Stratified flow over three-dimensional topography

In order to investigate flows over topography in an atmospheric context, we have studied experimentally the wake structure of axi-symmetric Gaussian obstacles towed through a linearly stratified fluid. Three dimensionless parameters govern the flow dynamics: F, the Froude number based on the topography height h; Re, the Reynolds number and the aspect ratio r = h/L, where L is the topography horizontal scale. Two-dimensional (2-D), saturated lee wave (SLW) and three-dimensional (3-D) regimes, as defined in Chomaz et al. (1993), are found to be functions of F and r only (Fig. 1) as soon as Re is larger than Re_c ≈ 2000. For F < 0.7 the flow goes around the obstacle and the motion in the wake is quasi-two-dimensional. This 2-D layer is topped by a region affected by lee wave motions with amplitude increasing with r and F. For 0.7 < F < 1/r, the flow is entirely dominated by a lee wave of saturated amplitude which suppresses the separation of the boundary layer from the obstacle. Above the critical value 1/r, the lee wave amplitude decreases with F and a recirculating zone appears behind the obstacle. Simultaneously, coherent large-scale vortices start to be shed periodically from the wake at a Strouhal number which decreases as 1/F until it reaches its neutral asymptotic value.     

Formation of a shelfbreak front by freshwater discharge

The circulation and transport of freshwater generated by an idealized buoyant source is studied using a three-dimensional primitive equation model. Freshwater enters the continental shelf, turns anticyclonically and moves downstream in the direction of Kelvin wave propagation. In the region close to the source, the flow reaches an equilibrium in the bottom boundary layer so that freshwater does not spread offshore any further. This offshore equilibrium distance increases as we move downstream until the freshwater is able to feel the presence of the shelfbreak. A shelfbreak front forms and the shelfbreak prevents any further offshore spreading of freshwater in the bottom boundary layer.Two complimentary mechanisms are responsible for the slow cross-shelf migration of freshwater and subsequent trapping of shelfbreak fronts: bottom stress and topographic changes. The shelfbreak creates an active, dynamic process preventing leakage from the continental shelf region to the slope region. However, the dynamical process that traps the front to the shelfbreak is still unclear.The location of the shelfbreak front depends on four dimensionless parameters: scaled inlet volume transport, scaled breadth, scaled “diffusivity” and scaled shelf width. We develop empirical relations for predicting the location of the frontal bottom intersection, given these parameters.     

Internal tide generation at a continental shelf/slope junction: A comparison between theory and a laboratory experiment

Observations of internal tide generation over continental slopes in a laboratory experiment have been carried out, with the objectives of making comparisons with linear generation theory and investigating its limitations. Both continuous and layered stratification have been considered. A measure of the amplitude of the barotropic tidal forcing (and hence of non-linearity) is given by the Froude Number F = u_sb/c_w, where u_sb is the maximum barotropic tidal velocity at the shelf break, and c_w is the long-wave speed of the lowest internal mode.For continuous stratification, good agreement was obtained for “steep” slopes (α/c > 1), where α is the slope at the continental slope and c is the slope of the internal wave rays of tidal frequency), even for quite large amplitude motions (F < 1.6), and the upper limit of its quantitative usefulness was not reached. For “flat” slopes (α/c < 1) reasonable agreement was also obtained, even up to quite amplitudes (F < 3.1), although some departure from linear theory was apparent.For two-layer flows the applicability of linear theory was much more restricted. For F 0.5 there was only qualitative agreement and for larger F (>1) significant differences were observed. The latter were due to the substantial advection and associated hydraulic jumps which occured seaward of the shelf-break during the ebb-phase of the barotropic tide. Shelf-break values of F > 1 are common in the ocean.     

Vortex–ridge interaction in a rotating fluid

The evolution of barotropic vortices interacting with a topographic ridge on a f-plane is studied by means of laboratory experiments in a rotating tank and numerical simulations. The initial condition in all experiments is a cyclonic vortex created at a certain distance from the ridge. The results are presented in two main scenarios: (a) weak interactions, which occur at early stages of the experiments, when the vortex is far from the ridge, and thus weakly experiences the influence of the topography. In these situations, the vortex slowly drifts towards the ridge with a leftward inclination due to the ascending slope of the topography. Such a behaviour is similar to the “northwestern” motion of cyclones over a weak sloping bottom. The circular shape of the monopolar vortex is preserved. (b) Strong interactions, in which the vortex core reaches the ridge and presents a more complicated evolution. The cyclone “climbs” to the top of the topography and crosses to the other side. Once the vortex experiences the opposite slope, it moves backwards trying to return to the original side of the ridge. For strong enough vortices, this process may be repeated a number of times until the vortex is dissipated by viscous effects. During these interactions the shape of the vortex is strongly deformed and several filaments are produced. In some cases the vortex is cleaved in two parts when crossing the ridge, one at each side of it and moving in opposite directions.Weak and strong interactions are numerically simulated by using a quasi-two-dimensional model. The results confirm that the vortex behaviour is governed by stretching and squeezing effects associated with changes in depth over the ridge and, at latter stages, by Ekman damping due to the solid bottom. The main results observed during strong interactions on a f-plane are also found on preliminar topographic β-plane experiments.     

An improved Lorentzian technique for evaluating resonance characteristics of the Earth-ionosphere cavity

The effectiveness of various formulations of the Lorentzian procedure for estimating Schumann resonance (SR) characteristics of the Earth-ionosphere waveguide from transient electromagnetic signals is tested in the limits of a simplified, spherically uniform model of the resonator. It is shown that the major improvement, in comparison with the “classic” Lorentzian formulation, is achieved by consideration of the intra-modal phase interference. The effect of the “limited frequency dispersion” inherent in the “classic” Lorentzian approach – that is of substantial importance at the lowest SR modes – can be effectively neutralized by interpolating the values for the propagation parameter between the adjacent modal frequencies. Several practical aspects of applying the Lorentzian procedure to transient signals are also discussed.     

Momentum and sensible heat fluxes calculated by the dissipation technique during the Ocean Storms Project

High frequency measurements of wind velocity and temperature were made during the Ocean Storms Project in November 1987. The dissipation method was applied to the resulting time series in order to determine friction velocities,u _*, and the characteristic temperature scale,t _*, at 1-min intervals. These values were then compared to the 1-min mean wind speed and air-sea temperature differences to determine relationships for the drag coefficient (C _d ) and Stanton number (C _h ). The drag coefficient was comparable to other values reported in the literature, although the variation with wind speed was greater than reported by other investigators. An examination of the residual time series indicated a systematic low frequency periodicity of about 2-hr duration which was attributed to a fluctuating wind interacting with the surface gravity wave field. The temperature fluctuations did not produce meaningful estimates ofC _h for stable conditions. For unstable conditions, a value of 1.09±0.02×10^–3 was found.     

The reflection and diffraction of internal waves from the junction of a slit and a half-space, with application to submarine canyons

We consider the three-dimensional reflection and diffraction properties of internal waves in a continuously stratified rotating fluid which are incident on the junction of a vertical slit and a half-space. This geometry is a model for submarine canyons on continental slopes in the ocean, where various physical phenomena embodying reflection and diffraction effects have been observed. Three types of incident wave are considered: (1) Kelvin waves in the slit (canyon); (2) Kelvin waves on the slope; and (3) plane internal waves incident from the half-space (ocean). These are scattered into Kelvin and Poincaré waves in the slit, a Kelvin wave on the slope and Poincaré waves in the half-space. Most of the discussion is centered around case (1). Various properties of the wave field are calculated for ranges of the parameters c/cot θ, γα and ƒ/ω where cot θ is the topographic slope, c is the internal wave ray slope, α is the canyon half-width, γ is the down-slope wave-number, ƒ is the Coriolis parameter and ω is the wave frequency. Analytical results are obtained for small γα and some approximate results for larger values of γα. The results show that significant wave trapping may occur in oceanic situations, and that submarine canyons may act as source regions for internal Kelvin waves on the continental slope.     

Interaction of a negatively buoyant line plume with a density interface

Laboratory experiments were carried out to investigate the interaction between turbulent line buoyant plumes and sharp density interfaces, with the aim of using the results to interpret oceanic observations pertinent to crack openings in the polar ice-cap (leads). These openings take the form of long narrow channels, and are often modeled as line bouyant plumes. The plumes descend as in a homogenoous fluid, impinge on the density interface, and then spread horizontally as gravity currents. Depending on the Richardson number , where Δb is the buoyancy jump across the interface, l_D is the half-width of the plume before the impingement and q₀is the buoyancy flux per unit length of the source, different flow patterns were identified. When Ri < 0.5, the plumes penetrate deep into the bottom layer, deflect horizontally and then spread while showing little vertical rise. When 0.6 < Ri < 5, the penetration is significant, but the fluid bounces back after entraining heavy fluid from the lower layer and then spreads horizontally above the interface as a gravity current. Appreciable mixing between this current and the lower layer was detected when Ri <1. When Ri > 10, the penetration was small and a sharp-nosed gravity current emerged some time after the impact. Measurements were made on the penetration depth, the velocities of the gravity current and the subsurface flow towards the plume, the entrainment rate and other wave parameters. Possible implications of the results for oceanic cases are also discussed.     

Combined wavelet and principal component analysis (WEof) of a scale-oriented model of coastal ocean gravity waves

Coastal ocean numerical modeling is basically the representation of the dynamics of the coastal ocean in a chosen range of length scales and over an associated frequency band, including the modeling of both coherent processes and associated transient processes. The ocean dynamical features can be individually identified by combining wavelet analysis for time and frequency localization and principal component analysis to “decorrelate” physically consistent structures. In the present paper, the so-called WEof analysis is applied for the extraction of external gravity waves and internal gravity wave lower modes in a simple case of a flat bottom, constant Brunt-Väisälä ocean. It is shown that, with some well known restrictive assumptions, WEof analysis is an efficient candidate for the recognition of frequency localized dynamical processes.     

Vertical divergence of fogwater fluxes above a spruce forest

Two almost identical eddy covariance measurement setups were used to measure the fogwater fluxes to a forest ecosystem in the “Fichtelgebirge” mountains (Waldstein research site, 786 m a.s.l.) in Germany. During the first experiment, an intercomparison was carried out with both setups running simultaneously at the same measuring height on a meteorological tower, 12.5 m above the forest canopy. The results confirmed a close agreement of the turbulent fluxes between the two setups, and allowed to intercalibrate liquid water content (LWC) and gravitational fluxes. During the second experiment, the setups were mounted at a height of 12.5 and 3 m above the canopy, respectively. For the 22 fog events, a persistent negative flux divergence was observed with a greater downward flux at the upper level. To extrapolate the turbulent liquid water fluxes measured at height z to the canopy of height h_c, a conversion factor 1/[1+0.116(z−h_c)] was determined. For the fluxes of nonvolatile ions, no such correction is necessary since the net evaporation of the fog droplets appears to be the primary cause of the vertical flux divergence. Although the net evaporation reduces the liquid water flux reaching the canopy, it is not expected to change the absolute amount of ions dissolved in fogwater.     

Stability classification by acoustic remote sensing

Two different Doppler acoustic sounders have been operated at the Kernforschungszentrum Karlsruhe (KfK) since 1982. It has been investigated whether meteorological data from these sounders can be used for dispersion modeling and monitoring in the environment of pollutant-emitting plants. Data from the sounders and from a 200 m high meteorological tower have been sampled continuously for intercomparison.Two schemes of stability classification are presented. They are based on 30-min mean values of the following meteorological data measured by the acoustic sounders: (a) standard deviation σ_w of the vertical wind speed and horizontal wind speed u, at a height of 100 m; and (b) standard deviation σ_φ of the vertical wind direction at a height of 100 m and vertical profile of the backscattered amplitude A_w.The class limits applied in these schemes are determined by “statistical equivalence” with a standard classification scheme. This standard scheme is based on σ_φ, measured by a vector vane at the 100 m level of the tower. Statistical equivalence in this context means that the frequency distributions of the classes are approximately equal at the same site and during the same period.The reliability of these schemes is investigated and compared to the standard scheme by correlation analysis. Finally, the schemes are compared with other commonly applied classification methods.     

A Parameterization of Bowen Ratio with Respect to Soil Moisture Availability

The Bowen ratio (B) is impacted by 5 environmental elements: soil moisture availability, m, the ratio of resist-ances between atmosphere and soil pores, ra/rd, atmospheric relative humidity, h, atmospheric stability, ΔT, and environment temperature. These impacts have been investigated over diverse surfaces, including bare soil, free water surface, and vegetation covered land, using an analytical approach. It was concluded that: (a) B is not a continuous function. The singularity exists at the condition αhcb=h, occurring preferably in the following conditions: weak turbulence, stable stratified stability, dry soil, and humid air, where hcb, defined by Eq.(11) is a critical variable. The existence of a singularity makes the dependence of B on the five variables very complicated. The value of B approaches being inversely proportional to m under the conditions m≥mfc (the soil capacity) and / or ra/rd→0. The proportional coefficient changes with season and latitude with relatively high values in winter and over the poles; (b) B is nearly independent of ra/rd during the day. The impact of m on B is much larger as compared to that of ra/rd on B, (c) when h increases, the absolute value of B also increases; (d) over bare soil, when the absolute surface net radiation increases, the absolute value of B will increase. The impact of RN on B is larger at night than during the day, and (e) over plant canopy, the singularity and the dependcies of B on m, ra , and h are modified as compared to that over bare soil. Also (i) during the daytime unstable condition, m exerts an even stronger impact on B, at night, however, B changes are weak in response to the change in m; (ii) the value of B is much more sensitive in response to the changes of turbulent intensity; (iii) the B response to the variation of h over a vegetation covered area is weaker; and (iv) the singularity exists at the condition hcp=h instead of αhcb=h as over bare soil, where hcp is defined by Eq.(49). The formulas derived over bare soil also hold the same when applied to free water bodies as long as they are visualized as a special soil in which the volumetric fraction of soil pore is equal to one and are fully filled with water. Finally, the above discussions, are used to briefly study the impact on the thermally induced mesoscale circulations.     

Laboratory studies of the effects of interrupted, sloping topography on intermediate depth boundary currents in linearly stratified fluids

Laboratory experiments are described which provide insight into the interaction of intermediate depth boundary currents (IDBCs) with interrupted sloping topography. Specifically, they contribute to the debate over meddy formation on the Iberian continental slope. The experiments were performed in a rectilinear rotating tank filled initially with a linearly-stratified fluid. A false bottom sloped away from the side-wall along which the current flowed, and was interrupted by a gap of variable length. The effects of varying gap length and rotation rate on the boundary current were observed.In the first of two sets of experiments, the current flowed above the slope, along the vertical sidewall. In the second, the current flowed along the sloping bottom. In the former, current nose speed was consistent with geostrophic predictions, but decreased in the presence of a gap in the topography. Kelvin wave radiation is postulated as a reason for this. The IDBCs exhibited vortical lateral intrusions at values of the Burger number Bu=(N₀/Ω)² at which counterpart flat-bottom studies had been stable, implying that the sloping topography had a de-stabilising effect. Energy measurements and qualitative observations suggest the intrusions were due to mixed barotropic/baroclinic instabilities, the latter dominating at higher rotation rates.In the second configuration, four distinct flows were observed, distinguished by the deformation radius:gap width ratio R_D/G^*. For a range of values of R_D/G^*, attached eddies formed at the upstream end of the gap. They remained at this position, unlike those in similar studies of surface boundary currents (Klinger, 1993). Their persistence and ability to move downstream – salient factors for meddy – formation were greater for a finite gap size than a permanent change from sloping to flat bottom.     

The effect of idealized water waves on the turbulence structure and kinetic energy budgets in the overlying airflow

The influence of an idealized moving wavy surface on the overlying airflow is investigated using direct numerical simulations (DNS). In the present simulations, the bulk Reynolds number is Re = 8000 (; where U₀ is the forcing velocity of the flow, h the height of the domain and v the kinematic viscosity) and the phase speed of the imposed waves relative to the friction velocity, i.e., the wave age varies from very slow to fast waves. The wave signal is clearly present in the airflow up to at least 0.15λ (where λ is the wave length) and is present up to higher levels for faster waves. In the kinetic energy budgets, pressure transport is mainly of importance for slow waves. For fast waves, viscous transport and turbulent transport dominate near the surface. Kinetic energy budgets for the wave and turbulent perturbations show a non-negligible transport of turbulent kinetic energy directed from turbulence to the wave perturbation in the airflow. The wave-turbulent energy transport depends on the size, tilt, and phase of the wave-induced part of the turbulent Reynolds stresses.According to the DNS data, slow waves are more efficient in generating isotropic turbulence than fast waves.Despite the differences in wave-shape as well as in Reynolds number between the idealized direct numerical simulations and the atmosphere, there are intriguing similarities in the turbulence structure. Important information about the turbulence above waves in the atmosphere can be obtained from DNS—the data must, however, be interpreted with care.     

Upstream stagnation points in stratified flow past obstacles

An experimental study has been made of stagnation points and flow splitting on the upstream side of obstacles in uniformly stratified flow. A range from small to large values of Nh/U (where N is the buoyancy frequency, h_m is the maximum obstacle height and U is the undisturbed fluid velocity) has been covered, for three obstacle shapes which are, respectively, axisymmetric, and elongated in the across-stream and in the downstream directions. Upstream stagnation for the first two of these models does not occur until Nh_m/U > 1.05, where it occurs at z ≈ h_m/2. On the central line below this point the flow descends and diverges, and we term this ‘flow splitting’. For the third model (elongated in the downstream direction), stagnation upstream first occurs at Nh_m/U ≈ 1.43, at z ≈ 0. Results for this obstacle are not consistent with the ‘Sheppard criterion’, and this upstream flow stagnation is not apparently related to lee wave overturning, in contrast to flow over two-dimensional obstacles.     

Approximation formulas for the microphysical properties of saline droplets

Microphysical theory has proven essential for explaining sea spray's role in transferring heat and moisture across the air–sea interface. But large-scale models of air–sea interaction, among other applications, cannot afford full microphysical modules for computing spray droplet evolution and, thus, how rapidly these droplets exchange heat and moisture with their environment. Fortunately, because the temperature and radius of saline droplets evolve almost exponentially when properly scaled, it is possible to approximate a droplet's evolution with just four microphysical endpoints: its equilibrium temperature, T_eq; the e-folding time to reach that temperature, τ_T; its equilibrium radius, r_eq; and the e-folding time to reach that radius, τ_r.Starting with microphysical theory, this paper derives quick approximation formulas for these microphysical quantities. These approximations are capable of treating saline droplets with initial radii between 0.5 and 500 μm that evolve under the following ambient conditions: initial droplet temperatures and air temperatures between 0 and 40 °C, ambient relative humidities between 75% and 99.5%, and initial droplet salinities between 1 and 40 psu.Estimating T_eq, τ_T, and τ_r requires only one-step calculations; finding r_eq is done recursively using Newton's method. The approximations for T_eq and τ_T are quite good when compared to similar quantities derived from a full microphysical model; T_eq is accurate to within 0.02 °C, and τ_T is typically accurate to within 5%. The estimate for equilibrium radius r_eq is also usually within 5% of the radius simulated with the full microphysical model. Finally, the estimate of radius e-folding time τ_r is accurate to within about 10% for typical oceanic conditions.     

Remote sensing of aerosols over the Solar Village, Saudi Arabia

Aerosol optical properties over Solar Village, Saudi Arabia have been studied using ground-based remote sensing observations through the Aerosol Robotic Network (AERONET). Our analysis covered 8 recorded years of aerosol measurements, starting from February 1999 through January 2007. The seasonal mean values of aerosol optical thickness (AOT), the Ångström wavelength exponent α and the surface wind speed (V), exhibit a one year cyclical pattern. Seasonal variations are clearly found in the shape and magnitude of the volume size distribution (VSD) of the coarse size mode due to dust emission. The Spring is characterized by dusty aerosols as the modal value of the exponent α was low ~ 0.25 while that of AOT was high ~ 0.3. The modal value of wind speed was the highest ~ 3.6 m/s in spring. The increase in wind speed is responsible for increasing the concentration of dust particles during Spring. Spring of 2003 has the highest mean values of AOT, V and VSD and the lowest mean value for the exponent α. The seasonal mean values of the exponent α are anticorrelated with those of the wind speed (r = − 0.63). The annual mean values of the exponent α are well correlated (r = 0.77) with those of the difference between the maximum and minimum values of temperature ΔT. They are anticorrelated (r = − 0.74) with the annual mean values of the relative humidity. Large aerosol particles and high relative humidity increase the radiative forcing. This results in reduction of the values of the temperature difference ΔT.     

Continuing current in multiple channel cloud-to-ground lightning

In this study we analyze the effects of continuing current initiated by strokes following a new channel to ground in multiple stroke flashes using high-speed video records, electric field measurements from a fast antenna and lightning detection network data. We observed that the long continuing current initiated by a stroke that follows a new channel also obeys the pattern in the initiation of long continuing current suggested by Rakov and Uman [Rakov, V.A., Uman, M.A., 2003. Lightning: Physics and Effects, 687pp., Cambridge Univ. Press, New York.]. We also verify that the statement of Rakov and Uman [Rakov, V.A. and Uman, M.A., 1990. Some properties of negative cloud-to-ground lightning flashes versus stroke order, Journal of Geophysical Research. 95, 5447–5453.] reporting that: “...strokes initiating long continuing currents tend to have lower initial electric field peak than regular strokes” is valid for strokes that create a new channel to ground and are followed by long continuing current (CC). Apparently the reduction of peak current value (I_p) when the stroke is followed by a long CC is stronger than the I_p increase that is commonly observed when strokes follow a new channel. We also find that the “exclusion zone” proposed by Saba et al. [Saba, M.M.F., Pinto, O. Jr., Ballarotti, M.G., 2006a. Relation between lightning return stroke peak current and following continuing current, Geophysical Research Letters 33, L23807, doi:10.1029/2006GL027455.] is valid for new channels initiating CC, and finally we verify that a number of strokes in the same channel larger than four or the existence of a long CC current do not always consolidate the channel in a multiple stroke flash.     

Near‐bottom currents and sediment transport on the inner Scotian Shelf: Sea‐floor response to winter storms during CASP

Abstract

As part of the Canadian Atlantic Storms Program (CASP), near‐bottom current velocity, pressure, light transmission (as a measure of suspended sediment concentration) and water temperature were recorded using a variety of instruments deployed in water depths of 20 to 37 m on the inner Scotian Shelf, during February and March 1986. Detailed mapping of a 12‐km² area encompassing the instrument mooring sites revealed a variety of bottom types. These include sand and gravel (both forming ripples at various scales), cobble‐boulder lags, and bedrock, resulting in bottom roughness estimates that vary widely (10^?4 m < k < 10° m) over short horizontal distances (of the order 10² m). The velocity data provided information on the near‐bottom current response to winter storms anda basis for computations of sediment load and transport rates. The near‐bottom mean flow showed distinct storm‐driven circulation patterns, with velocities roughly parallel to alongshore wind stress but opposed to shore‐normal wind. Wave‐induced oscillatory motions also showed marked increases during storms and frequently dominated the near‐bottom flow. Sediment load (depth‐integrated concentration) and transport were computed using a model in which the load is related to the excess normalized shear stress. The computed mean concentrations were compatible with the optical transmis someter data. These computations yielded estimates ranging up to 0.7 kg m^?2 for the mean sediment load and 443 kg m^?1 h^?1 for the net transport. Hindcast scour rates, of the order of 1 mm h^?1 under moderate storm conditions were generally compatible with depths of scour measured by divers.