arXiv subjects

Alastair D. Jenkins

Publications and source records attributed to Alastair D. Jenkins.

6 recordsLinked to original sources

arXiv2007

Commentary on `The Three-Dimensional Current and Surface Wave Equations' by George Mellor

The lowest order sigma-transformed momentum equation given by Mellor (J. Phys. Oceangr. 2003) takes into account a phase-averaged wave forcing based on Airy wave theory. This equation is shown to be generally inconsistent due to inadequate approximations of the wave motion. Indeed the evaluation of the vertical flux of momentum requires an estimation of the pressure $p$ and coordinate transformation function $s$ to first order in parameters that define the large scale evolution of the wave field, such as the bottom slope. Unfortunately there is no analytical expression for $p$ and $s$ at that order. A numerical correction method is thus proposed and verified. Alternative coordinate transforms that allow a separation of wave and mean flow momenta do not suffer from this inconsistency nor require a numerical estimation of the wave forcing. Indeed, the problematic vertical flux is part of the wave momentum flux, thus distinct from the mean flow momentum flux, and not directly relevant to the mean flow evolution.

physics.class-ph↗

arXiv2005

Steady f-plane circulation in basins with saddle-point bathymetry

J. Nilsson, G. Walin, and G. Brostroem (paper accepted by Journal of Marine Research, 2005) have recently shown how a velocity field in geostrophic and hydrostatic balance in an f-plane may be diagnosed from prescribed distributions of buoyancy and wind stress, in a basin with closed isobaths. I extend their analysis to cover basins with more complex depth contours, treating in particular the behaviour of the flow in the presence of a saddle point.

physics.ao-ph↗

arXiv2005

A simple model for the short-time evolution of near-surface current and temperature profiles

A simple analytical/numerical model has been developed for computing the evolution, over periods of up to a few hours, of the current and temperature profile in the upper layer of the ocean. The model is based upon conservation laws for heat and momentum, and employs an eddy diffusion parameterisation which is dependent on both the wind speed and the wind stress applied at the sea surface. Other parameters such as the bulk-skin surface temperature difference and CO$_2$ flux are determined by application of the Molecular Oceanic Boundary Layer Model (MOBLAM) of Schluessel and Soloviev. A similar model, for the current profile only, predicts a temporary increase in wave breaking intensity and decrease in wave height under conditions where the wind speed increases suddenly, such as, for example, during gusts and squalls. The model results are compared with measurements from the lagrangian Skin Depth Experimental Profiler (SkinDeEP) surface profiling instrument made during the 1999 MOCE-5 field experiment in the waters around Baja California. SkinDeEP made repeated profiles of temperature within the upper few metres of the water column. Given that no tuning was performed in the model, and that the model does not take account of stratification, the results of the model runs are in rather good agreement with the observations. The model may be suitable as an interface between time-independent models of processes very near the surface, and larger-scale three-dimensional time-dependent ocean circulation models. A straightforward extension of the model should also be suitable for making time-dependent computations of gas concentration in the near-surface layer of the ocean.

physics.ao-ph↗

arXiv2005

Reply to comment on `A simple model for the short-time evolution of near-surface current and temperature profiles'

This is our response to a comment by Walter Eifler on our paper `A simple model for the short-time evolution of near-surface current and temperature profiles' (arXiv:physics/0503186, accepted for publication in Deep-Sea Research II). Although Eifler raises genuine issues regarding our model's validity and applicability, we are nevertheless of the opinion that it is of value for the short-term evolution of the upper-ocean profiles of current and temperature. The fact that the effective eddy viscosity tends to infinity for infinite time under a steady wind stress may not be surprising. It can be interpreted as a vertical shift of the eddy viscosity profile and an increase in the size of the dominant turbulent eddies under the assumed conditions of small stratification and infinite water depth.

physics.ao-ph↗

arXiv2005

Thermodynamics and Economics

The application of principles of thermodynamics and statistical mechanics to economic systems is considered in a broad historical perspective, extending from prehistoric times to the present day. The hypothesis of maximum entropy production (MEP), which has been used to model complex physical systems such as fluid turbulence and the climate of the Earth and other planets, may be applied to human economic activity, subject to constraints such as the availability of suitable technology, and the nature of political control. Applied to the current abundance of available energy from fossil fuel reserves, MEP is shown to have significant policy implications.

cond-mat.stat-mech↗

arXiv2003

Wave duration/persistence statistics, recording interval, and fractal dimension

The statistics of sea state duration (persistence) have been found to be dependent upon the recording interval Δt. Such behavior can be explained as a consequence of the fact that the graph of a time series of an environmental parameter such as the significant wave height has an irregular, "fractal" geometry. The mean duration, \barτ, can have a power-law dependence on Δt as Δt -> 0, with an exponent equal to the fractal dimension of the level sets of the time series graph. This recording interval dependence means that the mean duration is not a well defined quantity to use for marine operational purposes. A more practical quantity may be the "useful mean duration", \barτ^u, estimated from the formula (\sumτ_i^2)/(\sumτ_i), where each interval [t_i,t_i+τ_i] satisfying the appropriate criterion is weighted by its duration. These results are illustrated using wave data from the Frigg gas field in the North Sea.

physics.ao-ph↗