelty of this formalism is the use of the isotropic turbulent viscosity based on a non-local time scale linked to a large-scale flow structure. The mechanism is first discussed qualitatively. On the basis of these discussions, the two-dimensional numerical simulation of the proposed model is performed, with an initially assumed superrotation, and the fast zonal flow is shown to be maintained, compared with the turbulent viscosity lacking the non-local time scale. The relationship of the present model with the current general circulation model simulation is discussed in light of a crucial role of the vertical viscosity.     

The structure of separated flow past a circular cylinder in a rotating frame

Abstract

This paper examines the detailed E ^1/4-layer structure of separated flow past a circular cylinder in a low-Rossby-number rotating fluid as the Ekman number E tends to zero. This structure is based on an initial proposal by Page (1987) but with some modifications in response to further evidence, outlined both in this paper and elsewhere, on the behaviour of E ^1/4-layer flows in this context. Numerical calculations for flow in an E ^1/4 shear layer along the separated free streamline are described and the mass flux from this layer is then used to calculate the higher-order flow within the separation bubble. The flow structure is found to have two forms, depending on the value of the O(1) parameter λ, and these are compared with results from published “Navier-Stokes” type calculations for the flow at small but finite values of E.     

Spatial variability of the surface energy balance of Lake Kasumigaura and implications for flux measurements

ABSTRACT

The spatial variability of the lake surface energy balance and its causes are not well-understood. Energy balance maps (90 m resolution) of Lake Kasumigaura (172 km²), Japan, obtained by interpolating station data and bulk equations, allowed an investigation of these issues. Due to lake-scale variations in meteorological variables and small-scale fluctuations of surface temperature, T_s, surface heat fluxes differed horizontally at two distinct scales, while radiative fluxes were more uniform. As the key variable to surface flux T_s was only homogeneous for directions with a longer fetch or under calm wind conditions. Using these findings, the suitability of two flux station locations, one at the centre of the lake and another within a cove, was considered. Although both locations satisfied the fetch requirements, T_s was not always found to be homogeneous in the cove, making this location less suitable for flux measurements, an issue that, to date, has been overlooked.     

Nonlinear dynamics of a stellar dynamo in a spherical shell

Abstract

A simple mean-field model of a nonlinear stellar dynamo is considered, in which dynamo action is supposed to occur in a spherical shell, and where the only nonlinearity retained is the influence of the Lorentz forces on the zonal flow field. The equations are simplified by truncating in the radial direction, while full latitudinal dependence is retained. The resulting nonlinear p.d.e.'s in latitude and time are solved numerically, and it is found that while regular dynamo wave type solutions are stable when the dynamo number D is sufficiently close to its critical value, there is a wide variety of stable solutions at larger values of D. Furthermore, two different types of dynamo can coexist at the same parameter values. Implications for fields in late-type stars are discussed.     

Improved Vertical Streambed Flux Estimation Using Multiple Diurnal Temperature Methods in Series

Analytical solutions that use diurnal temperature signals to estimate vertical fluxes between groundwater and surface water based on either amplitude ratios (A_r) or phase shifts (Δ?) produce results that rarely agree. Analytical solutions that simultaneously utilize A_r and Δ? within a single solution have more recently been derived, decreasing uncertainty in flux estimates in some applications. Benefits of combined (A_rΔ?) methods also include that thermal diffusivity and sensor spacing can be calculated. However, poor identification of either A_r or Δ? from raw temperature signals can lead to erratic parameter estimates from A_rΔ? methods. An add‐on program for VFLUX 2 is presented to address this issue. Using thermal diffusivity selected from an A_rΔ? method during a reliable time period, fluxes are recalculated using an A_r method. This approach maximizes the benefits of the A_r and A_rΔ? methods. Additionally, sensor spacing calculations can be used to identify periods with unreliable flux estimates, or to assess streambed scour. Using synthetic and field examples, the use of these solutions in series was particularly useful for gaining conditions where fluxes exceeded 1 m/d.     

Seasonal variation of land–atmosphere coupling strength over the West African monsoon region in an atmospheric general circulation model

Abstract

The seasonal variation of land–atmosphere coupling strength has been examined using an extended series of atmospheric general circulation model (AGCM) simulations. In the Western Sahel of Africa, strong coupling strength for precipitation is found in April and May, just prior to and at the beginning of the monsoon season. At this time, heat and water fluxes from the surface are strongly controlled by land conditions, and the unstable conditions in the lower level of the troposphere, as induced by local land state, allow the surface fluxes to influence the variability of convective precipitation—and thus the timing of monsoon onset.

Editor Z. W. Kundzewicz

Citation Yamada, T.J., Kanae, S., Oki, T., and Koster, R.D., 2013. Seasonal variation of land–atmosphere coupling strength over the West African monsoon region in an atmospheric general circulation model. Hydrological Sciences Journal, 58 (6), 1276–1286.     

Advanced insights into sources of vertical velocity in the ocean

Estimating vertical velocity in the oceanic upper layers is a key issue for understanding ocean dynamics and the transport of biogeochemical elements. This paper aims to identify the physical sources of vertical velocity associated with sub-mesoscale dynamics (fronts, eddies) and mixed-layer depth (MLD) structures, using (a) an ocean adaptation of the generalized Q-vector form of the ω-equation deduced from a primitive equation system which takes into account the turbulent buoyancy and momentum fluxes and (b) an application of this diagnostic method for an ocean simulation of the Programme Océan Multidisciplinaire Méso Echelle (POMME) field experiment in the North-Eastern Atlantic. The approach indicates that w-sources can play a significant role in the ocean dynamics and strongly depend on the dynamical structure (anticyclonic eddy, front, MLD, etc.). Our results stress the important contribution of the ageostrophic forcing, even under quasi-geostrophic conditions. The turbulent w-forcing was split into two components associated with the spatial variability of (a) the buoyancy and momentum (Ekman pumping) surface fluxes and (b) the MLD. Process (b) represents the trapping of the buoyancy and momentum surface energy into the MLD structure and is identified as an atmosphere/oceanic mixed-layer coupling. The momentum-trapping process is 10 to 100 times stronger than the Ekman pumping and is at least 1,000 times stronger than the buoyancy w-sources. When this decomposition is applied to a filamentary mixed-layer structure simulated during the POMME experiment, we find that the associated vertical velocity is created by trapping the surface wind-stress energy into this structure and not by Ekman pumping.     

Disturbed vertical E×B plasma drifts in the equatorial F2 region at solar minimum deduced from observed NmF2 and hmF2 variations

Ground-based ionosonde and magnetic-field observations on the equatorial station Huancayo, ESRO4 neutral-composition measurements, and theoretical model calculations were used to analyze disturbed E×B vertical plasma drift during the phase of solar minimum in 1973. Vertical drifts calculated for disturbed days do not show the systematic decrease often mentioned in publications, and demonstrate strong dependence on IMF-B_z changes. It is confirmed with the help of our drift calculations that B_z turnings to a northward direction result in a decrease (up to reversal) of normal Sq (eastward during daytime and westward at nighttime) in the zonal component of electric field. Southward B_z excursions enhance normal E_y both in daytime and nighttime hours. Model predictions of E_y’s reaction to IMF-B_z changes are discussed.     

On the mechanism of the post-midnight winter NmF2 enhancements: dependence on solar activity

The mechanism of the N_mF₂ peak formation at different levels of solar activity is analyzed using Millstone Hill IS radar observations. The h_mF₂ nighttime increase due to thermospheric winds and the downward plasmaspheric fluxes are the key processes responsible for the N_mF₂ peak formation. The electron temperature follows with the opposite sign the electron density variations in this process. This mechanism provides a consistency with the Millstone Hill observations on the set of main parameters. The observed decrease of the nighttime N_mF₂ peak amplitude with solar activity is due to faster increasing of the recombination efficiency compared to the plasmaspheric flux increase. The E × B plasma drifts are shown to be inefficient for the N_mF₂ nighttime peak formation at high solar activity.