Modelling long and intermediate waves in a harbor

1186

Mathematical and Computer Modelling Reports difference algorithm) for the depth-averaged velocities, and then solving the momentum equations for the vertical velocity profiles. The pollutant transport part of the model includes surface spreading of the slick, evaporation and dispersion into the water column, convection, and both horizontal and vertical dispersion of the pollutant plume. The model is applied to the simulation of a SOOO-barrelsurface spill in the Marjan offshore oil field. Key Words-Residual

current, pollutant transport, oil spill, (Arabian) Gulf, convection-diffusion

model

Appl.math.MooMingVol. 12,p. 391,1988

THERMODYNAMICALLY CONSISTENT k-Z MODELS FOR COMPRESSIBLE TURBULENT FLOWS GOODARZ AHMADI

Department of Mechanical and Industrial Engineering, Clarkson University, Potsdam, NY 13676, U.S.A. Abstract-Fundamental conservation laws for the mean turbulent flow of a compressible fluid are considered. The averaged form of the entropy inequality is described, and the thermodynamics of the mean turbulent field is studied. The free energy function and the coldness of turbulence are discussed, and several thermodynamical relationships are established. Based on the averaged Clausius-Duhem inequality, constitutive equations for the mean flow field are developed. The basic equations of motion for compressible flows are derived. The case of incompressible turbulent flows is discussed. It is shown that the resulting governing equations are similar to those of the existing two-equation k-Z mode1 of turbulence. Key

Worak-Turbulence turbulence

model, compressible

turbulence,

two-equation

model, thermodynamics

of

Appl.math.Model/@Vol. 12,p. 423,1988

MODELLING

LONG AND INTERMEDIATE IN A HARBOR WEN-LI

WAVES

CHIANG

Tetra Tech Inc., 630 N, Rosemead Blvd, Pasadena, CA 91107, U.S.A. Abstract-A transient model is utilized to study the effect of the proposed 2010/2020 master plan on wave conditions in Los Angeles and Long Beach harbors. The proposed plan consists of placing landfills and increasing basin and channel depths. The numerical model incorporates an implicit, finite-difference scheme to solve a set of hydrodynamic equations with a two-dimensional depth-averaged formulation. Long-wave equations are slightly revised such that the model can be applied to wave propagation in intermediate depths. The wave period under consideration ranges from 30 to 300 s. A base run was performed to study existing conditions. The results are compared with laboratory measurements. Although there is a slight discrepancy in the results, partially due to the different boundary conditions in the models, the general pattern and order of magnitude of the spectrum fit reasonably well with laboratory results. The numerical model is applied to the proposed 2010/2020 master plan to obtain spectra of relative wave height at a location of interest. Resonance appears at a wave period of 203 s. A contour map of relative maximum wave height is presented. Key Words-Mathematical

model, finite-difference, harbors, wave height