Nondivergent Flow Research Articles

Intensification Rates of Tropical Cyclone–Like Vortices in a Model with Downtilt Diabatic Forcing and Oceanic Surface Drag

Abstract Tropical cyclones are commonly observed to have appreciable vertical misalignments prior to becoming full-strength hurricanes. The vertical misalignment (tilt) of a tropical cyclone is generally coupled to a pronounced asymmetry of inner-core convection, with the strongest convection tending to concentrate downtilt of the surface vortex center. Neither the mechanisms by which tilted tropical cyclones intensify nor the time scales over which such mechanisms operate are fully understood. The present study offers some insight into the asymmetric intensification process by examining the responses of tilted tropical cyclone–like vortices to downtilt diabatic forcing (heating) in a 3D nonhydrostatic numerical model. The magnitude of the heating is adjusted so as to vary the strength of the downtilt convection that it generates. A fairly consistent picture of intensification is found in various simulation groups that differ in their initial vortex configurations, environmental shear flows, and specific positionings of downtilt heating. The intensification mechanism generally depends on whether the low-level convergence σb produced in the vicinity of the downtilt heat source exceeds a critical value dependent on the local velocity of the low-level nondivergent background flow in a reference frame that drifts with the heat source. Supercritical σb causes fast spinup initiated by downtilt core replacement. Subcritical σb causes a slower intensification process. As measured herein, the supercritical intensification rate is approximately proportional to σb. The subcritical intensification rate has a more subtle scaling, and expectedly becomes negative when σb drops below a threshold for frictional spindown to dominate. The relevance of the foregoing results to real-world tropical cyclones is discussed.

Construction of sea surface current vectors using a single HF radar: A theoretical study.

A technique called the stream and potential function method (SPFM) is presented to retrieve the sea surface current vector field from the radial-component measurements of only one high-frequency (HF) radar. SPFM estimates the surface current vector field jointly based on hydrodynamic constraints and a two-dimensional (2D) ocean current model. The current vector field is assumed to comprise two parts: nondivergent vortex flow and irrotational divergent flow; this guarantees that both the stream function and the potential function are considered. Physically, SPFM is embedded in a more physically consistent hydrodynamic framework that enables the spatiotemporal distribution characteristics of the current vector field at the sea surface to be effectively captured by a single HF radar. The evaluation of SPFM with HYCOM surface current dataset verifies that this approach is more reliable than the stream function method (SFM).

Two-dimensional turbulence on a sphere

Following Fjørtoft (Tellus, vol. 5, 1953, pp. 225–230) we undertake a spectral analysis of a non-divergent flow on a sphere. It is shown that the spherical harmonic energy spectrum is invariant under rotations of the polar axis of the spherical harmonic system and argued that a constraint of isotropy would not simplify the analysis but only exclude low-order modes. The spectral energy equation is derived and it is shown that the viscous term has a slightly different form than given in previous studies. The relations involving energy transfer within a triad of modes, which Fjørtoft (Tellus, vol. 5, 1953, pp. 225–230) derived under the condition that energy transfer is restricted to three modes, are derived under general conditions. These relations show that there are two types of interaction within a triad. The first type is where the middle mode acts as a source for the two other modes and the second type is where it acts as a sink. The inequality indicating cascade directions which was derived by Gkioulekas & Tung (J. Fluid Mech., vol. 576, 2007, pp. 173–189) in Fourier space under the assumptions of narrow band forcing and stationarity is derived in spherical harmonic space under the assumption of dominance of first type interactions. The double cascade theory of Kraichnan (Phys. Fluids, vol. 10, 1967, pp. 1417–1423) is discussed in the light of the derived equations and it is hypothesised that in flows with limited scale separation the two cascades may, to a large extent, be produced by the same triad interactions. Finally, we conclude that the spherical geometry is the optimal test ground for exploration of two-dimensional turbulence by means of simulations.

Bypass-Enabled Thread Compaction for Divergent Control Flow in Graphics Processing Units

Graphics processing units (GPUs) employ the single instruction multiple data (SIMD) hardware to run threads in parallel and allow each thread to maintain an arbitrary control flow. Threads running concurrently within a warp may jump to different paths after conditional branches. Such divergent control flow makes some lanes idle and hence reduces the SIMD utilization of GPUs. To alleviate the waste of SIMD lanes, threads from multiple warps can be collected together to improve the SIMD lane utilization by compacting threads into idle lanes. However, this mechanism induces extra barrier synchronizations since warps have to be stalled to wait for other warps for compactions, resulting in that no warps are scheduled in some cases. In this paper, we propose an approach to reduce the overhead of barrier synchronizations induced by compactions. In our approach, a compaction is bypassed by warps whose threads all jump to the same path after branches. Moreover, warps waiting for a compaction can also bypass this compaction when no warps are ready for issuing. In addition, a compaction is canceled if idle lanes can not be reduced via this compaction. The experimental results demonstrate that our approach provides an average improvement of 21% over the baseline GPU for applications with massive divergent branches, while recovering the performance loss induced by compactions by 13% on average for applications with many non-divergent control flows.

Postprocessing of standard finite element velocity fields for accurate particle tracking applied to groundwater flow

Particle tracking is a computationally advantageous and fast scheme to determine travel times and trajectories in subsurface hydrology. Accurate particle tracking requires element-wise mass-conservative, conforming velocity fields. This condition is not fulfilled by the standard linear Galerkin finite element method (FEM). We present a projection, which maps a non-conforming, element-wise given velocity field, computed on triangles and tetrahedra, onto a conforming velocity field in lowest-order Raviart-Thomas-Nédélec (mathcal {RTN}_{0}) space, which meets the requirements of accurate particle tracking. The projection is based on minimizing the difference in the hydraulic gradients at the element centroids between the standard FEM solution and the hydraulic gradients consistent with the mathcal {RTN}_{0} velocity field imposing element-wise mass conservation. Using the conforming velocity field in mathcal {RTN}_{0} space on triangles and tetrahedra, we present semi-analytical particle tracking methods for divergent and non-divergent flow. We compare the results with those obtained by a cell-centered finite volume method defined for the same elements, and a test case considering hydraulic anisotropy to an analytical solution. The velocity fields and associated particle trajectories based on the projection of the standard FEM solution are comparable to those resulting from the finite volume method, but the projected fields are smoother within zones of piecewise uniform hydraulic conductivity. While the mathcal {RTN}_{0}-projected standard FEM solution is thus more accurate, the computational costs of the cell-centered finite volume approach are considerably smaller.

Theoretical analysis of filmwise condensation in inclined tubes with nondivergent and irrotational flow components

The present theoretical study investigates laminar film condensation of a saturated vapor in inclined circular tubes. Nusselt thin film assumptions are implemented to derive the governing differential equations for mass, momentum, and energy. The impact of both rotation and divergence of the nonconservative Nusselt velocity vector field on film growth and mass conservation are investigated and a new film thickness equation was introduced. A transformation for effective peripheral angle during stratification is derived based on the assumed linear liquid-vapor interface of Chato at the lower region of the tube. The optimal inclination angle for heat transfer is 28.2° from the horizontal for a tube of infinite length. For a finite tube the inclination angle decreases with length from 90° to 28.2° but for tubes of length L* > 2, optimal inclination angle is in the range of 28.2° and 46.6°. An expression for entrance length, Le* was introduced as a function of inclination angle. The results for heat transfer ratio have been compared with experimental data and an empirical correlation from literature and a good agreement is obtained and shown between them.

Instability of planetary flows using Riemann curvature: a numerical study

ABSTRACTThe instability of ideal non-divergent zonal flows on the sphere is determined numerically by the instability criterion of Arnold (Ann. Inst. Fourier 1966, 16, 319) for the sectional curvature. Zonal flows are unstable for all perturbations besides for a small set which are in approximate resonance. The planetary rotation is stable and the presence of rotation reduces the instability of perturbations.

Ocean convergence and the dispersion of flotsam

Floating oil, plastics, and marine organisms are continually redistributed by ocean surface currents. Prediction of their resulting distribution on the surface is a fundamental, long-standing, and practically important problem. The dominant paradigm is dispersion within the dynamical context of a nondivergent flow: objects initially close together will on average spread apart but the area of surface patches of material does not change. Although this paradigm is likely valid at mesoscales, larger than 100 km in horizontal scale, recent theoretical studies of submesoscales (less than ∼10 km) predict strong surface convergences and downwelling associated with horizontal density fronts and cyclonic vortices. Here we show that such structures can dramatically concentrate floating material. More than half of an array of ∼200 surface drifters covering ∼20 × 20 km2 converged into a 60 × 60 m region within a week, a factor of more than 105 decrease in area, before slowly dispersing. As predicted, the convergence occurred at density fronts and with cyclonic vorticity. A zipperlike structure may play an important role. Cyclonic vorticity and vertical velocity reached 0.001 s-1 and 0.01 ms-1, respectively, which is much larger than usually inferred. This suggests a paradigm in which nearby objects form submesoscale clusters, and these clusters then spread apart. Together, these effects set both the overall extent and the finescale texture of a patch of floating material. Material concentrated at submesoscale convergences can create unique communities of organisms, amplify impacts of toxic material, and create opportunities to more efficiently recover such material.

The wave-induced flow of internal gravity wavepackets with arbitrary aspect ratio

We examine the wave-induced flow of small-amplitude, quasi-monochromatic, three-dimensional, Boussinesq internal gravity wavepackets in a uniformly stratified ambient. It has been known since Bretherton (J. Fluid Mech., vol. 36 (4), 1969, pp. 785–803) that one-, two- and three-dimensional wavepackets induce qualitatively different flows. Whereas the wave-induced mean flow for compact three-dimensional wavepackets consists of a purely horizontal localized circulation that translates with and around the wavepacket, known as the Bretherton flow, such a flow is prohibited for a two-dimensional wavepacket of infinite spanwise extent, which instead induces a non-local internal wave response that is long compared with the streamwise extent of the wavepacket. One-dimensional (horizontally periodic) wavepackets induce a horizontal, non-divergent unidirectional flow. Through perturbation theory for quasi-monochromatic wavepackets of arbitrary aspect ratio, we predict for which aspect ratios which type of induced mean flow dominates. We compose a regime diagram that delineates whether the induced flow is comparable to that of one-, two- or compact three-dimensional wavepackets. The predictions agree well with the results of fully nonlinear three-dimensional numerical simulations.

Parallel non-divergent flow accumulation for trillion cell digital elevation models on desktops or clusters

Continent-scale datasets challenge hydrological algorithms for processing digital elevation models. Flow accumulation is an important input for many such algorithms; here, I parallelize its calculation. The new algorithm works on one or many cores, or multiple machines, and can take advantage of large memories or cope with small ones. Unlike previous parallel algorithms, the new algorithm guarantees a fixed number of memory access and communication events per raster cell. In testing, the new algorithm ran faster and used fewer resources than previous algorithms, exhibiting ∼30% strong and weak scaling efficiencies up to 48 cores and linear scaling across datasets ranging over three orders of magnitude. The largest dataset tested had two trillion (2·1012) cells. With 48 cores, processing required 24 min wall-time (14.5 compute-hours). This test is three orders of magnitude larger than any previously performed in the literature. Complete, well-commented source code and correctness tests are available on Github.

Advection on Cut-Cell Grids for an Idealized Mountain of Constant Slope

Abstract Cut cells use regular or nearly regular polygonal cells to describe fields. For a given orography, some cells may be completely under the mountain, some completely above the mountain, and some are partially filled with air. While there are reports indicating considerably improved simulations with cut cells, inaccuracies may arise with some approximations, producing noise in fields near the surface. This behavior may depend strongly on the approximations made for the advection terms near the surface. This paper investigates the accuracy of advection for numerical schemes for a nondivergent flow near a mountain surface. The schemes use C-grid staggering with densities located at cell centers or on the corners of cells. Also, a nonconserving scheme is considered, which was used in the past with real-data cut-cell simulations. Since the cut cells near the surface create an irregular resolution, the accuracy and order of some approximations may break down near the surface. The objective of this paper is to find schemes having the same accuracy for advection near the surface as in the interior of the domain. As a test problem, uniform advection by a nondivergent velocity field is used with a 45° slope mountain (represented as a straight line) on a rectangular grid. Along the surface a sequence of triangular and pentagonal cells of quite different sizes are generated. Some schemes being discussed for cut cells lead to inaccurate and noisy solutions for this perfectly smooth mountain. A scheme using piecewise linear basis functions in a C grid with density points at the cell corners avoids these inaccuracies.

Estimating Eulerian Energy Spectra from Drifters

The relations between the kinetic energy spectrum and the second-order longitudinal structure function for 2D non-divergent flow are derived, and several examples are considered. The transform from spectrum to structure function is illustrated using idealized power-law spectra of turbulent inertial ranges. The results illustrate how the structure function integrates contributions across wavenumber, which can obscure the dependencies when the inertial ranges are of finite extent. The transform is also applied to the kinetic energy spectrum of Nastrom and Gage (1985), derived from aircraft data in the upper troposphere; the resulting structure function agrees well with that of Lindborg (1999), calculated with the same data. The transform from structure function to spectrum is then tested with data from 2D turbulence simulations. When applied to the (Eulerian) structure function obtained from the transform of the spectrum, the result closely resembles the original spectrum, except at the largest wavenumbers. The deviation at large wavenumbers occurs because the transform involves a filter function which magnifies contributions from large separations. The results are noticeably worse when applied to the structure function obtained from pairs of particles in the flow, as this is usually noisy at large separations. Fitting the structure function to a polynomial improves the resulting spectrum, but not sufficiently to distinguish the correct inertial range dependencies. Furthermore, the transform of steep (non-local) spectra is largely unsuccessful. Thus, it appears that with Lagrangian data, it is probably preferable to focus on structure functions, despite their shortcomings.

Structural instability of atmospheric flows under perturbations of the mass balance and effect in transport calculations

Several methods to estimate the velocity field of atmospheric flows, have been proposed to the date for applications such as emergency response systems, transport calculations and for budget studies of all kinds. These applications require a wind field that satisfies the conservation of mass but, in general, estimated wind fields do not satisfy exactly the continuity equation. An approach to reduce the effect of using a divergent wind field as input in the transport-diffusion equations, was proposed in the literature. In this work, a linear local analysis of a wind field, is used to show analytically that the perturbation of a large-scale nondivergent flow can yield a divergent flow with a substantially different structure. The effects of these structural changes in transport calculations are illustrated by means of analytic solutions of the transport equation.

The mean flow and long waves induced by two-dimensional internal gravity wavepackets

Through theory supported by numerical simulations, we examine the induced local and long range response flows resulting from the momentum flux divergence associated with with a two-dimensional Boussinesq internal gravity wavepacket in a uniformly stratified ambient. Our theoretical approach performs a perturbation analysis that takes advantage of the separation of scales between waves and the amplitude envelope of a quasi-monochromatic wavepacket. We first illustrate our approach by applying it to the well-studied case of deep water surface gravity waves, showing that the induced flow, UDF, resulting from the divergence of the horizontal momentum flux is equal to the Stokes drift. For a localized surface wavepacket, UDF is itself a divergent flow and so there is the well-known non-local response manifest in the form of a deep return flow beneath the wavepacket. For horizontally periodic and vertically localized internal wavepackets, the divergent-flux induced flow, uDF, is found from consideration of the vertical gradient of the vertical flux of horizontal momentum associated with the waves. Because uDF is itself a non-divergent flow field, this accounts entirely for the wave-induced flow; there is no response flow. Our focus is upon internal wavepackets that are localized in the horizontal and vertical. We derive a formula for the divergent-flux induced flow that, as in this case of surface wavepackets, is itself a divergent flow. We show that the response is a horizontally long internal wave that translates vertically with the wavepacket at its group velocity. Scaling relationships are used to estimate the wavenumber, horizontal extent, and amplitude of this induced long wave. At higher order in perturbation theory we derive an explicit integral formula for the induced long wave. Thus, we provide validation of Bretherton's analysis of flows induced by two-dimensional internal wavepackets [F. P. Bretherton, “On the mean motion induced by gravity waves,” J. Fluid Mech. 36, 785–803 (1969)] and we provide further analyses that give intuitive insights into the physics governing the properties of the induced long wave. In particular, consistent with momentum conservation, we show that the horizontally-integrated horizontal flow associated with the long wave is given exactly by the horizontal integral of uDF. However, qualitatively different from horizontally periodic internal waves, the vertical profile of the induced horizontal flow across the horizontally localized wavepacket is positive at the leading edge and negative at the trailing edge. These results are validated by the results of numerical simulations of a Gaussian wavepacket initialized in an otherwise stationary ambient.

The direct enstrophy cascade of two-dimensional soap film flows

We investigate the direct enstrophy cascade of two-dimensional decaying turbulence in a flowing soap film channel. We use a coarse-graining approach that allows us to resolve the nonlinear dynamics and scale-coupling simultaneously in space and in scale. From our data, we verify an exact relation due to Eyink [“Local energy flux and the refined similarity hypothesis,” J. Stat. Phys. 78, 335–351 (1995); Eyink “Exact results on scaling exponents in the 2D enstrophy cascade,” Phys. Rev. Lett. 74, 3800–3803 (1995)] between traditional 3rd-order structure function and the enstrophy flux obtained by coarse-graining. We also present experimental evidence that enstrophy cascades to smaller (larger) scales with a 60% (40%) probability, in support of theoretical predictions by Merilees and Warn [“On energy and enstrophy exchanges in two-dimensional non-divergent flow,” J. Fluid Mech. 69, 625–630 (1975)] which appear to be valid in our flow owing to the ergodic nature of turbulence. We conjecture that their kinematic arguments break down in quasi-laminar 2D flows. We find some support for these ideas by using an Eulerian coherent structure identification technique, which allows us to determine the effect of flow topology on the enstrophy cascade. A key finding is that “centers” are inefficient at transferring enstrophy between scales, in contrast to “saddle” regions which transfer enstrophy to small scales with high efficiency.

The Contribution of Extratropical Waves to the MJO Wind Field

Abstract A method for capturing the different dynamical components of the Madden–Julian oscillation (MJO) is presented. The tropical wind field is partitioned into three components using free-space Green’s functions: 1) a nondivergent component, 2) an irrotational component, and 3) a background or environmental flow that is interpreted as the influence on the tropical flow due to vorticity and divergence elements outside of the tropical region. The analyses performed in this study show that this background flow is partly determined by a train of extratropical waves. Space–time power spectra for each flow component are calculated. The strongest signal in the nondivergent wind spectrum corresponds to equatorial Rossby, mixed Rossby–gravity, and easterly waves. The strongest signal in the irrotational winds corresponds to Kelvin and inertia–gravity modes. The strongest signal in the power spectrum of the background flow corresponds to the wave band of extratropical Rossby waves. Furthermore, a coherence analysis reveals that the background flow has the highest coherence with geopotential height variations in the latitude bands from 30° to 45° in both the Northern and Southern Hemispheres. The flow partitions are further studied through a composite analysis based on the Wheeler–Hendon MJO index. Anomalies in the background flow are strongest in the western and central Pacific, possess an equivalent barotropic structure, and show an eastward propagation. By contrast, the irrotational and nondivergent winds possess a first-mode baroclinic structure. An oscillation in the zonally averaged background flow with the MJO phases is observed but contributes little to tropical angular momentum when compared to the nondivergent flow.

Absorbing aerosol‐induced change in the early monsoon Arabian Sea low‐level jet: Modeled transfer from anomalous heating to nondivergent kinetic energy

This study examines the impact of anomalous differential generation of available potential energy by absorbing aerosols on the transition and early active phases of the South Asian summer monsoon. Aerosol direct and indirect radiative forcings can modify tropospheric temperature profiles through direct absorption, scattering, and extended cloud lifetimes. Recent studies have suggested that over monthly and seasonal time scales, these effects can lead to modified flow and rainfall regimes in the South Asian monsoon region. Of special interest is the covariance of heating and temperature prior to active monsoon onset. It can be shown that anomalous generation of available potential energy due to absorption of shortwave radiation by aerosols can impact the cascade of energy from the local Hadley circulation to the monsoon nondivergent flow. In order to quantify the potential impact of aerosol radiative forcing and the resulting changes in monsoon onset timing and intensity, an ensemble of Weather Research and Forecasting with Chemistry regional weather and chemistry model forecasts are created for the South Asian summer monsoon region during May, June, and July. The forecasts including shortwave absorption by aerosol are compared to control forecasts in which aerosols only scatter shortwave radiation. The evolution of irrotational and nondivergent kinetic energy, generation of available potential energy and rainfall are presented. It is found that the ensemble with aerosol shortwave absorption contains on average a more intense dynamical onset over South India which is statistically significant compared to the ensemble variability. The more intense monsoon onset is related to a more intense Arabian Sea low‐level jet. In the ensemble with shortwave absorption by aerosol, the early season monsoon rainfall is diminished over South India and enhanced over the Northeastern Indian states.

Homotopy Continuation Based Non-Divergent Power Flow

This paper presents a non-divergent power flow using homotopy continuation method for power system static analysis. During power flow calculation with newly established network data in power system planning, divergence may occur because of the ill-condition by singularity of power flow Jacobian or bad initial guesses. The application of homotopy continuation method can lead the chosen initial guess to a closer solution to power flow equations in hybrid coordinate successfully and can provide further information on the convergence characteristic. This paper includes an illustrative example certifying the effectiveness of the proposed method.

Comment on “Particle dispersal due to interplay of motions in the surface layer of a small reservoir” (by P. Okely, J. Imberger, and K. Shimizu) and “Processes affecting horizontal mixing and dispersion in Winam Gulf, Lake Victoria” (by P. Okely, J. Imberger, and J. P. Antenucci)

Okely et al. (2010a,b) are concerned with horizontal dispersion and mixing in lakes and employ numerical modeling to estimate horizontal dispersion coefficients. In both papers, the dispersal of four numerical Lagrangian particles is employed to estimate dispersion coefficients, and the authors explicitly claim that ‘‘...this method measures horizontal dispersion due to large-scale horizontal shear only, and the influence of other processes, such as turbulent diffusion, is not accounted for’’ (Okely et al. 2010b, p. 591). However, we demonstrate here that without a diffusive process, e.g., molecular or turbulent diffusion, the dispersal rate estimated from Lagrangian particles as in Okely et al. (2010a,b) should be zero in principal for largescale nondivergent horizontal flow fields, independent of the horizontal shear. The particle dispersal presented by Okely et al. (2010a,b) is not a measure of horizontal dispersion due to horizontal shear but depends on the initial position of the particles and the divergence of the simulated mean flow field and may be affected by undersampling of the flow field, since only four particles were considered. Whereas the study of Okely et al. (2010b) was entirely based on this Lagrangian particle technique, Okely et al. (2010a) compared horizontal dispersion coefficients estimated from this technique with coefficients determined from the spread of numerically simulated tracer distributions. According to Okely et al. (2010a), their horizontal dispersion coefficients agree reasonably well with an estimate based on the assumption that the effects of vertical shear and vertical turbulent mixing (Kz) determine horizontal dispersion (see Table 1 and Eq. 11 in Okely et al. 2010a). Okely et al. (2010a, p. 1875) state that ‘‘The vertical shear dispersion scaling was a good approximation for the magnitude and spatial variation of the average horizontal dispersion rates.’’ However, the horizontal dispersion coefficients obtained from Eq. 11 using the observed vertical diffusivities are an order of magnitude smaller than the values presented in Table 1 of Okely et al. (2010a) and thus are substantially smaller than the horizontal dispersion coefficients obtained from the tracer simulations. Hence, the combined effect of vertical shear and vertical diffusion cannot explain the large horizontal dispersion in the simulation of Okely et al. (2010a). Finally, the Lagrangian particle technique and also the dispersion of the simulated tracer clouds appear to depend mainly on the horizontal divergence of the simulated flow field. Comparison of simulated and observed particle tracks and horizontal currents at a single location indicates that the quality of the simulated flow field is not sufficient to provide the divergence of the true flow field in the lakes studied. Hence, Okely et al. (2010a,b) may provide estimates of the spread of particles and tracers in their simulated flow field but cannot contribute information on horizontal particle dispersal or horizontal dispersion and mixing under field conditions in lakes.

Semi-Lagrangian methods in air pollution models

Abstract. Various semi-Lagrangian methods are tested with respect to advection in air pollution modeling. The aim is to find a method fulfilling as many of the desirable properties by Rasch andWilliamson (1990) and Machenhauer et al. (2008) as possible. The focus in this study is on accuracy and local mass conservation. The methods tested are, first, classical semi-Lagrangian cubic interpolation, see e.g. Durran (1999), second, semi-Lagrangian cubic cascade interpolation, by Nair et al. (2002), third, semi-Lagrangian cubic interpolation with the modified interpolation weights, Locally Mass Conserving Semi-Lagrangian (LMCSL), by Kaas (2008), and last, semi-Lagrangian cubic interpolation with a locally mass conserving monotonic filter by Kaas and Nielsen (2010). Semi-Lagrangian (SL) interpolation is a classical method for atmospheric modeling, cascade interpolation is more efficient computationally, modified interpolation weights assure mass conservation and the locally mass conserving monotonic filter imposes monotonicity. All schemes are tested with advection alone or with advection and chemistry together under both typical rural and urban conditions using different temporal and spatial resolution. The methods are compared with a current state-of-the-art scheme, Accurate Space Derivatives (ASD), see Frohn et al. (2002), presently used at the National Environmental Research Institute (NERI) in Denmark. To enable a consistent comparison only non-divergent flow configurations are tested. The test cases are based either on the traditional slotted cylinder or the rotating cone, where the schemes' ability to model both steep gradients and slopes are challenged. The tests showed that the locally mass conserving monotonic filter improved the results significantly for some of the test cases, however, not for all. It was found that the semi-Lagrangian schemes, in almost every case, were not able to outperform the current ASD scheme used in DEHM with respect to accuracy.