Geostrophic Adjustment Process Research Articles

Wave-vortex dynamics in rotating shallow water

We investigate how two-dimensional turbulence is modified when the incompressibility constraint is removed, by numerically integrating the full Saint-Venant (shallow-water) equations. In the case of small geopotential fluctuations considered here, we find no energy exchange between the inertio-gravitational and the potentio-vortical components of the flow. At small scales, the potentio-vortical component behaves as if the flow were incompressible, while we observe an intense direct energy cascade within the inertio-gravitational component. At large scales, the reverse potentio-vortical energy cascade is reduced when the level of inertio-gravitational energy is high. Looking at the effect of rotation, we find that a fast rotation rate tends to inhibit all three cascades. In particular, the inhibition of the inertio-gravitational energy cascade towards small scales implies that the geostrophic adjustment process is hindered by an increase of rotation. Concerning the structure of the coherent vortices emerging out of these decaying turbulent flows, we observe that the smallest scales are concentrated inside the vortex cores and not on their periphery.

Numerical Study of an Observed Orogenic Mesoscale Convective System. Part 2: Analysis of Governing Dynamics

Abstract A detailed analysis of the dynamics and thermodynamics responsible for the structure, growth and propagation of an orogenic mesoscale convective system simulated in two dimensions is made. The process of scale interaction is addressed through Fourier analysis and Reynolds averaging analysis of representative predicted variables, diabatic forcing and momentum acceleration terms. Additional dynamical analysis is accomplished through sensitivity experiments in which Coriolis, diabatic heating and ambient airflow are varied. The general conclusion is that the simulated orogenic development is a geostrophic adjustment process to convective heating which is itself modulated and maintained by orographically induced flow systems. The heating scales range over a nearly continuous spectrum ranging from 10–250 km. The heating occurs in response to primary advective gravity modes. The larger-scale gravity-wave disturbances modulate the smaller scales by organizing mean upward vertical motion patterns. The la...

Wind fluctuations near a cold vortex-tropopause funnel system observed by the MU radar

Vertical and temporal variations of three-dimensional wind velocity associated with an upper-tropospheric cold vortex-tropopause funnel system were observed by an MST radar in Japan (the MU radar). Marked changes of vertical velocity and horizontal wind direction were found between the inside and outside of the cold vortex. The vertical velocity activity outside the vortex was asymmetric; it was most active in a sector before the vortex. Unsaturated internal gravity waves in their generation stage contribute predominantly to the vertical velocity activity, suggesting that tropospheric occluded cyclones may be a possible source of middle-atmospheric gravity waves through the geostrophic adjustment process.

A Mesoscale Gravity Wave Event Observed during CCOPE. Part III: Wave Environment and Probable Source Mechanisms

Synoptic and special mesoscale observations taken during the Cooperative Convective Precipitation Experiment (CCOPE) are used to describe the multiscale environment of a gravity wave event, understand the wave-environment interactions that led to the development of severe thunderstorms, and asses possible wave-generation mechanisms. The storms formed sequentially as a packet of gravity waves propagated across a stationary thunderstorm outflow boundary. Convection developed most rapidly in that part of the mesonetwork in which existed the combination of relatively high parcel buoyant energy, weak restraining inversion, strong storm downdraft potential, and substantial vertical wind shear (associated with a mesoscale jet streak). Synoptic-scale analysis reveals that the waves were excited north of a stationary front and within the right exit region of the jet streak as it approached a stationary ridge in the 300 mb height field. Strong indications of unbalanced flow were diagnosed within the gravity wave source region. Hence, it is suggested that the propagation of the jet streak toward the ridge resulted in the shedding of a gravity-inertia wave packet in a association with a geostrophic adjustment process, which in turn triggered severe thunderstorms along the preexisting outflow boundary. A shear instability analysis conducted upon a representative CCOPE sounding shows that the vertical shear associated with the jet also could have served as a wave energy source, since a wave critical level was found at which the calculated Richardson number fell to a value Ri∼¼. Additional analyses indicate that the observed waves were nondispersive and hydrostatic and that vertical energy propagation was impeded by a wave duct associated with the presence of the critical level and lower-tropospheric static stability. The highly coherent nature of the waves, which persisted for many horizontal wavelengths, is explained by this ducting mechanism. These results would seem to point to both geostrophic adjustment and shear instability as plausible wave source mechanisms. It is conjectured that the observed waves were generated by geostrophic adjustment processes, additional energy was supplied through interaction with the critical level, and their coherence maintained through the ducting mechanism.

Appalachian Cold-Air Damming

Appalachian cold-air damming is investigated by means of 1) a 50-yr monthly climatology, 2) a synoptic case study of the event of 21–23 March 1985 and 3) an investigation of the flow structure and force balance within the cold dome. The climatology reveals cold-air damming is a year-round phenomenon in the southern Appalachians with the most frequent, prolonged and intense events occurring in winter (particularly December and March) when three-five events per month can be expected. Cold-air damming is least frequent and intense in July. The synoptic case study reveals that cold-air damming is critically dependent upon the configuration of the synoptic-scale flow. The cold dome can be identified by a “U” shaped ridge (trough) in the sea level isobar (thermal) patterns and the 930-mb height (temperature) fields representative of conditions at the base of the inversion overlying the cold dome. Differential horizontal and vertical thermal advection, as well as adiabatic and evaporative cooling, are responsible for the configuration of a strongly sloping inversion at the top of the cold dome and the pronounced baroclinic zone along the eastern edge of the cold dome. Evaporative cooling accounts for roughly 30% of the total cooling in parts of the dome, while adiabatic cooling explains a similar percentage of the cooling adjacent to the mountain slopes. An accelerated flow nearly parallel to the mountains within the cold dome is identified and shown to be linked to the evolution of the synoptic-scale pressure field. The mountain-parallel component of the pressure gradient force is the primary acceleration source. The force balance on the accelerated flow after cold dome formation is geostrophic in the cross-mountain direction and antitriptic in the along-mountain direction. A geostrophic adjustment process is triggered from the formation of a region of small-scale ridging against the mountain slopes as cold air is constrained by the mountains to remain along the eastern slopes. The tendency for the Coriolis force to turn the flow toward the mountain is negated and the flow within the cold dome is directed ready parallel to the mountains and down the large-scale pressure gradient. Cold dome drainage occurs with the advection of the cold air toward the coast in response to synoptic-scale pressure falls accompanying coastal cyclogenesis.

The Synoptic Setting and Possible Energy Sources for Mesoscale Wave Disturbances

Thirteen case studies of mesoscale wave disturbances (characterized by either a singular wave of depression or wave packets with periods of 1–4 h, horizontal wavelengths of 50–500 km, and surface pressure perturbation amplitudes of 0.2–7.0 mb) are reviewed to isolate common synoptic features for these cases and to shed light on possible energy sources for the waves. A strong thermal inversion in the lower troposphere (north of a frontal boundary) and a jet streak propagating toward a ridge axis in the upper troposphere are commonly observed in all the cases. In general, the area of wave activity is bounded by the jet axis to the west or northwest, a surface front to the southeast, an inflection axis (between the trough and ridge axes) to the southwest and the ridge axis to the northeast. The conditions specified by Lindzen and Tung as being necessary to form a wave duct, which include the existence of the lower-tropospheric inversion, seem to be met in many of these cases. This suggests that a ducting mechanism contributes to the long duration of these wave events by preventing the vertical propagation of wave energy. Questions are raised concerning the role of either convection or shear instability as source mechanisms for the generation of these mesoscale wave disturbances. The observed development of the waves within the exit region of a jet streak propagating toward an upper-level ridge axis is shown to be consistent with the hypothesis that the actual energy source needed to initiate and sustain thew wave events may be related to a geostrophic adjustment process associated with upper-tropospheric jet streaks.

Mean Fields Induced by Local Gravity-Wave Forcing in the Middle Atmosphere

The role of geostrophic adjustment in the middle atmosphere for given wave packet forcing by a three-dimensional hydrostatic model is examined. It is shown that the induced fields consist of two different kinds of modes. One, produced by forcing vorticity only, is steady quasi-geostrophic flow; this is restricted to the forcing region. The other, produced by both forcing vorticity and forcing divergence, is oscillatory, and is in the form of gravity waves propagating out of the forcing region plus inertial oscillations in the forcing region. The scales and amplitudes of the induced gravity waves are determined by the forcing. For a typical example, a 200 km x 200 km gravity wave packet of momentum flux 0.5 N/sq m absorbed in a layer of 5 km thickness centered near 18 km altitude, the gravity waves spread to a larger region about 1000 km x 1000 km at a level 7 km above the forcing region. At that level, the horizontal and vertical wavelengths of the induced waves are about 300 km and 7 km respectively, and the momentum flux is substantially reduced to 0.0004 N/sq m. The results suggest that geostrophic adjustment processes may play an important role in specifying the gravity wave spectrum in the middle atmosphere.

Jet Streak Dynamics and Geostrophic Adjustment Processes during the Initial Stages of Lee Cyclogenesis

A numerical experiment is described which explores the relationship between upper-level potential vorticity advection and cyclogenesis on the leeward side of mountain barriers. A multilevel primitive equation model framed in isentropic coordinates is used to simulate the growth of a wave disturbance on the cold front associated with a preexisting “parent” cyclone. The effect of a mountain barrier placed in the path of the advancing cold front and the effect of an enhanced upper-level jet streak on the growth rate of the disturbance are investigated. Enhancement of the jet streak is accomplished by altering the geostrophic potential vorticity in a region upstream of the mountain barrier and solving for the corresponding man and geostrophic velocity field. The experiment suggests a strong connection between the intensity of the jet weak impinging on the barrier and the pressure fall in the lee. We also find that the strongest leeside pressure fall in this experiment is not accompanied by a conversion of available potential energy to kinetic energy. This suggests that geostrophic adjustment processes, rather than baroclinic instability, may cause the rapid initial growth of some, though possibly not all, lee cyclones.

On the geostrophic adjustment process of oceanic motions: Chen, Changsheng and Zenghao Qin, 1985. Scientia sin., (B)28(10):1093–1109

In this paper, some important features of the geostrophic adjustment process of largescale motions in a barotropic and a baroclinic oceans are systematically investigated by means of the scale analysis. For the barotropic ocean, the constraint of the horizontal scale on the linear theory of geostrophic adjustment process is given and the dispersive mechanism of the unbalanced energy in the response of the flow field in the oceanic interior to a steady wind field is expounded. For the baroclinic ocean, the effects of the water depth and density stratification on the solution of geostrophic balance state are taken into account. As examples, some major properties of the geostrophic equilibrium state in the ocean of finite depth and in a two-layer model ocean which are different from those in the atmoshere are discussed in detail. In addition, a conservation equation for the nonlinear model is derived through introducing some simplications in which only the nonlinear potential flow and vertical transport of mass field are considered.

Preliminary results from the long-term upper-ocean study (LOTUS)

The Long-Term Upper-Ocean Study (LOTUS) is a two-year experiment at 34°N, 70°W, in deep water over the Hatteras abyssal plain, 330 km from major topography and the mean path of the Gulf Stream. The observations began in May 1983. The principal measurements are from an array of three subsurface moorings and one surface mooring carrying meteorological instrumentation as well as near-surface current meters. Some basic meteorological and engineering data are telemetered back via the ARGOS system, but most of the data are self-recorded. Other observations in the program include XBT sections, CTD profiles, and cooperative efforts with other investigators to obtain satellite imagery and other in situ measurements. The main scientific goals of the experiment are: to obtain a description of the local response of the upper ocean to a potpourri of atmospheric forcing in a variety of environmental situations, such as in the presence of Gulf Stream rings or near oceanic fronts, and even to try and describe the statistical response to the fluctuating forcing; to investigate the energy level of the internal wave field over several seasons and during the passage of various forcing and environmental events as mentioned above; and to obtain the complete profile of eddy kinetic energy. We display here selected results from the first year of LOTUS, especially those that do not require the analysis of the complete array of measurements and supporting data. Of particular interest is the eddy energy kinetic energy profile showing a nearly constant energy in the top 500 m; the abyssal eddy energy is also about half the expected level for the site. The high-frequency internal wave field at 200–500 m depths shows a seasonal variation (high in the winter, low in the early fall) that cannot be ascribed to changes in the hydrography; at greater depths the winter maximum is still visible. At each depth the energy varies from a half or a third to 2 or 3 times the mean energy at that depth. Some of the energetic events in the near-inertial field are apparently unconnected to local 3ind events, and may instead be related to the edge of strong mesoscale oceanic currents; perhaps they are being radiated during the process of geostrophic adjustment by the mesoscale features.

Numerical Simulation of Nonlinear Jet Streak Adjustment

Abstract The geostrophic adjustment process in a propagating jet maximum is studied through numerical experiments performed with a two-layer, nonlinear primitive equation model. Gravity-inertia modes generated by the jet streak from an initial three-dimensional balanced flow are isolated with the aid of diagnostic quasi-geostrophic and balance models. Them modes appear to represent gravitational subsynoptic “signal” rather than “noise,” and their behavior is examined as a function of initial core strength. Persistent unbalanced patterns relative to the jet core are discovered, whose amplitude increases approximately as the square of the Rossby number. Their behavior is suggestive of forced, rather than free, ageostrophic modes, and their existence implies that the “four-cell” vertical motion pattern characteristic of jet streaks in filtered models may be significantly altered in a real jet streak. The free response to initial data imbalances placed at varying locations in a jet streak environment is explo...

Inertial Oscillations on the Continental Shelf of the Gulf of Lions—Observations and Theory

Abstract Observations in the Gulf of Lions (northwestern Mediterranean Sea) in summer have shown that gusts of wind lasting a few days generate transient upwellings and inertial motions. Oscillations at the inertial frequency were observed in current meter data near the shore and at a frequency 10% greater in the temperature data. Vertical coherences in current meter data show a strong baroclinic mode at frequencies greater than inertial frequency. A simple one-dimensional two-layer transient model suggests that these motions are associated with two different physical processes. The first process describes the local response of the ocean to meteorological forcing, the second is associated with the propagation of long internal waves generated in the transient phase of the geostrophic adjustment process. As suggested by the model, the direction of propagation of the internal waves is computed from current and temperature data measured at one point and it is found that the shore is the source zone.

Lamb waves originating in nongeostrophic disturbances: A case study

On July 1, 1973, large amplitude atmospheric waves occurred simultaneously in the troposphere and ionosphere over the southern part of Africa. The waves were observed at eight stations on a ground level pressure record, on vertical incidence ionograms, and on Faraday rotation records. Both a Fourier and a band filter analysis show significant wave amplitudes in two narrow period bands around 85 and 65 min, respectively. The waves were excited at low heights near the south coast of Africa and propagated toward the equator with horizontal phase trace speeds of the order of the lower atmosphere sound speed. An analysis of surface weather maps indicates that there was a close spatial and temporal coincidence of the observed waves and nongeostrophic winds, confirming the hypothesis that atmospheric waves may be generated during geostrophic adjustment processes. Wave calculations in a realistic model atmosphere over a rigid surface show that the observed wave properties can be best explained in terms of the Lamb mode. An energy estimate confirms that the nongeostrophic disturbance could in fact provide the energy necessary to explain the amplitudes and the period of occurrence of the observed waves.

Lamb waves originating in non-geostrophic perturbations

A LAMB wave is a purely compressional wave mode in an isothermal atmosphere at rest above a horizontal rigid surface1. It travels only horizontally, with a phase velocity equal to the speed of sound and its energy density decreases exponentially with height. Bretherton2 and Garret3 have concluded that such a mode may exist in the temperature-and wind-stratified atmosphere of the Earth, with its energy mainly located at heights below 30 km. Lamb waves belong to the family of acoustic–gravity waves which, according to Rossby4 and Obukhov5, may be excited by non-geostrophic perturbations in a rotating stratified fluid until the fluid has returned to a quasi-geostrophic steady state. Here we report the observation of Lamb-wave generation in the troposphere during a geostrophic adjustment process.

The Role of Variable Coriolis Parameter in the Propagation of Inertia-Gravity Waves During the Process of Geostrophic Adjustment

Abstract This analysis treats the transient inertia-gravity wave response of a shallow fluid to an impulsive addition of momentum. The Coriolis parameter varies with latitude, but Rossby waves are not considered. The square of the Coriolis term is approximated by a constant term plus a term linear in the northward coordinate. In this approximation, monochromatic waves, which reach a turning point at the latitude where the wave frequency equals the local Coriolis frequency, are given by Airy functions. A contour integral solution to the initial value problem is expressed as a Fourier integral over wave frequency with an Airy function argument and is evaluated approximately using the stationary phase technique. The solution at a given latitude is first dominated by waves from the source and then waves reflected from turning points poleward of the source. The results are applied to give a qualitative description of the wake of a hurricane moving over a stratified ocean.

The effect of horizontal shear flow on geostrophic adjustment in a barotropic fluid

The effect of a basic horizontal shear flow on the linear geostrophic adjustment process in an unbounded barotropic fluid is investigated. It is shown that the basic flow is absolutely stable to axially symmetric transverse disturbances and that energy is not abstracted from the basic flow through the action of Reynolds stresses. A potential vorticity equation is derived and solved numerically in order to determine the relative amount of initial energy which is partitioned to geostrophic kinetic and available potential energy, as a function of the initial current width. It is also shown that, in contradistinction to the adjustment process in an atmosphere with a basic state at rest, a significant portion of geostrophic energy resides in the low wave-number part of the energy spectrum. This latter feature is most noticeable when a large gradient of the basic flow exists. DOI: 10.1111/j.2153-3490.1969.tb00428.x

An asymptotic solution of the tidal equations

The Cauchy problem for the β-plane form of the tidal equations is solved for both oscillatory and delta function initial data. The radius of deformation is assumed to be much less than the radius of the earth, and in accord with this assumption a ray approximation is employed.It is shown that, owing to the rapid rate of propagation of inertio-gravity waves, the motion in its initial development tends towards geostrophic balance. However, the solution given by the ray approximation is singular on certain surfaces in space and time, the envelopes of the rays. A local boundary-layer theory is employed to correct this deficiency. The existence of these caustics implies that the process of geostrophic adjustment is more complicated than hitherto imagined.

On Nonlinear Geostrophic Adjustment

Abstract Nonlinear features of the geostrophic adjustment process in a one-dimensional barotropic atmosphere are investigated by means of a perturbation expansion in the Froude number. The initial unbalanced velocity field is a continuous (nonconstant) even function of the spatial coordinate. The steady-state solution shows the southward shift of the axes of maximum geostrophic velocity and zero pressure, first found by Rossby. In addition, the geostrophic fields are asymmetric about their respective axes. The nonlinear oscillation of the whole current system approaches the inertial period and decays like t−½ as time t→∞. However, this oscillation continues for a significantly longer time, before approximate geostrophic balance is reached, than the “adjustment time” determined from a linear analysis. A possible shortcoming in the quasi-geostrophic approximation, used in some large-scale dynamical models, is indicated by this result.