Magnetic interpretation of dyke anomalies using derivatives

The horizontal and vertical derivative profiles of magnetic anomalies of dykes show some interesting properties. The points of zero derivatives and the points where the derivatives are equal are conjugate point pairs. A method of interpretation of dyke anomalies is suggested, which utilizes the distances between these points.Notation F Magnetic anomaly in total intensity - Z Depth to top of the dyke - 2T Width of the dyke - Geological dip of the dyke - I Effective intensity of magnetisation in the plane of profile - Dip of effective magnetisation vector in the plane of profile - Strike angle of the dyke - i Magnetic dip - Q – - Q _f –+arctan (sin coti) - I _f      

On the magnetic memory phenomenon in rocks and its bearing on palaeomagnetic measurements

Summary The results of recent extensive studies on the low field hysteresis in basalts from India and East Africa and the memory phenomenon observed in some of the rocks have been found to have a direct bearing on the various parameters such asQ _n,Q _tn, stability by the A.C. field technique etc. which are of great importance in rock-magnetism. It has been found that rocks having low Curie temperature (it _c ) and not exhibiting memory phenomenon are ideally suited for palaeomagnetic studies. Also, rocks having relatively higher it _c often exhibit memory phenomenon, given inconsistent NRM directions and show an irregular behaviour on A.C. field cleaning. In using the latter rock types for palaeomagnetic work one has to take a number of precautions which are clearly brought out by the studies described in this paper.     

Chemical and Isotopic Composition of Waters and Dissolved Gases in Some Thermal Springs of Sicily and Adjacent Volcanic Islands, Italy

Hydrochemical (major and some minor constituents), stable isotope ( and , δ13C_TDIC total dissolved inorganic carbon) and dissolved gas composition have been determined on 33 thermal discharges located throughout Sicily (Italy) and its adjacent islands. On the basis of major ion contents, four main water types have been distinguished: (1) a Na-Cl type; (2) a Ca-Mg > Na-SO₄-Cl type; (3) a Ca-Mg-HCO₃ type and (4) a Na-HCO₃ type water. Most waters are meteoric in origin or resulting from mixing between meteoric water and heavy-isotope end members. In some samples, δ¹⁸O values reflect the effects of equilibrium processes between thermal waters and rocks (positive ¹⁸O-shift) or thermal waters and CO₂ (negative ¹⁸O-shift). Dissolved gas composition indicates the occurrence of gas/water interaction processes in thermal aquifers. N₂/O₂ ratios higher than air-saturated water (ASW), suggest the presence of geochemical processes responsible for dissolved oxygen consumption. High CO₂ contents (more than 3000 cc/litre STP) dissolved in the thermal waters indicate the presence of an external source of carbon dioxide-rich gas. TDIC content and δ¹³C_TDIC show very large ranges from 4.6 to 145.3 mmol/Kg and from –10.0‰ and 2.8‰, respectively. Calculated values indicate the significant contribution from a deep source of carbon dioxide inorganic in origin. Interaction with Mediterranean magmatic CO₂ characterized by heavier carbon isotope ratios ( value from -3 to 0‰ vs V-PDB (CAPASSO et al., 1997, GIAMMANCO et al., 1998; INGUAGGIATO et al., 2000) with respect to MORB value and/or input of CO₂-derived from thermal decomposition of marine carbonates have been inferred.     

Power-law Distributions of Offspring and Generation Numbers in Branching Models of Earthquake Triggering

We consider a general stochastic branching process,which is relevant to earthquakes as well as to many other systems, and we study the distributions of the total number of offsprings (direct and indirect aftershocks in seismicity) and of the total number of generations before extinction. We apply our results to a branching model of triggered seismicity, the ETAS (epidemic-type aftershock sequence) model. The ETAS model assumes that each earthquake can trigger other earthquakes (aftershocks). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. Due to the large fluctuations of the number of aftershocks triggered directly by any earthquake (fertility), there is a large variability of the total number of aftershocks from one sequence to another, for the same mainshock magnitude. We study the regime in which the distribution of fertilities is characterized by a power law ~1/¹⁺. For earthquakes we expect such a power-distribution of fertilities with =b/ based on the Gutenberg-Richter magnitude distribution ~ 10^–bm and on the increase ~ 10^–m of the number of aftershocks with the mainshock magnitude m. We derive the asymptotic distributions p_r(r) and p_g(g) of the total number r of offsprings and of the total number g of generations until extinction following a mainshock. In the regime < 2 for which the distribution of fertilities has an infinite variance, we find This should be compared with the distributions obtained for standard branching processes with finite variance. These predictions are checked by numerical simulations. Our results apply directly to the ETAS model whose preferred values =0.8–1 and b=1 puts it in the regime where the distribution of fertilities has an infinite variance. More generally, our results apply to any stochastic branching process with a power-law distribution of offsprings per mother     

The Local Magnitude Scale in the Korean Peninsula

A formula to determine the local magnitude (M_L) following Richters original definition was empirically derived for the Korean Peninsula. A total of 1,644 digital seismograms from 142 Korean earthquakes that occurred from 1997 to 2000 were corrected for instrument response and convolved with the nominal Wood-Anderson torsion seismograph response to be appropriate for the original definition of M_L. Then, the zero-to-peak amplitude was measured in millimeters on the synthetic Wood-Anderson seismogram. Multiple regression analysis was conducted to determine distance and station correction terms for the measured peak amplitudes. The best-fit solution for M_L yielded the following formula for the Korean Peninsula:where A() and S denote the peak amplitude on the synthetic Wood-Anderson seismogram at distance and the station correction term, respectively. Note that the second term, distance correction, was adjusted with Richters M_L, taking into consideration attenuation differences between the Korean Peninsula and southern California, where Richter originally introduced M_L. On average, the magnitudes determined in this study are nearly the same as those determined by the Korea Institute of Geoscience and Mineral Resources (KIGAM), but are larger than those of the Korea Meteorological Administration (KMA) by as much as 0.36.     

A numerical study of the heat transfer through a fluid layer with recirculating flow between concentric and eccentric spheres

A numerical study has been made of the heat transfer through a fluid layer with recirculating flow. The outer fluid surface was assumed to be spherical, while the inner surface consisted of a sphere concentrically or eccentrically located with respect to the outer spherical surface. The recirculating flow was assumed to be driven by a gas flow creating stress on the fluid's outer surface so that creeping (low Reynolds number) flow developed in its interior. The present study solves the Stokes equation of motion and the convective diffusion equation in bispherical coordinates and presents the streamline and isotherm patterns.Nomenclature a _i inner sphere radius - a _d outer sphere radius - A ₁ defined by equation (5) - A ₂ defined by equation (6) - B ₁ defined by equation (7) - B ₂ defined by equation (8) - c dimensional factor for bispherical coordinates - C constant in equation (4) - d narrowest distance between the two eccentric spheres - E ² operator defined by equation (1) in spherical coordinates and by equation (21) in bispherical coordinates - G modified vorticity, defined in equation (22) - G ^* non-dimensional modified vorticity, defined in equation (28) - h metric coefficient of bispherical coordinate system, defined in equation (18) - k _w thermal conductivity of water - K ₁ defined by equation (9) - K ₂ defined by equation (10) - N _Re Reynolds number=2a _dU/gn - N _Pe,h Peclet number=2a _dU/ - n integer counter - q heat flux - r radius - r ^* non-dimensional radius=r/a _d - S surface area - t time - t ^* non-dimensional time=t/a _d ² - T temperature - T _o temperature at inner sphere surface - T _a temperature at outer sphere surface - T ^* non-dimensional temperature;=(T–T _o)/(T_a–T_o) - u velocity - u _r radial velocity in spherical coordinates - u angular velocity in spherical coordinates - u radial velocity in bispherical coordinates - u angular velocity in bispherical coordinates - U free stream velocity - u _r ^* =u _r/U - u ^* =u /U - u ^* =u /U - u ^* =u /U Greek symbols a ₁ small displacement - vorticity, defined in equation (17) - ^* non-dimensional vorticity, defined in equation (27) - radial bispherical coordinates - _o bispherical coordinate of inner sphere - _a bispherical coordinate of outer sphere - angular coordinate in spherical coordinates - thermal diffusivity - _w thermal diffusivity of water - kinematic viscosity - angular bispherical coordinate - spherical coordinate - streamfunction - non-dimensional streamfunction for spherical coordinates, = /(U a _d ² ) - ^* non-dimensional streamfunction for bispherical coordinates, defined in equation (26)     

Water uptake and equilibrium sizes of aerosol particles at high relative humidities: Their dependence on the composition of the water-soluble material

Equilibrium water uptake and the sizes of atmospheric aerosol particles have for the first time been determined for high relative humidities, i.e., for humidities above 95 percent, as a function of the particles chemical composition. For that purpose a new treatment of the osmotic coefficient has been developed and experimentally confirmed. It is shown that the equilibrium water uptake and the equilibrium sizes of atmospheric aerosol particles at large relative humidities are significantly dependent on their chemical composition.List of symbols A proportionality factor - a _w activity of water in a solution - c _{p v} specific heat of water vapour at constant pressure - c _w specific heat of liquid water - f relative humidity - l _w specific heat of evaporation of water - M _i molar mass of solute speciesi - M _s mean molar mass of all the solute species in a solution - M _w molar mass of water - m ₀ mass of an aerosol particle in dry state - m _i mass of solute speciesi - m _s mass of solute - m _w mass of water taken up by an aerosol particle in equilibrium state - m total molality=number of mols of solute species in 1000 g of water - m _i molality of solute speciesi - m _k total molality of a pure electrolytek - O(m ²) remaining terms being of the second and of higher powers ofm - p ⁺ standard pressure - p total pressure of the gas phase - p pressure within a droplet - p ₁,p ₂,p ₃ coefficients in the expansion of M - p _1i, p_2i, p_3i specific parameters of ioni - p _s saturation vapour pressure - p _w water vapour pressure - R _w individual gas constant of water - r radius of a droplet - r ₀ equivalent volume radius of an aerosol particle in dry state - T temperature - T ₀ standard temperature - T ₁ temperature of the pure water drop in the osmometer - v _w specific volume of pure water - z _i valence of ioni - _i relativenumber concentration of ioni in a solution - correction term due to the adsorption of ions at liquid-solid interfaces - activity coefficient of solute speciesi in a solution, related to molalities - I bridge current - T temperature difference between solution and pure water drop in the osmometer - exponential mass increase coefficient - _w specific chemical potential of water vapour - _w specific chemical potential of water - ⁰ _w specific chemical potential of pure water vapour - ⁰ _w specific chemical potential of pure water - ₀ density of an aerosol particle in dry state - _w density of pure water - surface tension of a droplet - ₀ surface tension of pure water, i.e., at infinite dilution of the solute - osmotic coefficient - _k osmotic coefficient of a solution of a pure electrolytek - _k osmotic coefficient of a solution of a mixed solute - _M fugacity coefficient of water vapour - ^s _{i=1 i} z ² _i This work is part of a Ph.D. thesis carried out at the Meteorological Institute of the Johannes Gutenberg-Universität, Mainz.     

A note on tidal current rotation

The rotational form of the vertically averaged equations of motion is applied to derive a formula, linear friction included, which establishes a direct connection between sense of rotation of tidal currents and features of tidal amphidromic systems. Two factors in the formula, called and , influence the sense of rotation of tidal currents; the factor involves the frequency of the tidal signal , the Coriolis parameter f, and the linear friction coefficient r. The sign of the cross-product of the logarithm of sea-surface elevation (), and phase () gradients determines whether the factor favors clockwise or anticlockwise sense of rotation. is a unit vector and is the angle between ln and . The limits ||0, ||0 and 0 lead to a clockwise sense of rotation in the Northern Hemisphere. 0 favors anticlockwise rotation in the Northern Hemisphere. Friction and low frequencies favor an anticlockwise sense of rotation. The theory works well in semi-enclosed regions like the North Sea. Although only linear friction and sea-surface elevation gradients were considered, there are ocean regions where the agreement between theory and observations is also good.Responsible Editor: Hans Burchard     

Electromagnetic scattering due to deformed inhomogeneous bodies (Part I: Sphere)

Summary The potential technique of the perturbation has been employed to find the analytical expressions for the response of conducting bodies of irregular shapes. In Part I spherical bodies and in Part II cylindrical ones are considered. The conductivities are assumed to be finite and radially varying. The deformation of the boundaries in both the cases are considered to be of the typek _p =r ₀[1++f ₁(, )] where is the perturbation parameter. Calculations have been made for uniform as well as non-uniform excitation fields. Since the models represent the geological ore-formation more closely, the results will find application in preparing type curves for induction prospecting.N.G.R.I. Contribution No. 70-194.     

Moto di un vortice sulla Terra e sua influenza sulla polodia

Riassunto Si suppone la Terra avvolta da un velo di un fluido perfetto incomprimibile messo in rotazione da un vortice doppio puntiforme. Si calcola l'energia cinetica totale della Terra e del fluido in funzione degli angoli di Eulero , , , che esprimono il moto della Terra rispetto a una terna inerziale, e degli angoli ₀, ₀ esprimenti il moto del vortice rispetto alla Terra. Si determinano i predetti angoli in funzione del tempo mediante le equazioni di Lagrange; risulta che il moto del vortice è caratterizzato da ₀= const., e che la sua influenza sulla polodia è trascurabile.

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Summary Supposing the Earth sorrounded by a veil of an incompressible perfect fluid rotationally moved by a point shaped double vortex, the Author calculates the total kinetic energy of the system as a function of the Eulerian angles , , which expres the Earth motion referred to an inertial tern, and of the angles ₀, ₀ for the vortex motion referred to the Earth. He determines the above said angles as temporal functions by means of the equations of Lagrange. It results that the vortex motion is determined by ₀= const., and that its influence on the rate of rotation of the Earth is negligeable.

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Comunicazione presentata alla 2^a. Assemblea annuale della «Società Italiana di Geofisica e Meteorologia» (Genova, 23–25 Aprile 1954).     

A note on the stress-dilatancy relation for simulated fault gouge

Theoretical constraints on the stress-dilation relation for a deforming Coulomb material requirev ifC=0 andv sin^-1( _m / _m ) always, wherev is the dilation angle, is the friction angle,C is cohesion, _m is the maximum shear stress, and _m is the mean effective stress. Recent laboratory measurements of friction and dilatancy of simulated fault gouge show that small amplitude shear-load cycling causes compaction and consolidation. Comparison of the data with theory indicates that such load cycling produces: (1) increased coefficient of friction (or friction angle), (2) increased cohesion, and (3) increased dilatancy rate (or dilation angle). Under certain conditions of load cycling without significant plastic shear strain accumulation ( ^p <0.005) we find thatv exceeds both and, in contrast to theory, sin^-1( _m / _m ). This result is interpreted in terms of enhanced cohesion and overconsolidation, which lead to residual stresses within the gouge. An analogy is drawn between these special loading conditions and those extant on natural faults. In particular, our results imply that jostling and minor stress variations associated with microearthquakes may produce strengthening of fault gouge and changes in the fault zone's stress-dilatancy relation. Hence, compaction associated with microseismicity may lead to subsequent dilation of fault gouge, even for faults with large displacement rates and large net offsets (e.g., San Andreas). In regions where such dilation persists over sufficient displacements (on the order of the critical slip distance for seismic faulting) it may tend to inhibit unstable slip.     

The coalescence of water drops II. The coalescence problem and coalescence efficiency

By the use of the model of approaching drops (Arbel and Levin, 1977) the coalescence efficiencies of drops are computed. It is found that for interactions of drops at their terminal velocities the coalescence depends both on the size of the large drop and on the size ratio of the interacting drops in agreement with the experimental results of Whelpdale and List (1971) and Levin and Machnes (1977).The results were found to be sensitive to the assumption of the drops deformation and to the critical separation distance. This distance is defined as the distance at which the drops begin to merge. The variations of the coalescence efficiency with these parameters is discussed.Appendix: List of symbols D distance between the deformed surfaces of the drops - D _o initial value ofD - D _s stop distance, the distance at which the impact velocity vanishes - D _c critical coalescence distance - E collection efficiency - E ₁ collision efficiency - E ₂ coalescence efficiency - E _2R coalescence efficiency for collisions with stationary targets - F _c centrifugal force - p ratio of the radii of the interacting drops - r _o initial distance between drops' centers - R _L radius of larger drop - R _s radius of smaller drop - R _D radius of deformation - v approach velocity of two deformed surfaces - v _o initial value ofv - V _i impact velocity (given negative sign when drops approach each other) - V _c critical impact velocity - W _i velocity of the smaller drop at infinity for it to reachD _o with velocityv _o - x _i impact distance, the distance between the trajectories of the two drops - x _c critical impact distance for coalescence -  average critical impact distance for coalescence - X _c critical impact distance for collisions - coefficient of deformation given in equation 1 - _i impact angle defined byWhelpdale andList (1971) given also inArbel andLevin (1977) - coefficient of deformation given in equation 2 - viscosity of air - _i impact angle used inArbel andLevin (1977) and here - _c critical angle for coalescence - average critical angle for coalescence On sabbatical leave (1976–77) from the Department of Geophysics and Planetary Sciences, Tel Aviv University, Ramat Aviv, Israel.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

On the free oscillations of a laterally heterogeneous earth model

Summary The equations of motion for the free oscillations of a heterogeneous spherical earth model are derived. It is found that the lateral variations of density and elastic moduli couple the odd(even) harmonics of the spheroidal oscillations with themselves as well as with the even (odd) harmonics of the torsional oscillations.List of symbols r, , Spherical coordinates;r is the radial distance from earth's center, is the co-latitude, and is the east longitude - r Space vector denoting a point with coordinatesr, , and - Gradient operator - ² Laplacian operator - _ij Kronecker's delta function - I Identity matrix - i      

Laboratory measurements of spatial fluctuation and attenuation of elastic waves by scattering due to random heterogeneities

To study the effects of strong scattering on elastic waves, spatial fluctuation and scattering attenuation ofP waves were examined by laboratory experiments for 2-D models of random media approximately characterized by a triangular correlation function in the range of 2<ka<33, wherek is the wave number anda is the correlation distance of the heterogeneities, i.e., the heterogeneity size. The results obtained are as follows: (1) Forka>10, both the intensity and the correlation distance of the amplitude fluctuation are approximate for any phase of theP-wave train. The correlation distance nearly agrees with the heterogeneity size. These fluctuation properties are quite consistent with the theoretical prediction by the forward-scattering approximation. (2) For 3<ka<6, the fluctuation intensity becomes stronger in later phases of theP-wave train. This shows that scattering is approximately isotropic, and therefore, the scattered energy increases with time within theP-wave train. The correlation distance of the amplitude fluctuation disagrees with the heterogeneity size, and it shows a frequency-dependent property decreasing from 7a to 4a with the increase ofka from 3 to 6. These properties for 3<ka<6 have not yet been predicted theoretically. (3) Forka<3, though the fluctuation is considerably smaller compared with that ofka>10 and 3<ka<6, the fluctuation property is considered similar to that of 3<ka<6. (4) The observed scattering attenuation,Q ^–1, increases withka forka<3, has a peak aroundka=35, and then decreases withka. (5) When _min = 15° and = 0.075, the theoreticalQ ^–1 curve, predicted by the approximate theory of Wu, roughly matches the observedQ ^–1 values, where _min is the minimum scattering angle measured from the propagation direction of theP waves and is the rms of fractional velocity fluctuation. This suggests that the energy scattered in the range of >15° is lost from theP waves, while the energy scattered in the range of <15° is retained; and that the approximate theory overestimates by about three times the value of the model media used owing to the neglect of multiple scattering. (6) When the size of velocity heterogeneities responsible for forward scattering at 3<ka<6 is estimated from the _min value of 15° on the basis of Wu's theory, it nearly agrees with the correlation distance for the initial phase of theP-wave train.     

A multivariate gamma distribution arising from a Markov model

A Markov chain{X _t }, which has been useful for modelling in hydrology, can be specified by the Laplace transform (LT) of the conditional p.d.f. ofX _t+1 givenX _t =x _t , which is assumed to be of the exponential formH()exp{-G()x _t }. For appropriate choice ofH andG the marginal distribution ofX _t is the (univariate) gamma distribution. In this case, the joint p.d.f. ofX _t +1,...,X _t+n and its LT, are obtained, and this is extended to a seasonal version of the chain. A simple method of generating observations from these multivariate gamma distributions is noted, and the joint LT is applied to the problem of determining moments of weighted sums of such variables.     

Far-field Gravity and Tilt Signals by Large Earthquakes: Real or Instrumental Effects?

A wide set of dynamics phenomena (i.e., Geodynamics, Post Glacial Rebound, seismicity and volcanic activity) can produce time gravity changes, which spectrum varies from short to long (more than 1 year) periods. The amplitude of the gravity variations is generally in the order of consequently their detection requires instruments with high sensitivity and stability: then, high quality experimental data. Spring and superconducting gravimeters are intensively used with this target and they are frequently jointed with tiltmeters recording stations in order to measure the elasto-gravitational perturbation of the Earth. The far-field effects produced by large earthquakes on records collected by spring gravimeters and tiltmeters are investigated here. Gravity and tilt records were analyzed on time windows spanning the occurrence of large worldwide earthquakes; the gravity records have been collected on two stations approximately 600 km distant. The background noise level at the stations was characterized, in each season, in order to detect a possible seasonal dependence and the presence of spectral components which could hide or mask other geophysical signals, such as, for instance, the highest mode of the Seismic Free Oscillation (SFO) of the Earth. Some spectral components (6.5; 8; 9; 14, 20, 51) have been detected in gravity and tilt records on the occasion of large earthquakes and the effect of the SFO has been hypothesized. A quite different spectral content of the EW and NS tiltmeter components has been detected and interpreted as a consequence of the radiation pattern of the disturbances due to the earthquakes. Through the analysis of the instrumental sensitivity, instrumental effects have been detected for gravity meters at very low frequency.F.S.E. (Fondo Sociale Europeo -European Community -)     

Generalized thermoelastic longitudinal waves in unbounded medium

Summary In this paper the generalized thermoelastic longitudinal waves and the temperature field set up due to coupling of the displacement and the temperature fields, with heat wave travelling with certain finite velocity, in an unbounded medium are studied. The thermoelastic displacement potential and the temperature field at any point are obtained in terms of the surface integrals involving the potential, the temperature and their normal derivatives.Notation x _i the cartesian coordinate system,i=1,2,3 - n (u _i) the displacement vector - (/x _i) the del operator - _t /t the derivative with respect to time - T _o the temperature corresponding to the natural stat of zero stress and strain - T Absolute temperature - c _e the specific heat - , Lamé's constants - ₀ the density - coefficient of linear thermal expansion - K thermal conductivity coefficient - _kk u - ₀ the relaxation time     

Deformation of a homogeneous gravitating sphere by internal dislocations

Summary An explicit solution is obtained for the system of equations describing the spheroidal motion in a homogeneous, isotropic, gravitating, elastic medium possessing spherical symmetry. This solution is used to derive the Green's dyad for a homogeneous gravitating sphere. The Green's dyad is then employed to obtain the displacement field induced by tangential and tensile dislocations of arbitrary orientation and depth within the sphere.Notation G Gravitational constant - a Radius of the earth - A _o =4/3 G - Perturbation of the gravitational potential - Circular frequency - V _p ,V _s Compressional and shear wave velocities - k _p =/V _p - k _s =/V _s - k _p [(2.8)] - , [(2.17)] - f _l ⁺ Spherical Bessel function of the first kind - f _l ^– Spherical Hankel function of the second kind - x =r - y =r - x _o =r _o - y _o =r_o - x =r k _s - y =r k _p - x _o =r _o k _s - y _o =r _o k _p - =a - =a - [(5.17)] - _{m, l}      

Reservoir lifetime and heat recovery factor in geothermal aquifers used for urban heating

Simple models are discussed to evaluate reservoir lifetime and heat recovery factor in geothermal aquifers used for urban heating. By comparing various single well and doublet production schemes, it is shown that reinjection of heat depleted water greatly enhances heat recovery and reservoir lifetime, and can be optimized for maximum heat production. It is concluded that geothermal aquifer production should be unitized, as is already done in oil and gas reservoirs.Nomenclature a distance between doublets in multi-doublet patterns, meters - A area of aquifer at base temperature, m² drainage area of individual doublets in multidoublet patterns, m² - D distance between doublet wells, meters - h aquifer thickness, meters - H water head, meters - Q production rate, m³/sec. - r _e aquifer radius, meters - r _w well radius, meters - R _g heat recovery factor, fraction - S water level drawdown, meters - t producing time, sec. - T aquifer transmissivity, m²/sec. - v stream-channel water velocity, m/sec. - actual temperature change, °C - theoretical temperature change, °C - water temperature, °C - heat conductivity, W/m/°C - _r rock heat conductivity, W/m/°C - _aC_a aquifer heat capacity, J/m³/°C - _aC_r rock heat capacity, J/m³/°C - _WC_W water heat capacity, J/m³/°C - aquifer porosity, fraction     

The role of wavegroup velocity in the blocking problem

Considering the blocking problem as a baroclinic instability problem in a dispersive wave system with diabatic heating effects, it is of great interest to investigate the role of wavegroup velocityv _gr in blocking processes, becausev _gr controls the energy transfer in the wave field. Using a Newtonian Cooling —type of forcing with a phase differencek to the main field and taking the linearized version of a two-level model, the phase speedc _r, the group velocityv _gr and the growth ratekc _i have been obtained as analytical functions of the mean zonal windU, the thermal windU _T, the coefficient of diabatic heating x, the phase differencek and the wavelengthL. Now the hypothesis is introduced, that a blocking should be expected, ifv _gr has a maximum value in the vicinity ofL _o, for whichc _r vanishes and thee-folding timet=1/kc _i (kc _i>0) is smaller than 6 days (see condition (20) in the text). One finds, that for special parameter combinations (U _T, U, ), where 15 m/secU _T25m/sec,U=10m/sec, 0.8·10^–51.5·10^–5 [sec^–1], certain valuesL _o with an appropriate phase differencek exist, which satisfy the conditions mentioned above (for values see Table 2). TherebyL _o varies within the range 8500 km <L _o<11000 km corresponding to the preferred planetary blocking wavenumber 2 in middle latitudes 50°<<70° N.