The influence of mesoscale topography on the stability and growth rates of a two-layer model of the open ocean

Abstract

The influence of mesoscale topography on the baroclinic instability of a two-layer model of the open ocean is considered. For westward velocities in the top layer (U), and for a sinusoidal topography independent of x or longitude (a cross-stream topography), the critical value of U (U_c ) leading to instability is the same as when there is no topography. The wavelength of the unstable perturbation corresponding to U _c is shortened. For a given wavevector (k) of the perturbation the system becomes stable (as also in the absence of topography) for large values of |U|. The minimum value of the shear leading to stability is, however, significantly reduced by the topography.

For sufficiently large values of the height of the topographic features, instabilities appear which are localized within a narrow range of the shear. These instabilities are studied for a topography that depends both on x and y.

For a cross-stream topography the growth rates are somewhat smaller than those without topography and they depend only weakly on k_y . For the topographies considered here which depend both on x and y, perturbations with different values of k_y can again have roughly the same growth rate.

In the case of stable oscillations, variations in the eddy energy with very long periods are made possible by the coexistence of topographic modes with closely lying periods.     

On steady and travelling waves over bottom topography in the model of homogeneous flow in a beta-plane channel

Abstract

A spectral low-order model is proposed in order to investigate some effects of bottom corrugation on the dynamics of forced and free Rossby waves. The analysis of the interaction between the waves and the topographic modes in the linear version of the model shows that the natural frequencies lie between the corresponding Rossby wave frequencies for a flat bottom and those applying in the “topographic limit” when the beta-effect is zero. There is a possibility of standing or eastward-travelling free waves when the integrated topograhic effect exceeds the planetary beta-effect.

The nonlinear interactions between forced waves in the presence of topography and the beta-effect give rise to a steady dynamical mode correlated to the topographic mode. The periodic solution that includes this steady wave is stable when the forcing field moves to the West with relatively large phase speed. The energy of this solution may be transferred to the steady zonal shear flow if the spatial scale of this zonal mode exceeds the scale of the directly forced large-scale dynamical mode.     

The effect of flow at Maud Rise on the sea-ice cover – numerical experiments

 The role of seamounts in the formation and evolution of sea ice is investigated in a series of numerical experiments with a coupled sea ice–ocean model. Bottom topography, stratification and forcing are configured for the Maud Rise region in the Weddell Sea. The specific flow regime that develops at the seamount as the combined response to steady and tidal forcing consists of free and trapped waves and a vortex cap, which is caused by mean flow and tidal flow rectification. The enhanced variability through tidal motion in particular modifies the mixed layer above the seamount enough to delay and reduce sea-ice formation throughout the winter. The induced sea-ice anomaly spreads and moves westward and affects an area of several 100 000 km². Process studies reveal the complex interaction between wind, steady and periodic ocean currents: all three are required in the process of generation of the sea ice and mixed layer anomalies (mainly through tidal flow), their detachment from the topography (caused by steady oceanic flow) and the westward translation of the sea-ice anomaly (driven by the time-mean wind).     

Possible modulation of migrating diurnal tide by latitudinal gradient of zonal wind observed by SABER/TIMED

Temperature data from SABER/TIMED and Empirical Orthogonal Function(EOF) analysis are taken to examine possible modulations of the temperature migrating diurnal tide(DW1) by latitudinal gradients of zonal mean zonal wind(■). The result shows that z increases with altitudes and displays clearly seasonal and interannual variability. In the upper mesosphere and lower thermosphere(MLT), at the latitudes between 20°N and 20°S, when ■ strengthens(weakens) at equinoxes(solstices) the DW1 amplitude increases(decreases) simultaneously. Stronger maximum in March-April equinox occurs in both z and the DW1 amplitude. Besides, a quasi-biennial oscillation of DW1 is also found to be synchronous with ■. The resembling spatial-temporal features suggest that ■ in the upper tropic MLT probably plays an important role in modulating semiannual, annual, and quasi-biennial oscillations in DW1 at the same latitude and altitude. In addition, ■ in the mesosphere possibly affects the propagation of DW1 and produces SAO of DW1 in the lower thermosphere. Thus, SAO of DW1 in the upper MLT may be a combined effect of ■ both in the mesosphere and in the upper MLT, which models studies should determine in the future.     

The TKE dissipation rate in the northern South China Sea

The microstructure measurements taken during the summer seasons of 2009 and 2010 in the northern South China Sea (between 18°N and 22.5°N, and from the Luzon Strait to the eastern shelf of China) were used to estimate the averaged dissipation rate in the upper pycnocline 〈ε _p〉 of the deep basin and on the shelf. Linear correlation between 〈ε _p〉 and the estimates of available potential energy of internal waves, which was found for this data set, indicates an impact of energetic internal waves on spatial structure and temporal variability of 〈ε _p〉. On the shelf stations, the bottom boundary layer depth-integrated dissipation \( {\widehat{\varepsilon}}_{\mathrm{BBL}} \) reaches 17–19 mW/m², dominating the dissipation in the water column below the surface layer. In the pycnocline, the integrated dissipation \( {\widehat{\varepsilon}}_{\mathrm{p}} \) was mostly ∼10–30 % of \( {\widehat{\varepsilon}}_{\mathrm{BBL}} \). A weak dependence of bin-averaged dissipation \( \overline{\varepsilon} \) on the Richardson number was noted, according to \( \overline{\varepsilon}={\varepsilon}_0+\frac{\varepsilon_{\mathrm{m}}}{{\left(1+ Ri/R{i}_{\mathrm{cr}}\right)}^{1/2}} \), where ε ₀ + ε _m is the background value of \( \overline{\varepsilon} \) for weak stratification and Ri _cr = 0.25, pointing to the combined effects of shear instability of small-scale motions and the influence of larger-scale low frequency internal waves. The latter broadly agrees with the MacKinnon–Gregg scaling for internal-wave-induced turbulence dissipation.

     

Preliminary results of strong ground motion simulation for the Lushan earthquake of 20 April 2013, China

The earthquake occurred in Lushan County on 20 April, 2013 caused heavy casualty and economic loss. In order to understand how the seismic energy propagates during this earthquake and how it causes the seismic hazard, we simulated the strong ground motions from a representative kinematic source model by Zhang et al. (Chin J Geophys 56(4):1408–1411, 2013) for this earthquake. To include the topographic effects, we used the curved grids finite difference method by Zhang and Chen (Geophys J Int 167(1):337–353, 2006), Zhang et al. (Geophys J Int 190(1):358–378, 2012) to implement the simulations. Our results indicated that the majority of seismic energy concentrated in the epicentral area and the vicinal Sichuan Basin, causing the XI and VII degree intensity. Due to the strong topographic effects of the mountain, the seismic intensity in the border area across the northeastern of Boxing County to the Lushan County also reached IX degree. Moreover, the strong influence of topography caused the amplifications of ground shaking at the mountain ridge, which is easy to cause landslides. These results are quite similar to those observed in the Wenchuan earthquake of 2008 occurred also in a strong topographic mountain area.     

The TKE dissipation rate in the northern South China Sea

The microstructure measurements taken during the summer seasons of 2009 and 2010 in the northern South China Sea (between 18°N and 22.5°N, and from the Luzon Strait to the eastern shelf of China) were used to estimate the averaged dissipation rate in the upper pycnocline 〈ε _p〉 of the deep basin and on the shelf. Linear correlation between 〈ε _p〉 and the estimates of available potential energy of internal waves, which was found for this data set, indicates an impact of energetic internal waves on spatial structure and temporal variability of 〈ε _p〉. On the shelf stations, the bottom boundary layer depth-integrated dissipation $ {\widehat{\varepsilon}}_{\mathrm{BBL}} $ reaches 17–19 mW/m², dominating the dissipation in the water column below the surface layer. In the pycnocline, the integrated dissipation $ {\widehat{\varepsilon}}_{\mathrm{p}} $ was mostly ～10–30 % of $ {\widehat{\varepsilon}}_{\mathrm{BBL}} $ . A weak dependence of bin-averaged dissipation $ \overline{\varepsilon} $ on the Richardson number was noted, according to $ \overline{\varepsilon}={\varepsilon}_0+\frac{\varepsilon_{\mathrm{m}}}{{\left(1+ Ri/R{i}_{\mathrm{cr}}\right)}^{1/2}} $ , where ε ₀ + ε _m is the background value of $ \overline{\varepsilon} $ for weak stratification and Ri _cr?=?0.25, pointing to the combined effects of shear instability of small-scale motions and the influence of larger-scale low frequency internal waves. The latter broadly agrees with the MacKinnon–Gregg scaling for internal-wave-induced turbulence dissipation.     

Catchment-scale vulnerability assessment of groundwater pollution from diffuse sources using the DRASTIC method: a case study

Abstract

The catchment-scale groundwater vulnerability assessment that delineates zones representing different levels of groundwater susceptibility to contaminants from diffuse agricultural sources has become an important element in groundwater pollution prevention for the implementation of the EU Water Framework Directive (WFD). This paper evaluates the DRASTIC method using an ArcGIS platform for assessing groundwater vulnerability in the Upper Bann catchment, Northern Ireland. Groundwater vulnerability maps of both general pollutants and pesticides in the study area were generated by using data on the factors depth to water, net recharge, aquifer media, soil media, topography, impact of vadose zone, and hydraulic conductivity, as defined in DRASTIC. The mountain areas in the study area have “high” (in 4.5% of the study area) or “moderate” (in 25.5%) vulnerability for general pollutants due to high rainfall, net recharge and soil permeability. However, by considering the diffuse agricultural sources, the mountain areas are actually at low groundwater pollution risk. The results of overlaying the maps of land use and the groundwater vulnerability are closer to the reality. This study shows that the DRASTIC method is helpful for guiding the prevention practices of groundwater pollution at the catchment scale in the UK.

Citation Yang, Y. S. & Wang, L. (2010 Yang, Y. S. and Wang, L. 2010. A review of modelling tools for implementation of the EU Water Framework Directive in handling diffuse water pollution. Water Resour. Manage., 24: 1819–1843.  [Google Scholar]) Catchment scale vulnerability assessment of groundwater pollution from diffuse sources using the DRASTIC method: a case study. Hydrol. Sci. J. 55(7), 1206–1216.     

Reference hydrologic networks II. Using reference hydrologic networks to assess climate-driven changes in streamflow

Abstract

Reference hydrologic networks (RHNs) can play an important role in monitoring for changes in the hydrological regime related to climate variation and change. Currently, the literature concerning hydrological response to climate variations is complex and confounded by the combinations of many methods of analysis, wide variations in hydrology, and the inclusion of data series that include changes in land use, storage regulation and water use in addition to those of climate. Three case studies that illustrate a variety of approaches to the analysis of data from RHNs are presented and used, together with a summary of studies from the literature, to develop approaches for the investigation of changes in the hydrological regime at a continental or global scale, particularly for international comparison. We present recommendations for an analysis framework and the next steps to advance such an initiative. There is a particular focus on the desirability of establishing standardized procedures and methodologies for both the creation of new national RHNs and the systematic analysis of data derived from a collection of RHNs.

Editor Z.W. Kundzewicz; Associate editor K. Hamed

Citation Burn, D. H., et al., 2012 Whitfield, P.H. 2012. Reference hydrologic networks, I. The status of national reference hydrologic networks for detecting trends and future directions. Hydrological Sciences Journal, 57(8) this issue[Taylor & Francis Online] , [Google Scholar]. Reference hydrologic networks II. Using reference hydrologic networks to assess climate-driven changes in streamflow. Hydrological Sciences Journal, 57 (8), 1580–1593.     

An alternative depth-integrated formulation for granular avalanches over temporally varying topography with small curvature

An alternative formulation is proposed for deriving depth-integrated equations for gravity-driven granular avalanches over a non-trivial topography with small curvature. The coordinate system of Bouchut and Westdickenberg (2004 Bouchut, F and Westdickenberg, M. 2004. Gravity driven shallow water models for arbitrary topography. Commun. Math. Sci., 2: 359–389. [Crossref] , [Google Scholar]) is combined with the unified coordinate (UC) method, so that it can evolve in accordance with the entrainment–deposition processes at the basal surface. The resultant mass and momentum equations are formulated as a conservation system of the Cartesian components of the conservative physical variables. The motion of the flows is driven by the basal topography-induced pressure, pressure gradient, and resisted by the basal friction. The best benefit of this formulation is that it greatly simplifies the computation of the varying coordinate orientations. The features and advantages of this formulation are illustrated by the sliding-mass examples where we simulate the motion of a finite mass of granular material sliding down an inclined chute, running through a transition zone, and being deposited onto a horizontal plane.     

Numerical study of tides in Ontario Lacus,a hydrocarbon lake on the surface of the Saturnian moon Titan

In the context of the emergence of extra-terrestrial oceanography, we adapted an existing oceanographic model, SLIM (www.climate.be/slim), to the conditions of Titan, a moon of Saturn. The tidal response of the largest southern lake at Titan’s surface, namely Ontario Lacus, is simulated. SLIM solves the 2D, depth-averaged shallow water equations on an unstructured mesh using the discontinuous Galerkin finite element method, which allows for high spatial resolution wherever needed. The impact of the wind forcing, the bathymetry, and the bottom friction is also discussed. The predicted maximum tidal range is about 0.56 m in the southern part of the lake, which is more than twice as large as the previous estimates (see Tokano, Ocean Dyn 60:(4) 803–817 10.1007/s10236-010-0285-3 (Tokano 2010)). The patterns and magnitude of the current are also markedly different from those of previous studies: the tidal motion is not aligned with the major axis of the lake and the speed is larger nearshore. Indeed, the main tidal component rotates clockwise in an exact period of one Titan day and the tidal currents can reach 0.046 ms ^?1 close to the shores depending on the geometry and the bathymetry. Except for these specific nearshore regions, the current speed is less than 0.02 ms ^?1. Circular patterns can be observed offshore, their rotational direction and size varying along the day.     

Wave-induced topographic formstress in baroclinic channel flow

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

A Survey of Precipitation-Induced Atmospheric Cold Pools over Oceans and Their Interactions with the Larger-Scale Environment

Pools of air cooled by partial rain evaporation span up to several hundreds of kilometers in nature and typically last less than 1 day, ultimately losing their identity to the large-scale flow. These fundamentally differ in character from the radiatively-driven dry pools defining convective aggregation. Advancement in remote sensing and in computer capabilities has promoted exploration of how precipitation-induced cold pool processes modify the convective spectrum and life cycle. This contribution surveys current understanding of such cold pools over the tropical and subtropical oceans. In shallow convection with low rain rates, the cold pools moisten, preserving the near-surface equivalent potential temperature or increasing it if the surface moisture fluxes cannot ventilate beyond the new surface layer; both conditions indicate downdraft origin air from within the boundary layer. When rain rates exceed \(\sim\) 2 mm h\(^{-1}\), convective-scale downdrafts can bring down drier air of lower equivalent potential temperature from above the boundary layer. The resulting density currents facilitate the lifting of locally thermodynamically favorable air and can impose an arc-shaped mesoscale cloud organization. This organization allows clouds capable of reaching 4–5 km within otherwise dry environments. These are more commonly observed in the northern hemisphere trade wind regime, where the flow to the intertropical convergence zone is unimpeded by the equator. Their near-surface air properties share much with those shown from cold pools sampled in the equatorial Indian Ocean. Cold pools are most effective at influencing the mesoscale organization when the atmosphere is moist in the lower free troposphere and dry above, suggesting an optimal range of water vapor paths. Outstanding questions on the relationship between cold pools, their accompanying moisture distribution and cloud cover are detailed further. Near-surface water vapor rings are documented in one model inside but near the cold pool edge; these are not consistent with observations, but do improve with smaller horizontal grid spacings.     

Convection in rotating annular channels heated from below. Part 2. Transitions from steady flow to turbulence

We report the results of fully three-dimensional numerical simulations of nonlinear convection in a Boussinesq fluid in an annular channel rotating about a vertical axis with lateral no-slip or stress-free sidewalls, stress-free top and bottom, uniformly heated from below, a problem first studied by Davies-Jones and Gilman (1971 Davies-Jones, RP and Gilman, PA. 1971. Convection in a rotating annulus uniformly heated from below.. J. Fluid Mech., 46: 65–81.  [Google Scholar]) and Gilman (1973 Gilman, PA. 1973. Convection in a rotating annulus uniformly heated from below. Part 2. Nonlinear results. J. Fluid Mech., 57: 381–400.  [Google Scholar]). A substantial range of the Rayleigh number R (R_c≤R≤O(100 R_c)), where R_c denotes the critical value at the onset of convection) is considered. It is found that the wall-localized convection mode, unaffected by the velocity boundary condition imposed on the sidewalls, is nonlinearly robust. Both directions of travelling waves, one propagating against the sense of rotation near the outer sidewall and the other propagating in the same sense as the rotation in the vicinity of the inner sidewall, are always present in the nonlinear solutions. In contrast to nonlinear convection in a rotating Bénard layer, neither convection rolls nor the Küpper–Lortz instability can exist in a rotating annular channel because of the effect of the sidewalls. It is the nonlinear interaction between the wall-localized modes and the internal mode that plays an essential role in determining the nonlinear properties of convection in a rotating annular channel. Our studies reveal systematically the various nonlinear phenomena, from steady travelling waves trapped in the vicinities of the sidewalls to convective turbulence exhibiting columnar structure.     

Streamflow dynamics in a Mediterranean temporary river

Abstract

Mediterranean rivers are characterized by the irregularity of flow, harsh hydrological fluctuations and a profound transformation as the result of human activity. In this study, we investigate the streamflow response of a Mediterranean temporary river in which different groundwater, agriculture and urban contributions play an important role. Streamflow was measured at three nested gauging stations installed along Na Borges River, a lowland agricultural catchment (319 km²) on the island of Mallorca. Based on two hydrological years (2004/05 and 2005/06), potential evapotranspiration and surface water–groundwater interaction generated a succession of four different hydrological periods playing an important role in baseflow dynamics. The runoff coefficients were very low (<5%). At the event scale, groundwater also controlled runoff response, being very different according to hydrogeology, antecedent conditions and human impacts. During dry seasons, wastewater and karstic spring discharges maintain an influent regime into some streams. As a result, intense rainstorms in late summer generated water volumes over the impervious urban surfaces involved, with the result that quickflow was significant because the hydrological pathways were active. Citation Estrany, J., Garcia, C. & Alberich, R. (2010 Estrany, J., Garcia, C. and Batalla, R. J. 2010. Hydrological response of a small Mediterranean agricultural catchment. J. Hydrol., 380(1-2): 180–190. doi:10.1016/j.jhydrol.2009.10.035[Crossref] , [Google Scholar]) Streamflow dynamics in a Mediterranean temporary river. Hydrol. Sci. J. 55(5), 717–736.      

Topographic proxies from 2-D numerical analyses

We use 2D numerical analyses at ground motion stations from the NGA-West2 dataset to develop parameters to predict the effect of surface topography on response spectra. The simplistic numerical analyses use sinusoidal input motions, uniform soil profiles, elastic soil properties, and absorbing boundary conditions. We define several topographic parameters for stations using the natural logarithm of 2D amplifications in peak ground acceleration of a sinusoidal input motion in different orientations. The natural log of 2D amplifications when averaged over multiple orientations is found to have the most predictive power among the studied parameters. We also explore the relationship between the topographic parameters developed in this study, and the topographic parameters developed at the same sites in an earlier study (Rai et al. in Earthq Spectra, 2016b).     

Non-local memory effects of the electromotive force by fluid motion with helicity and two-dimensional periodicity

In mean-field dynamo theory, the electromotive force term 〈u′ × B′〉 due to small-scale fields connects the small-scale magnetic field with the large-scale field. This term is usually approximated as the α-effect, assumed to be instantaneous in time and local in space. However, the approximation is valid only when the magnetic Reynolds number Rm is much less than unity, and is inappropriate when Rm ? 1, which is the condition satisfied in the Earth's core or solar convection zone. We introduce a function φ _qr as a non-local and non-instantaneous generalization of the usual α-effect and examine its behaviour as a function of Rm in the range 1/64 ≤ Rm ≤ 10 for a kinematic dynamo model. We use the flow of G.O. Roberts 1972 Roberts, GO. 1972. Dynamo action of fluid motions with two-dimensional periodicity. Phil. Trans. Roy. Soc. London Ser. A, 271: 411–454. [Crossref], [Web of Science ®] , [Google Scholar] (Phil, Trans. Roy. Soc. London Ser. A, 1972, 271, 411–454), which is steady and has non-zero helicities and two-dimensional periodicity. As a result, we identify three regions in Rm space according to the behaviour of the function φ _qr : (i) Rm ? 1/4, where the function φ _qr is local and instantaneous and can be approximated by the traditional α and β effects, (ii) 1/4 ? Rm ? 4, where the deviation from the traditional α and β effects increases and non-localness and non-instantaneousness increase, and (iii) Rm ? 4, where boundary layers develop fully and non-localness and non-instantaneousness are prominent. We show that the non-local memory effect for Rm ? 4 strongly affects the dynamo action and explains an observed augmentation of the growth rate in the dispersion relation. The results imply that the non-local memory effect of the electromotive force should be important in the geodynamo or the solar dynamo.