An analytical model for ice-edge upwelling

Abstract

This paper presents an analytical, two-dimensional model of the wind-induced homogeneous circulation near the edge of an ice pack floating on the ocean surface. It is shown that a vertical shear layer arises under the ice edge, by which the wind-driven geostrophic motion in the open ocean is matched to the flow region underneath the ice. As in coastal upwelling models, this shear layer consists of a thin E ^1/2-layer inside a thicker E ^1/4-layer (E being the Ekman number). Under certain conditions the shear layer produces a vertical mass flux from the bottom to the surface Ekman layer. Near the surface this upwelling flux is concentrated in the narrow E ^1/2-layer. Comparison with observations of upwelling at the edge of a polar ice pack shows good agreement.     

Artificial modification of ionosphericE-layer by high power radio transmitters

Some anomalous TV receptions in India on band I have been interpreted as being propagated viaF-layer artificially modified by high power broadcast transmitters. In this paper, the possibility of VHF communication by artificially modifiedE-layer is discussed. The presented theoretical analysis shows that high-power broadcast trasmitters can produce substantial changes in temperature and ionisation in theE-layer. The rate of energy transfer from the wave to the medium particles has also been computed. Model calculations are made for a transmitter located near Calcutta. The possibility of the extra-ionisation producing field-aligned structures to support VHF communication is discussed.     

The equatorial dynamics of a deep homogeneous ocean

Abstract

The flow properties of an homogeneous fluid which is bounded by two concentric spheres and two meridional planes which intersect along a diameter of the spheres are investigated. The spheres rotate about this diameter with slightly different angular velocities. As in the axisymmetric case studied by Proudman (1956) and Stewartson (1966) the viscous terms in the equations of motion are important only in boundary layers on the spheres and on the cylinder C which circumscribes the inner sphere and which has generators parallel to the axis of rotation, provided the Ekman number E is small. In the inviscid region the velocities are independent of the coordinate measuring distance along the axis of rotation and are much weaker, by a factor 0(E ^½), than the velocities in the Ekman layer on the driving surface (outer sphere). (It is assumed that the reference frame is fixed in the slower rotating inner sphere.) If the separation of the spheres is small compared to their radii then the asymmetric circulation inside C is characterized by an intense jet along the western wall. Loss of fluid from this jet sustains the eastward and northward flow in the inviscid interior where motion is driven by the suction of the Ekman layer on the outer sphere. (Geophysical conventions have been adopted.) Outside C an intense current is present on the eastern, not western, wall while motion in the inviscid region is westward, and away from the axis of rotation. Though there is no transport across C in the inviscid region, the meridional transport of the Ekman layer on the outer sphere is continuous across C and increases, through suction, as the equator is approached until it drains into an eastward flowing equatorial current of width 0(E ^1/7). The eastern boundary current outside C and shear layers on C carry this fluid to the intersection of C and the western wall where it feeds the western boundary current inside C.

The relation between this study and the experiments of Baker and Robinson (1970) is discussed.     

On the spin-up of a stably stratified,electrically conducting fluid. Part 2: Spin-up controlled by the mac layer

Abstract

The linear spin-up of a stably stratified, electrically conducting fluid within an electrically insulating cylindrical container in the presence of an applied axial magnetic field is analyzed for those cases in which electric currents generated within the steady MAC layer control the fluid interior, The MAC layer is a new boundary layer first studied by Loper (1976a) which controls the fluid in the parameter range E/α² ? σS ? α²/E, α² ? 1 Where E = vωL², 2α² = σB²/pω and σS = vN²/κω;². The problem is solved using the Laplace transform and four new spin-up times are obtained. Combined into one expression they are t = ω;^?1E-½[1+(σSE/α⁶)^½ + δα^-2] [1+(σSE/α^{6 1/4}]^?1 where δ = σμv. The internal spin-up mechanisms for this problem are shown to be very similar to those discussed in part 1 (Loper, 1976b). The ten known spin-up times are summarized and their inter-relationships are investigated. It is shown how to obtain the seven hydromagnetic spin-up times from a simple torsional Alfvén wave model involving a single parameter which measures the strength of the boundary layer dissipation. Finally, the present theory is applied to the solar spin-down problem and it is found that if the magnetic field in the solar interior is at least as strong as the interplanetary field of 10^-5 gauss, then the hydromagnetic spin-down time is much shorter than the Eddington-Sweet time and is comparable to the age of the sun.     

Rotating flow over long shallow ridges

Abstract

The flow of a rotating homogeneous, incompressible fluid past a long ridge is investigated. An analysis is presented for flows in which E ? 1, Ro ～ E^½, H/D ～ E⁰, h/D ～ E^½ and cosα ～ E⁰ where E is the Ekman number, Ro the Rossby number, H/D the fluid depth to ridge width ratio, h/D the ridge height to ridge width ratio and α the angle between the free stream flow and a line perpendicular to the ridge axis. The analysis includes effects of the nonlinear inertial terms. Particular examples of a ridge of triangular cross section and a sinusoidal topography are investigated in some detail. Experiments are presented for a triangular ridge which are in good agreement with the theory.     

Neutral gas composition changes and E×B vertical plasma drift contribution to the daytime equatorial F2-region storm effects

Theoretical model calculations along with ground-based observations from Huancayo ionosonde station and ESRO-4 gas analyzer data, were used to estimate the contribution of neutral gas composition changes and E×B vertical plasma drift to the observed F2-layer storm effects at the geomagnetic equator. Atomic oxygen concentration increase may give the main contribution to the positive NmF2 effect when drift velocity changes are small, but negative storm effects, on the other hand, are related mostly to vertical drift variations.     

Asymptotic treatment of the stability of a rotating layer of fluid with rigid boundaries

Abstract

Chandrasekhar (1961) has summarized the stability results of Bénard convection in a rotating fluid for the cases where the boundary surfaces are both rigid and free, and for both exchange of stabilities and overstability. His analysis provides very accurate results for a limited range of Taylor number J. Bisshopp and Niiler (1965) presented an asymptotic analysis of the rigid boundary problem for exchange of stabilities which is valid for very large Taylor number. The present paper makes use of modern rotating fluid theory to develop an approximate scheme for evaluating the Rayleigh number and other parameters and variables. Known asymptotic results for the free boundary problem at large J are used and an expansion in powers of E^1/6 (the Ekman number, E = 2J ^?½) yields a sequence of equations and appropriate boundary conditions for the rigid boundary problem. After the algorithm for the calculation is developed, results are given for the problem to second order in the expansion parameter for the case of exchange of stabilities and to first order in the expansion parameters for the overstable case. Ekman boundary layers are important in the development as one might expect. However, an additional, diffusive boundary layer of thickness E^? is necessary to provide the details of the temperature field. This boundary layer is the thermal response in the vertical direction to the horizontal spacing of the cells which is also order E^?. The horizontal spacing of the cells is essentially a series of contiguous, Stewartson (1957) layers of thickness E^?.     

Symmetric baroclinic instability for small ekman numbers

Abstract

The stability of a zonal shear flow to symmetric baroclinic perturbations is examined when the Ekman number, E, is asymptotically small. It is assumed, following Antar and Fowlis (1982), that the zonal Row is generated by imposing a constant horizontal temperature gradient γ* at the horizontal boundaries, and by maintaining a constant temperature difference δT* between them. The boundaries are at rest relative to a rotating frame.

Features of the neutral stability curve are determined for several ranges of values of δT/E ^1/3, where δT = δT*/Hγ* and H is the depth of the fluid layer, and all values of the Prandtl number, [sgrave]. In some cases it is possible to determine the whole curve analytically. The most important feature of the results is that the neutral stability curve is closed.

The results are compared to the numerical integrations of Antar and Fowlis (1982). The qualitative features of the solutions are in accord and the quantitative results are, in most cases, as good as can be expected for E only as small as ～ 10^?4. The implications of the results for experimental observations of symmetric baroclinic instability are explored.     

On the spin-up of a stably stratified,electrically conducting fluid. Part 1: Spin-up controlled by the hartmann layer

Abstract

The linear spin-up of a stably stratified, electrically conducting fluid within an electrically insulating cylindrical container in the presence of an applied axial magnetic field is analyzed for those cases in which electric currents generated within the steady Hartmann boundary layer control the fluid interior. It is shown how to obtain the known spin-up times for a homogeneous, nonconducting fluid (τ = E ^-½), a stably stratified, nonconducting fluid (τ = (σS/E, E ^?1) and a homogeneous conducting fluid (τ = α^?1 E ^-½) from the present formulation where τ = v/ωt, E = v/ωL ², σS = vN²/κω² and 2α² = σB²/pω. The problem is solved in the parameter range E?α²?1, α²/E?σS using the Laplace transform and two new spin-up times are obtained. Combined into one expression, they are τ = (1 + δ)α^?1E^-½ where δ = σμv. The spin-up mechanism is investigated and it is found that, in contrast to the homogeneous, conducting case, torsional Alfvén waves may be instrumental in the spin-up of a stratified conducting fluid. The effects of viscous and ohmic diffusion on the torsional Alfvén wave fronts are studied and the following regimes are identified: 0 < δ ?E/α², spin-up by meridional circulation of electric current with no Alfvén waves; E^-½/α ? δ ? 1, spin-up by meridional circulation of electric current with transient Alfvén waves; α/E^½ ? δ ? α²/E, spin-up by meridional circulation of current with weak Alfvén waves; 1 ? δ ? α/E^½, spin-up by strong Alfvén waves; α^½/E ? δ ? α²/E, spin-up by viscous diffusion with transient Alfvén waves; α/E ? δ < ∞, spin-up by viscous diffusion with no Alfvén waves.     

Spin-up of a two-layer fluid in a rotating cylinder

Abstract

we report the results of experiments on the spin-up of two layers of immiscible fluid with a free upper surface in a rotating cylinder over a wide range of internal Froude numbers. Observations of the evolution of the velocity field by particle tracking indicates that spin-up of the azimuthal velocity in the upper layer take much longer than in a homogeneous fluid. Initially, spin-up occurs at a rate comparable to that of homogeneous fluid but, at high internal Froude number, a second phase follows in which the remaining lative motion decays much more slowly. Quantitative comparison of these measurements to the theory of Pedlosky (1967) shows good agreement.

Visualization of the interface displacement during spin-up detected the presence of transient azimuthal variations in the interface elevation over a wide range of Froude (F), Ekman (E), and Rossby (ε) number. nalysis of the occurrence of the asymmetric variations using the parameter space (Q, F), where Q = E ^1/2/ε, suggested by the baroclinic instability theory and experiments of Hart (1972), showed that the flow was stable for Q > 0.06 with no discernable dependence on F. This result, together with the prediction of Pedlosky's theory that radial gradient of potential vorticity in the two layers have opposite signs, suggests at the baroclinic instability mechanism was responsible for the asymmetries. The location and timing of these instabilities may account for the discrepancies between the observations and the Pedlosky (1967) theory.     

The equatorial dynamics of a shallow,homogeneous ocean

Abstract

It is shown that the linear equatorial dynamics of a shallow ocean is characterized by two boundary layers of width γ^? L and γL (γ is the Ekman number of the flow, assumed small, and L is a horizontal dimension of the basin). In the γ^? layer stress in the bottom Ekman layer is comparable to that in the surface Ekman layer. In the γ layer vertical friction is important throughout the depth of the ocean. Should the Rossby number ? be so large as to invalidate a linear theory (? > γ^5/3), then inertial effects become important at a distance ?^2/5 L from the equator. The role played in the circulation of the basin by the non-linear equatorial current first studied by Charney (1960) is shown to be similar to that of the γ layer of the linear theory. Though lateral friction is unimportant in a linear model of the flow, shear layers at the equator are found to be a necessary feature of non-linear flow.     

Two-dimensional density currents in a confined basin

We present new experimental results on the mechanisms through which steady two-dimensional density currents lead to the formation of a stratification in a closed basin. A motivation for this work is to test the underlying assumptions in a diffusive “filling box” model that describes the oceanic thermohaline circulation (Hughes, G.O. and Griffiths, R.W., A simple convective model of the global overturning circulation, including effects of entrainment into sinking regions, Ocean Modeling, 2005, submitted.). In particular, they hypothesized that a non-uniform upwelling velocity is due to weak along-slope entrainment in density currents associated with a large horizontal entrainment ratio of E _eq ?～?0.1. We experimentally measure the relationship between the along-slope entrainment ratio, E, of a density current to the horizontal entrainment ratio, E _eq, of an equivalent vertical plume. The along-slope entrainment ratios show the same quantitative decrease with slope as observed by Ellison and Turner (, 6, 423–448.), whereas the horizontal entrainment ratio E _eq appears to asymptote to a value of E eq?=?0.08 at low slopes. Using the measured values of E _eq we show that two-dimensional density currents drive circulations that are in good agreement with the two-dimensional filling box model of Baines and Turner (Baines, W.D. and Turner, J.S., Turbulent buoyant convection from a source in a confined region, J. Fluid. Mech., 1969, 37, 51–80.). We find that the vertical velocities of density fronts collapse onto their theoretical prediction that U =-2^?2/3 B ^1/3 E _eq ^2/3 (H/R) ζ, where U is the velocity, H the depth, B the buoyancy flux, R the basin width, E _eq the horizontal entrainment ratio and?ζ?= z/H the dimensionless depth. The density profiles are well fitted with?Δ?= 2^?1/3 B ^2/3 E _eq ^?2/3 H _-1 [ln(ζ )?+?τ ], where?τ?is the dimensionless time. Finally, we provide a simple example of a diffusive filling box model, where we show how the density stratification of the deep Caribbean waters (below 1850?m depth) can be described by a balance between a steady two-dimensional entraining density current and vertical diffusion in a triangular basin.     

A numerical study of detached shear layers in a rotating sliced cylinder

Abstract

The low Rossby number flow in a rotating cylinder with an inclined bottom, of small slope, is examined when part of the lid of the container is rotating at a slightly different rate. The resulting flow is calculated numerically by solving the governing equations for the two-dimensional geostrophic motion which approximates the flow in most of the fluid including the inertially-modified E ^¼ -layers. The presence of ageostrophic regions, on the container walls and beneath the velocity discontinuity on the lid, is accounted for in the governing equations and their boundary conditions. This study supplements previous work on this configuration, in which the zero Rossby number flow was calculated and experimental results were presented, by enabling a direct comparison to be made between the results of the low Rossby number theory and the experiments. The numerical results for a range of Rossby and Ekman numbers compare well with those from the experiments despite a severe limitation on the size of the Rossby number arising from the analysis in the ageostrophic part of the detached shear layer.     

Numerical simulation of the <Emphasis Type="Italic">F</Emphasis>2-layer stratification and appearance of the <Emphasis Type="Italic">F</Emphasis>3 and <Emphasis Type="Italic">G</Emphasis> layers in the equatorial ionosphere: The morphology of the phenomena

This work is devoted to a numerical simulation of the equatorial ionosphere, performed using the GSM TIP model completed with a new block for calculating the electric field. It has been indicated that the usage of the wind system calculated according to the MSIS-90 model makes it possible to reproduce the electromagnetic drift velocities at the equator, the effect of the F2-layer stratification, and the appearance of the F3 layer in the equatorial ionosphere. The calculations performed using the modified GSM TIP model made it possible to detect a maximum in the electron density vertical profile at an altitude of ∼1000 km, formed by H⁺ ions, which we called the G layer. If this layer actually exists, it can be observed during sounding the low-latitude ionosphere from satellites during dark time of day.     

Temporal dynamics of soil water balance components in a karst range in southeastern Spain: estimation of potential recharge

Abstract

This paper analyses the temporal dynamics of soil water balance components in a representative recharge area of the Sierra de Gádor (Almeria, southeastern Spain) in two hydrological years. Two approaches are used to estimate daily potential recharge (PR): Approach 1 based on deriving PR from the water balance as the difference between measurements of rainfall (P) and actual evapotranspiration (E) obtained by eddy covariance; and Approach 2 with PR obtained from the dynamic pattern of the soil moisture (θ) recorded at two depths in the site's thin soil (average 0.35 m thickess). For the hydrological year 2003/04, which was slightly drier than the 30-year average, E accounted for 64% of rainfall and occurred mainly in late spring and early summer. The PR estimated by Approach 1 was 181 ± 18 mm year^-1 (36% of rainfall), suggesting an effective groundwater recharge in the study area. In the unusually dry hydrological year 2004/05, E was about 215 mm year^-1, close to the annual rainfall input, and allowing very little (8 ± 12 mm year^-1) PR according to Approach 1. Estimation of PR based on Approach 2 resulted in PR rates lower than those found by Approach 1, because Approach 2 does not take into account the recharge that occurs through preferential flow pathways (cracks, joints and fissures) which were not monitored with the θ probes. Moreover, using Approach 2, the PR estimates differed widely depending on the time scale considered: with daily mean θ data, PR estimation was lower, especially in late spring, while θ data at 30 min resolution yielded a more reliable prediction of the fraction of total PR resulting from the downward movement of soil water by gravity.

Citation Cantón, Y., Villagarcía, L., Moro, M. J., Serrano-Ortíz, P., Were, A., Alcalá, F. J., Kowalski, A. S., Solé-Benet, A., Lázaro, R. & Domingo, F. (2010) Temporal dynamics of soil water balance components in a karst range in southeastern Spain: estimation of potential recharge. Hydrol. Sci. J. 55(5), 737–753.     

The 1975 sub-terminal lavas, mount etna: a case history of the formation of a compound lava field

The 1975 sub-terminal activity was characterised by low effusion rates (0.3–0.5 m³ s⁻¹) and the formation of a compound lava field composed of many thousands of flow units. Several boccas were active simultaneously and effusion rates from individual boccas varied from about 10⁻⁴ to 0.25 m³s⁻¹. The morphology of lava flows was determined by effusion rate (E): aa flows with well-developed channels and levees formed when E > 2 × 10⁻³ m³ s⁻¹, small pahoehoe flows formed when 2 × 10⁻³ m³ s⁻¹ >E > 5 > 10⁻⁴ m³ s⁻¹ and pahoehoe toes formed when E < 5 × 10⁻⁴ m³ s⁻¹. There was very little variation with time in the effusion temperature, composition or phenocryst content of the lava.New boccas were commonly formed at the fronts of mature lava flows which had either ceased to flow or were moving slowly. These secondary boccas developed when fluid lava in the interior of mature aa flows either found a weakness in the flow front or was exposed by avalanching of the moving flow front. The resulting release of fluid lava was accompanied by either partial drainage of the mature flow or by the formation of a lava tube in the parent flow. The temperature of the lava forming the new bocca decreased with increasing distance from the source bocca (0.035°C m⁻¹). It is demonstrated from the rate of temperature decrease and from theoretical considerations that many of the Etna lavas still contained a substantial proportion of uncooled material in their interior as they came to rest. The formation of secondary boccas is postulated to be one reason why direct measurements of effusion rates tend, in general, to overestimate the total effusion rates of sub-terminal Etna lava fields.     

Measurement of evaporation from the forest floor in a deciduous forest throughout the year using microlysimeter and closed‐chamber systems

Evaporation from the forest floor (E_FF) in a deciduous broadleaf forest was measured using microlysimeter and closed‐chamber systems. The microlysimeter was used at six points in the experimental basin, and measurements gave different E_FF values at different points. This could be attributed to the local photoenvironment of each sampling point, rather than to litter conditions, if the spatial variation in air temperature (Ta) or vapour pressure deficit (VPD) at the forest floor was small within this basin. A detachable microlysimeter measured condensation in the litter layer during the night, indicating that the litter layer, as well as the mulch layer, played a role in preventing evaporation from the soil layer. The closed‐chamber system made it possible to continuously measure long‐term E_FF. E_FF was closely related to VPD; even during the night, when solar radiation was zero, E_FF amounted to 14·0% of the daily E_FF. The daily E_FF was 0·20 ± 0·13 mm day^?1 during the study period, with two seasonal peaks: in late spring (0·31 mm day^?1 in April) and early fall (0·22 mm day^?1 in September). The former peak has been reported from two deciduous forests in Japan and is strongly related to the solar radiation reaching the forest floor when the trees are dormant. Copyright © 2008 John Wiley & Sons, Ltd.     

Physical mechanism of strong negative storm effects in the daytime ionospheric F2 region observed with EISCAT

A self-consistent method for daytime F-region modelling was applied to EISCAT observations during two periods comprising the very disturbed days 3 April 1992 and 10 April 1990. The observed strong N_e decrease at F2-layer heights originated from different physical mechanisms in the two cases. The negative F2-layer storm effect with an N_mF2 decrease by a factor of 6.4 on 3 April 1992 was produced by enhanced electric fields (E 85 mV/m) and strong downward plasma drifts, but without any noticeable changes in thermos-pheric parameters. The increase of the O⁺ + N₂ reaction rate resulted in a strong enrichment of the ionosphere with molecular ions even at F2-layer heights. The enhanced electric field produced a wide mid-latitude daytime trough on 03 April 1992 not usually observed during similar polarization jet events. The other strong negative storm effect on 10 April 1990 with a complete disappearance of the F2-layer maximum at the usual heights was attributed mainly to changes in neutral composition and temperature. A small value for the shape parameter S in the neutral temperature profile and a low neutral temperature at 120 km indicate strong cooling of the lower thermosphere. We propose that this cooling is due to increased nitric oxide concentration usually observed at these heights during geomagnetic storms.     

Analytical procedures for weekly hydrological droughts: a case of Canadian rivers

Abstract

Two entities of importance in hydrological droughts, viz. the longest duration, L_T , and the largest magnitude, M_T (in standardized terms) over a desired time period (which could also correspond to a specific return period) T, have been analysed for weekly flow sequences of Canadian rivers. Analysis has been carried out in terms of week-by-week standardized values of flow sequences, designated as SHI (standardized hydrological index). The SHI sequence is truncated at the median level for identification and evaluation of expected values of the above random variables, E(L_T ) and E(M_T ). SHI sequences tended to be strongly autocorrelated and are modelled as autoregressive order-1, order-2 or autoregressive moving average order-1,1. The drought model built on the theorem of extremes of random numbers of random variables was found to be less satisfactory for the prediction of E(L_T ) and E(M_T ) on a weekly basis. However, the model has worked well on a monthly (weakly Markovian) and an annual (random) basis. An alternative procedure based on a second-order Markov chain model provided satisfactory prediction of E(L_T ). Parameters such as the mean, standard deviation (or coefficient of variation), and lag-1 serial correlation of the original weekly flow sequences (obeying a gamma probability distribution function) were used to estimate the simple and first-order drought probabilities through closed-form equations. Second-order probabilities have been estimated based on the original flow sequences as well as SHI sequences, utilizing a counting method. The E(M_T ) can be predicted as a product of drought intensity (which obeys the truncated normal distribution) and E(L_T ) (which is based on a mixture of first- and second-order Markov chains).

Citation Sharma, T. C. & Panu, U. S. (2010) Analytical procedures for weekly hydrological droughts: a case of Canadian rivers. Hydrol. Sci. J. 55(1), 79–92.     

Instability of flows near the onset of convection in a rotating layer with stress-free horizontal boundaries

We investigate instability of convective flows of simple structure (rolls, standing and travelling waves) in a rotating layer with stress-free horizontal boundaries near the onset of convection. We show that the flows are always unstable to perturbations, which are linear combinations of large-scale modes and short-scale modes, whose wave numbers are close to those of the perturbed flows. Depending on asymptotic relations of small parameters α (the difference between the wave number of perturbed flows and the critical wave number for the onset of convection) and ε (ε² being the overcriticality and the perturbed flow amplitude being O(ε)), either small-angle or Eckhaus instability is prevailing. In the case of small-angle instability for rolls the largest growth rate scales as ε^8/5, in agreement with results of Cox and Matthews (Cox, S.M. and Matthews, P.C., Instability of rotating convection. J. Fluid. Mech., 2000, 403, 153–172) obtained for rolls with k = k _c . For waves, the largest growth rate is of the order ε^4/3. In the case of Eckhaus instability the growth rate is of the order of α².