George F. Carrier

Water waves of finite amplitude on a sloping beach

In this paper, we investigate the behaviour of a wave as it climbs a sloping beach. Explicit solutions of the equations of the non-linear inviscid shallow-water theory are obtained for several physically interesting wave-forms. In particular it is shown that waves can climb a sloping beach without breaking. Formulae for the motions of the instantaneous shoreline as well as the time histories of specific wave-forms are presented.

Diffusion Theory of Nonequilibrium Dissociation and Recombination

The coupled vibration—dissociation—recombination process for molecules and atoms has been examined. Techniques for solving the appropriate master equations for both quantum (discrete) and classical (continuous) models are given. It is shown that the process is most easily treated classically and that in this case the master equation can be reduced to an equivalent diffusion equation. It is assumed that, after an initial vibration transient, during which reactions are negligible, the process may be treated using the steady‐state approximation. During the steady‐state phase, the usual phenomenological rate equations are valid and the ratio of the forward and reverse rate constants is the equilibrium constant, though the individual rate constants are depressed below their equilibrium values.Comparison of the results with other theoretical work shows general agreement for similar models; comparison with shock‐tube experiments on molecular dissociation and stellarator experiments on ionic recombination is enco...

Tsunami run-up and draw-down on a plane beach

Tsunami run-up and draw-down motions on a uniformly sloping beach are evaluated based on fully nonlinear shallow-water wave theory. The nonlinear equations of mass conservation and linear momentum are first transformed to a single linear hyperbolic equation. To solve the problem with arbitrary initial conditions, we apply the Fourier–Bessel transform, and inversion of the transform leads to the Green function representation. The solutions in the physical time and space domains are then obtained by numerical integration. With this semi-analytic solution technique, several examples of tsunami run-up and draw-down motions are presented. In particular, detailed shoreline motion, velocity field, and inundation depth on the shore are closely examined. It was found that the maximum flow velocity occurs at the moving shoreline and the maximum momentum flux occurs in the vicinity of the extreme draw-down location. The direction of both the maximum flow velocity and the maximum momentum flux depend on the initial waveform: it is in the inshore direction when the initial waveform is predominantly depression and in the offshore direction when the initial waves have a dominant elevation characteristic.

THE MAGNETOHYDRODYNAMIC FLOW PAST A FLAT PLATE

The uniform steady flow of an incompressible, viscous, electrically conducting fluid is distorted by the presence of a symmetrically oriented semi-infinite flat plate. The ambient magnetic field is coincident with the ambient velocity field. The description of the resulting fields depends on the physical co-ordinates measured in units of Reynolds number and on the two parameters e = ωμν and β = μ H 2 /ρ v 2 . This description of the fields is approximated in three different ways and essentially covers the full range of e and β. In particular, when β [Gt ] 1, no steady flow which is uniform at large distances from the plate exists.

Asymptotic analyses of the buckling of imperfect columns on nonlinear elastic foundations

Abstract The buckling of a model imperfection-sensitive structure is studied, by a variety of techniques, for various kinds of deterministic and stochastic initial imperfections. The structure considered is an infinitely long column on a “softening” nonlinear elastic foundation. The techniques used are perturbation expansions (including the “two-time” variety), equivalent linearization and truncated hierarchy approximations; in all cases, asymptotic results are sought for small imperfection magnitudes, and the effects of the various kinds of imperfections are compared.

On the theory of the wind-driven ocean circulation

A surface distribution of stress is imposed on an ocean enclosed by two continental boundaries; the resulting transport circulation is studied between two latitudes of zero surface wind-stress curl, within which the curl reaches a single maximum. Under the assumption that turbulent transfer of relative vorticity has a minimum effect on the mean circulation, inviscid flow patterns are deduced in the limit of small transport Rossby number. Inertial currents, or naturally scaled regions of high relative vorticity, occur on both the eastern and the western continental coasts. Limits on the relative transports of the currents are obtained and found to depend on the direction of variation of the wind-stress curl with latitude, relative to that of the Coriolis accelerations. The most striking feature of the inviscid flow is a narrow inertial current the axis of which lies along the latitude of maximum wind-stress curl. All eastward flow occurs in this midlatitude jet.A feature of the flow which cannot remain essentially free of turbulent processes is the integrated vorticity relationship, since the imposed wind-stress distribution acts as a net source of vorticity for the ocean. Heuristic arguments are used together with this integral constraint to deduce the presence and strength of the turbulent diffusion which must occur in the region of the mid-latitude jet. It is further inferred that the turbulent meanders of the jet must effect a net meridional transport of relative vorticity.

Wind-Aided Firespread Across Arrays of Discrete Fuel Elements. II. Experiment

Abstract Laboratory-scale experiments on wind-aided firespread across an array of very-small-diameter (1.3-4.4-mm), discrete fuel elements were carried out in a specially designed wind tunnel. The rate of firespread, ty, is inferred from the output of streamwise-disiributed, near-bed-surface thermocouples. The fuel consists of an array of identical, regularly arranged, wooden, toothpick-like Tuel elements, positioned upright in shallow holes drilled in a ceramic substrate. Adoption of this well-defined fuel bed facilitates repetition. Extensive testing suggests that νy ∼ (U/m)1/2 over a wide range of the uniform ambient wind speed U and the fuel-mass distribution m (fuel, per unit planform area of the bed, consumed with firefront passage). The effects on the firespread rate of other parameters investigated and reported include the type of wood species; fuel-element length; fuel-element diameter; fuel-bed width, including streamwise-varyjng width; enhanced moisture content of the substratum and/or fuel; sm...

Stoichiometry and Flameholder Effects on a One-Dimensional Flame

Abstract The steady one-dimensional isobaric combustion of a gaseous premixture of fuel and oxidant under a direct one-step irreversible Arrhenius-type exothermic chemical reaction is studied analytically for constant, but general, Lewis-Semenov number. Limit-process expansions are used to obtain solutions in the physically interesting limit of activation temperature large relative to the hot-boundary temperature. The eigenvalue or critical flow speed for an adiabatic system is established as a function of departure from stoichiometry. It is emphasized that, for relatively small departures from stoichiometry, the bimolecular system behaves as a monopropellant decomposition, to lowest order of approximation, because the richer reactant is effectively undepleted. The porous-disk-type flameholder for a flat-flame burner is modeled as a (nonadiabatic) heat source (supercritical flow speed) or heat sink (subcritical flow speed). The flame stand-off distance and the amount of departure of the hot-boundary tempe...

Some effects of stratification and geometry in rotating fluids

The phenomena which occur in a fluid contained in a rotating system are strongly influenced by the density gradients in that fluid and by certain features of the geometry. In this paper, we study several specific phenomena which involve stratification and/or irregular surface topography and some phenomena which arise because of an equatorial geometry. Although several of these studies are motivated by particular geophysical questions, we do not treat comprehensively any geophysical phenomenon. Nevertheless, the inferences we draw from these studies do much to clarify the roles of the mechanisms underlying various geophysical phenomena and these inferences should be of value when comprehensive geophysical investigations are attempted.

Cyclic Absorption/Desorption of Gas in a Liquid Wall Film,

Abstract —The unsteady one-dimensional cyclic absorption and desorption of a dilute amount of gas in a thin (constant-thickness),isothermal (constant-property) liquid layer on an impervious noncatalytic wall is examined. The pertinent conditions are taken to be (1) thermodynamic equilibrium (such that Henrys law holds at the two-phase interface), and (2) diffusional resistance of the liquid layer being rate-controlling (such that the problems for the liquid layer, and for the bulk gas contiguous to it, decouple). Specifically, the mass fraction of the gaseous species of interest is taken to be known, and of square-wave periodic character, at the two-phase interface, so attention is concentrated on the total gaseous content of the liquid layer as a function of time. While start-up (in which the liquid layer is taken to be initially free of gaseous content) is considered, primary interest is in steady periodic operation in which no residual influence of the initial condition remains. The model is developed...