Baroclinic Effects Research Articles

A numerical study of the vorticity field generated by the baroclinic effect due to the propagation of a planar pressure wave through a cylindrical premixed laminar flame

The importance of vorticity production in combustion systems has been highlighted previously by several authors (Markstein 1964; Picone et al. 1984). The consequent distortion and enlargement of flame surfaces can lead to substantial enhancement of the burning rate which may be beneficial or disastrous depending on the physical context. We describe the results of numerical simulations of an experimental configuration similar to that described by Scarinci & Thomas (1992), who examined the effect of initially planar pressure signals on two-dimensional flame balls. The flame ball is here set-up from ignition using a code, based on the second-order Godunov scheme described by Falle (1991). A simple Arrhenius reaction scheme is adopted in modelling a unimolecular decomposition. As in previous papers (Batley et al. 1993 a, b) the thermal conductivity is assumed to vary linearly with temperature, and the Lewis and Prandtl numbers are taken as unity. A short time after ignition, when the flame ball has reached a radius of approximately 2 cm, a very short-lengthscale pressure step disturbance is introduced, propagating towards the combustion region. As the signal crosses the flame, the interaction of the sharp, misaligned pressure and density gradients, creates a strong vorticity field. The resulting roll-up of the flame eventually divides it into two smaller rotating reacting regions. In order to gauge the effect of the chemical reaction and in particular the viscous diffusion on the evolution of the vorticity field, the results are compared with analogous solutions of the Euler equations.

Maintenance of continental boundary-layer shear through counter-gradient vorticity flux in a barotropic model

The use of a classical eddy parametrization in the analysis of continental boundary currents leads to the diffusion of momentum and relative vorticity and fails to recognize that the relevant eddies are dominated by the conservation of potential vorticity, which in turn may produce an increase in the mean relative vorticity. To illustrate this effect, we examine a non-inflected barotropic shear flow destabilized by the cross-steam variation in the bottom topògraphy of a continental slope. The finiteamplitude evolution of the waves is analysed in a simple model with a step-like bottom topography and with a piecewise-uniform potential vorticity distribution. The increase in maximum mean vorticity is computed for various values of the Rossby number and the topographic elevation, and it is suggested that a similar effect, taking into account the isopycnal topography as well as the isobaths, could maintain the large inshore shear of the Gulf Stream. Cross-shelf transport of different water ‘types’ (i.e. potential vorticity and passive tracers) are also computed and suggested to be pertinent to the more realistic oceanic problem involving baroclinic effects. The numerical calculation employs the well-known method of contour dynamics, and the Green's function appropriate for the step-like topography is derived.

A three-dimensional numerical model of the response of the Australian North West Shelf to tropical cyclones

AbstractA three-dimensional barotropic and baroclinic model is developed to simulate currents and temperature changes induced by tropical cyclones traversing the continental shelf and slope region of the Australian North West Shelf. The model is based on a layered, explicit, finite difference formulation using the nonlinear primitive equations with an embedded entrainment scheme; a mixed-surface-layer interface is defined, which is allowed to shift from one interface to another, depending on the strength of a storm. The model has been tested by simulating the currents and temperature changes induced by tropical cyclones Orson and Ian. The modelled currents and temperatures agreed well with the available measured records except near the seabed. It has been found that the pre-storm currents have very little influence on the peak of the storm-induced currents and the currents in the wake of a tropical cyclone. The model contained no coefficients which must be calibrated for a particular application and clearly illustrated the importance of the baroclinic effects on the storm-induced response over the North West Shelf of Australia.

Baroclinic eddy generation at a sharp corner in a rotating system

Laboratory experiments were conducted to investigate the generation of anticyclonic gyres by separation of a surface current from a coast in a rotating, two layer system. The experiments were motivated by the hypothesis that the flow of coastal currents around capes can generate oceanic eddies, as well as by the observation of gyres at the mouths of various straits. In the experiments the gyre is formed when the current, which flows with the coast to its right if one is oriented in the downstream direction, encounters a sharp convex corner. The current overshoots the corner, loops to the right, and reattaches to the coast downstream of the corner. Between the current loop and the coast is an anticyclone whose width grows with time. If a countercurrent flows under the surface current, a similar separation in the lower layer results in the generation of a cyclone as well; under some circumstances the cyclone and anticyclone advect each other away from the coast as a heton. Previous studies on related systems found that the corner must be sufficiently sharp for a gyre to form. I show that for a very sharp corner the angle made by the corner must be above a critical value of between 40° and 45° for a gyre to form. This is in contrast to nonrotating flows of comparable Rayleigh number, which will separate from a sharp corner at virtually any angle. For angles below the critical value, the current profile downstream of the corner changes as a function of corner angle, indicating that it is the stagnation of the flow nearest the wall which causes the anticyclone to form. This stagnation is reminiscent of the two‐dimensional, nonrotating picture of viscous boundary layer dynamics forcing separation of a boundary current. However, the gyre grows more slowly when the lower layer is much thicker than the upper layer, indicating that baroclinic processes are at least quantitatively important in the generation of the gyre. By varying the initial condition of the current, it is shown that the gyre formation is not a product of the interaction of the nose of the current with the corner. In conclusion, the experiments indicate that the basic mechanism of gyre formation may be viscous boundary effects as in nonrotating systems, but that rotation tends to inhibit eddy generation while baroclinic effects tend to enhance it.

A tidal simulation of Ariake Bay—A tideland model

A three-dimensional primitive σ-coordinate model is developed to allow for tideland. The model determines the coastline position each time step based on a minimum threshold depth, and extrapolates the three-dimensional predictive variables onto tideland only when the water depth exceeds that threshold value, assuring that the extrapolation is consistent with physics as well as with the numerical scheme involved. The model is applied to an M2 tide in the northern estuary of Ariake Bay characterized by the large tideland. The model successfully simulates flood and ebb tides during which a large area of tideland is covered and uncovered with water due to the large tidal difference in sea level. The model also reproduces a strong salinity front caused by the freshwater runoff from Chikugo river. The general patterns of model-computed tidal flows and density front are consistent with data available in this region. The mean flow field averaged over a twelve hour period shows a strong northward current along the slope accompanied by anticyclonic eddies over tideland, the latter feeding a southward transport along the eastern coast. It is shown that such a circulation pattern is enhanced by the joint effect of baroclinicity and bottom relief. Finally, some implications of model results are discussed in relation to the fishery.

A thermal front within the marine atmospheric boundary layer over the Agulhas Current south of Africa: Composite aircraft observations

Aircraft cross‐section observations across the northern edge of the warm Agulhas Current to the south of Africa are used to form composite results of mean and turbulent meteorological parameters over a 4‐day period characterized by winter zonal westerlies. Across a sea surface temperature (SST) front of 8°C (40 km)−1 near 35°S, 23°E, surface heat fluxes and wind stress increase fivefold. The moist unstable marine atmospheric boundary layer is 400 m deeper on the warm side of the SST front, and turbulent variances increase with SST in a logarithmic correlation (r = +0.76). A jetlike core of accelerated winds (17 m s−1) over the axis of warmest water is found. Its existence is thought to be due to secondary circulations set up by enhanced pressure gradients and baroclinic effects. The sharp thermal front is quasi‐stationary and semipermanent during synoptic prefrontal conditions and zonal flows and lies approximately over the 200‐m isobath in association with the Agulhas Current.

Numerical Simulation on 2D/3D Reacting Free Shear Layer.

The evolution of two- and three-dimensional vortical structures in an initially nonpremixed temporally developing reacting mixing layer is simulated by solving the time-dependent, compressible Navier-Stokes equations. The result of the numerical simulations shows that, as the evolution of hydrodynamic instability is suppressed, and the vorticity and the amount of chemical product are reduced by the baroclinic effect and volumetric expansion due to reaction heat release. In the case of temperature dependent diffusivities, the vorticity is reduced as well, in comparison with the temperature-independent case. Structures of the cores, ribs and legs are observed in the three dimensional mixing layer. Similarities between the distributions of spanwise vorticity and product mass fraction, and between those of streamwise vorticity and reaction rate, can be identified when the pairing process is saturated which may imply that the streamwise vortical dynamics plays an essential role in the progress of the chemical reaction.

The Halting Effect of Baroclinicity in Vortex Merging

We study the quasigeostrophic merging dynamics of axisymmetric baroclinic vortices to understand how baroclinicity affects merging rates and the development of the nonlinear cascade of enstrophy. The initial vortices are taken to simulate closely the horizontal and vertical structure of Gulf Stream rings. A quasigeostrophic model is set with a horizontal resolution of 9 km and 6 vertical levels to resolve the mean stratification of the Gulf Stream region. The results show that the baroclinic merging is slower than the purely barotropic process. The merging is shown to occur in two phases: the first, which produces clove-shaped vortices and diffusive mixing of vorticity contours; and the second, which consists of the sliding of the remaining vorticity cores with a second diffusive mixing of the internal vorticity field. Comparison among Nof, Cushman–Roisin, Polvani et al., and Dewar and Killworth merging events indicates a substantial agreement in the kinematics of the process. Parameter sensitivity experiments show that the decrease of the baroclinicity parameter of the system, Γ2, [defined as Γ2 = (D2f02)/(N02H2)], increases the speed of merging while its increase slows down the merging. However, the halting effect of baroclinicity (large Γ2 or small Rossby radii of deformation) reaches a saturation level where the merging becomes insensitive to larger Γ2 values. Furthermore, we show that a regime of small Γ2 exists at which the merged baroclinic vortex is unstable (metastable) and breaks again into two new vortices. Thus, in the baroclinic case the range of Γ2 determines the stability of the merged vortex. We analyze these results by local energy and vorticity balances, showing that the horizontal divergence of pressure work term [∇·(pv)] and the relative-vorticity advection term (v·∇∇2ψ) trigger the merging during the first phase. Due to this horizontal redistribution process, a net kinetic to gravitational energy conversion occurs via buoyancy work in the region external to the cores of the vortices. The second phase of merging is dominated by a direct baroclinic conversion of available gravitational energy into kinetic energy, which in turn triggers a horizontal energy redistribution producing the final fusion of the vortex centers. This energy and vorticity analysis supports the hypothesis that merging is an internal mixing process triggered by a horizontal redistribution of kinetic energy.

On shock polar analysis and analytical expressions for vorticity deposition in shock-accelerated density-stratified interfaces

Vorticity is deposited due to baroclinic effects on the surface of a density-stratified interface accelerated by a shock. An analytical expression is presented, derived from shock polar analysis, for circulation per unit length on a fast–slow planar density interface inclined at an angle to the incident shock. The analytical expression is integrated to yield total circulation on nonplanar interfaces (sinusoidal and semicircular interfaces) accelerated by shocks. The analytical results agree well with diagnostics from numerical experiments using a second-order Godunov code for the Euler equations.

Annual Velocity Variations in the Labrador Current

Abstract Analyses of CTD and current meter data obtained between 1978 and 1988 off southern Labrador reveal two distinct regimes in the Labrador Current. The first lies over the shelf and upper slope and is the traditional Labrador Current transporting cold low-salinity water south from Baffin Bay and Hudson Strait. The main branch of this flow, located over the shelf break, exhibits an annual variation in speed with a minimum in March–April and a maximum in October. Historical temperature and salinity data suggest this variation is related to the fact that the annual variation in steric height is 0.1 m greater over the continental shelf than over the deep ocean. The greater amplitude over the shelf is due to the large salinity variations induced by the additional freshwater in spring and summer, which is largely confined to the waters over the shelf. The effect of the annual variation in salinity is also examined through diagnostic estimates of the Joint Effect of Baroclinicity and Relief (JEBAR). These ...

A finite element model for tides and resonance along the north coast of British Columbia

A finite element, barotropic, tidal model is developed for the north coast of British Columbia. The model is run with eight tidal constituents and the results are compared with the Flather (1987) finite difference model, and with extensive tide gauge and current meter observations. Although the tidal potential, Earth tide, and loading tide are included in the forcing, their inclusion is shown to change the largest M2 amplitudes by only 2.5% and the largest K1 amplitudes by less than 1%. Root mean square differences between observed and calculated sea level amplitudes and phases are within 1.9 cm and 2.9° for all but one constituent, but the model currents do not in general, compare as favourably. The barotropic currents observed in Hecate Strait are reproduced well, but elsewhere evidence is shown that model inaccuracies are due to baroclinic effects. Tidal residual currents calculated by the model suggest the existence of eddies off the tip of Cape St. James, Cape Chacon, and around Goose Island and Learmonth Banks. The shallow water constituents in Hecate Strait are shown to have significant contributions from the constructive interference of signals propagating into Dixon Entrance and Queen Charlotte Sound. Using the model, the longest resonant period of the system is estimated to be 7.6 hours with an energy dissipation parameter, Q, of 9.5.

The Effect of Gulf Stream-induced Baroclinicity on U.S. East Coast Winter Cyclones

Abstract Midlatitude cyclones develop off the Carolinas during winters and move north producing gale-force winds, ice, and heavy snow. It is believed that boundary-layer and air-sea interaction processes are very important during the development stages of these East Coast storms. The marine boundary layer (MBL) off the mid- Atlantic coastline is highly baroclinic due to the proximity of the Gulf Stream just offshore. Typical horizontal distances between the Wilmington coastline and the western edge of the Gulf Stream vary between 90 and 250 km annually, and this distance can deviate by over 30 km within a single week. While similar weekly Gulf Stream position standard deviations also exist at Cape Hatteras, the average annual distance to the Gulf Stream frontal zone is much smaller off Cape Hatteras, normally ranging between 30 and 100 km. This research investigates the low-level baroclinic conditions present prior to observed storm events. The examination of nine years of data on the Gulf Stream position...

A 3D, finite element model for baroclinic circulation on the Vancouver Island continental shelf

This paper describes the development and application of a 3-dimensional model of the barotropic and baroclinic circulation on the continental shelf west of Vancouver Island, Canada. A previous study with a 2D barotropic model and field data revealed that several tidal constituents have a significant baroclinic component (the K1 in particular). Thus we embarked on another study with a 3D model to study the baroclinic effects on the residual and several selected tidal constituents. The 3D model uses a harmonic expansion in time and a finite element discretization in space. All nonlinear terms are retained, including quadratic bottom stress, advection and wave transport (continuity nonlinearity). The equations are solved as a global and a local problem, where the global problem is the solution of the wave equation formulation of the shallow water equations, and the local problem is the solution of the momentum equation for the vertical velocity profile. These equations are coupled to the advection-diffusion equation for density so that density gradient forcing is included in the momentum equations. However, the study presented here describes diagnostic calculations for the baroclinic residual circulation only. The model is sufficiently efficient that it encourages sensitivity testing with a large number of model runs. In this sense, the model is akin to an extension of analytical solutions to the domain of irregular geometry and bottom topography where this parameter space can be explored in some detail. In particular, the consequences of the sigma coordinate system used by the model are explored. Test cases using an idealized representation of the continental shelf, shelf break and shelf slope, lead to an estimation of the velocity errors caused by interpolation errors inherent in the sigma coordinate system. On the basis of these estimates, the computational grid used in the 2D model is found to have inadequate resolution. Thus a new grid is generated with increased accuracy in the region of the shelf break. However, even with increased resolution, spurious baroclinic circulation seaward of the shelf break and in the vicinity of Juan de Fuca canyon remained a significant problem when the pressure gradient terms were evaluated using the σ coordinate system and using a realistic density profile. With the new grid, diagnostic calculations of the barotropic and baroclinic residual circulation are performed using forcing from the observed σ t (density) field and from the gradient of this field.

Effects of Surface Baroclinicity on Frontal Overrunning along the Central Gulf Coast

Along the United States Gulf coast and over the northern Gulf of Mexico, frontal overrunning occurs frequently. Cyclogenesis over the Gulf is often associated with this type of weather system. Effects of baroclinic fields on frontal overrunning are investigated from synoptic and climatological points of view. It is found that, from October through April, the orientation of the shelf break is a very important baroclinic characteristic because fronts tend to stall there rather than at the physical coastline. To further substantiate this deduction dynamically, the local geostrophic vorticity field over the western Louisiana-upper Texas shelf region is estimated monthly. The correlation coefficient between the vorticity field and the frequency of frontal overrunning along the central Gulf coast was 0.86. For forecasting applications, a simple formula is provided to estimate this local vorticity from the temperature difference between Lake Charles, Louisiana, and buoy station 42002 in the deep Gulf.

Model of the Algerian Current's instability

A preliminary “small-perturbation” analytical study of a non-dissipative idealized model of the Algerian Current is mad, with the aim of identifying major characteristics scales and investigating the reality of possible classical instability mechanisms. The simple configuration is shown to be stable, from a linear perturbation point of view. The GHER 3D Primitive Equation Model is then applied to a more realistic investigation of the Algerian Current. The GHER model is non-linear, three-dimensional, with turbulent closure, mode splitting and a σ-coordinate formulation. The numerical simulation shows the development and mature pattern of the instability in excellent agreement with the observations. The relative importance of the existence of a coastal boundary layer, the nature of the initial perturbation, baroclinic and non-linear effects on the instability mechanism is discussed.

Spatial features of the near-surface and midwater circulation patterns off western and southern South Africa and their role in the life histories of various commercially fished species

Currents on the South African shelf have been measured on 13 cruises since an Acoustic Doppler Current Profiler (ADCP) was installed on F.R.S. Africana in 1989. Most previous descriptions of the West Coast (Benguela) system, including the baroclinic jet currents off the Cape Peninsula and Cape Columbine, the latter clearly diverging into a dominant offshore arm and a weaker inshore arm, have been confirmed. This baroclinic flow originates along the south-western margin of the Agulhas Bank. Measurements of the inshore features of the Agulhas Current have shown strong WSW – SSW flow aligned with the bathymetry, but with significant shelf-edge north-eastward return flows. The velocity differences between the surface and depth reveal barotropic dominance in all inshore areas and over the central Agulhas Bank. The West Coast outer shelf displays variable baroclinic effects, reflecting the importance of frontal features and cross-shelf flow. SSW flow on the outer eastern Agulhas Bank appears responsible for an offshore loss of eggs from this region. The funnelling of anchovy eggs from the western Agulhas Bank to the West Coast was clear, but this "funnel" was found to have holes through which substantial loss of eggs offshore is also probable. The currents on the Agulhas Bank and the West Coast are discussed with regard to the life histories of various commercially fished species, in addition to anchovy. The study concludes that hypotheses relating environmental factors and recruitment need to consider the variety of potential options in terms of life history contained within the prevailing current system.

Subtidal Response of Scotian Shelf Circulation to Local and Remote Forcing. Part II: Barotropic Model

A linear, barotropic numerical model that features realistic bathymetry of the Scotian Shelf provides solutions forced by steady and periodic wind stress that are generally incoherent on spatial scales of the shelf width. Closed circulation cells occur in association with, and on the scales of, major bathymetric features. Bathymetrically steered flow is prevalent, and more evident at lower frequencies. Model transport forced by a coastally trapped wave propagating across the backward boundary is not sensitive to the model structure of the incident wave; bathymetry rapidly modifies the wave form as it propagates in the free direction. Higher modes and reflected waves are probably dissipated over short distances by mattering and strong bottom stress. Patterns seen in the model solutions are consistent with results from more fundamental models, and are readily explained by relatively simple vorticity balances. Model results generally reproduce the diverse local and nonlocal velocity responses observed on the Scotian Shelf during winter. The model is more effective in accounting for the remote contribution to circulation. Wind-forced results generally reflect the observed directional variability, and are similar in magnitude to observations inside the 100-m isobath but underestimate the actual current response at deeper stations. It is speculated that spatial variability in wind stress, an effect not addressed in this work, may be responsible for some of this difference. The significant of baroclinic effects in deeper water, which cannot be discounted, is also beyond the scope of this model. Nevertheless, the fairly good agreement between the model and observed current responses to local and nonlocal forcing confirms the importance of bathymetric modifications to Scotian Shelf circulation at subtidal frequencies.

Angular-momentum budget of shallow waters on a rotating sphere.

The covariant formulation of shallow-water theories on a rotating sphere is derived, taking into account the non-Euclidean geometry of the spherical surface. Geometric and dynamic consistency of the inertial and gravitational forces require particular consideration. Covariant diagnostics and equations of motion uniquely determine the energy and angular-momentum budgets. It is shown that the absence of pressure and frictional torques is insufficient to conserve the angular-momentum vector with respect to the rotation axis. On the other hand, it will be seen that in the framework of shallow-water theory topography does not affect the torque. The specific form of the inertial forces on a rotating sphere gives rise to a modified momentum vector, which is conservable under appropriate circumstances. Baroclinic effects are discussed in the framework of covariant bishallow-water theory.

A Three-Dimensional Numerical Investigation of a Carolina Coastal Front and the Gulf Stream Rainband

Abstract A three-dimensional mesoscale planetary boundary layer (PBL) numerical model is used to investigate mesoscale circulations over the Carolina coastal and Gulf Stream baroclinic zones. Idealized ambient onshore and offshore flows are investigated, which represent the synoptic conditions during the Intensive Observation Period-2 (IOP-2) of the 1986 Genesis of Atlantic Lows Experiment (GALE). For the easterly onshore flow, a confluence zone appears west of the Gulf Stream in response to the effect of the oceanic baroclinicity. The confluence zone is nearly parallel to the coastline and the SST isotherms, with northeasterly (southwesterly) flow to the west (east). A shallow coastal front forms below 2 km as the cyclonic shear of the ageostrophic flow becomes strong. Quasi-stationary rainbands are produced by cumulus convection along the coastal front. The northern part of the front and the rainbands later encroach inland as the cold air intensity over ground weakens due to onshore warm air advection. ...

Interpretations of the JEBAR Term

Abstract In diagnostic calculations of the ocean's circulation, the so-called JEBAR (joint effect of baroclinicity and relief) term may induce a significant depth-average current field, as has been noted in the oceanographic literature. Here we present two consistent interpretations of this term. In the equation governing the vorticity of the depth-averaged current, a topographic vortex-stretching term proportional to the dot product of depth-averaged velocity and the depth gradient arises. We show that JEBAR corrects this term by removing the contribution of the geostrophic flow referenced to the bottom, which cannot generate topographic vortex stretching. In the evolution equation for the vorticity of the depth-integrated flow, a bottom-torque term is present. We show that the JFBAR term discussed above enters here as a contribution to the bottom torque, emphasizing the role of JEBAR as a forcing term. We also show that when a diagnostic calculation is formulated completely in terms of the transport str...