Journal of Engineering Mechanics

Artificial upwelling and mixing is a new technology for enhancing open ocean mariculture using nutrient-rich deep ocean water. A wave-driven artificial upwelling device was developed based on mathematical modeling and hydraulic experiments. Results of the numerical modeling are in good agreement with hydraulic experiments. The mathematical model was applied to simulate the operation of a prototype device in typical Hawaiian waves. The prototype device consists of a buoy with a water chamber 4.0 m in diameter, a flow-controlling valve, and a long tail pipe 300 m in length and 1.2 m in diameter. This device can produce an upwelling flow of 0.62 m³/s in regular Hawaiian waves with a period of 12 s and a wave height of 1.9 m. Two analytical solutions to the simplified governing equations were also derived that provide a basis for the derivation of predictive equations, useful for preliminary engineering design and analysis.

The flow and scalar field in the cross section of a bent-over momentum jet in cross-flow has been investigated via a 2D numerical solution of the governing equations with similarity transformation. The semianalytical model employs a free shear layer model for turbulent closure and the assumption of a constant velocity in the direction of the cross-flow; the entire solution depends solely on a dimensionless turbulent mixing parameter λ that measures the relative importance of advection and diffusion. The computed streamlines and vorticity field clearly indicate a vortex-pair flow for all λ. The shape of the scalar distribution, however, grows from a circular cell to a kidney-shaped double peak structure. Using a value of λ = 55, the computed jet trajectory and spreading and the cross-sectional shape are in good agreement with the experiments, although the dilution is somewhat overpredicted. The results suggest a free shear layer model of ε = 0.0272W_ml*, where ε, W_m, and l* are the eddy viscosity, maximum velocity, and half-width in the bent-over jet cross section, respectively.

An expository review is given on various theories of modeling weakly to strongly nonlinear, dispersive, time-evolving, three-dimensional gravity-capillary waves on a layer of water. It is based on a new model that allows the nonlinear and dispersive effects to operate to the same full extent as in the Euler equations. Its relationships with some existing models are discussed. Various interesting phenomena will be illustrated with applications of these models and with an exposition on the salient features of nonlinear waves in wave-wave interactions and the related processes of transport of mass and energy.

This paper considers surface gravity-capillary waves in an ideal fluid of finite depth and generalizes exact evolution equations for free gravity waves obtained by Dyachenko et al. to those for forced gravity-capillary waves. The model derived here describes the time evolution of the free surface and the velocity potential evaluated at the free surface under external pressure forcing. Two integro-differential equations are written explicitly in terms of these two dependent variables, and no extra step is required to close the system. These equations are solved numerically for the particular case of stationary periodic waves, and the results compared with analogous ones available in the literature.

The general planar motion of an elliptic cylinder through an inviscid and incompressible fluid in the vicinity of a fixed circular cylinder is investigated analytically. The velocity potential is derived by using the successive-image method and the perturbation method, and it is used to determine the hydrodynamic interactions between them. In a relative coordinate system moving with the uniform flow, the kinetic energy of the fluid is expressed as a function of 15 generalized added masses due to the motion of these two cylinders. The generalized added masses are then employed to determine the translational and rotational motion of the elliptic cylinder based on the dynamic equations of motion that are obtained from Lagrange's equations of motion. Numerical results show that the initial configuration of the elliptic cylinder greatly affects its subsequent motions.

The third-order analytical solutions for the strong interactions among three free-wave components are derived using two well-known perturbation methods, namely, the mode-coupling method and the Zakharov equation method. A term-by-term comparison of their solutions shows that the two methods render virtually identical results. The validity and convergence range of the solution are investigated for the interacting free-wave components of various frequencies but within the frequency range of storm seas. It is found that the solution may encounter two types of convergence difficulties, which occur, respectively, in the cases (1) when two of the interacting free-wave components are of quite different frequencies; and (2) when two of the interacting free-wave components are very close in frequency but the frequency of the third free-wave component is relatively larger or smaller.

Numerical simulations of the planar starting jets were conducted using a two-length-scale turbulence model and a hydraulic code to study the effect of friction on 2D turbulence in shallow open-channel flow. The simulation results were compared with the data of the starting jets obtained in a recent series of laboratory experiments conducted in a large tank of small thickness. Dividing the turbulence energies into large and small scales, and calculating the energies with separate models, the observed friction effects on the 2D large-scale turbulent motion were correctly simulated by a two-length-scale turbulence model. To maintain the large-scale turbulence in the shallow shear flow, the production of turbulence energy by the transverse shear must be greater than the dissipation of the energy by friction. The critical gradient bed-friction number obtained from the simulations of the starting jets was S_c ≃ 0.08, which is consistent with the experimental observations in other shallow turbulent flows.

The present work demonstrates that the assumption of wall similarity in the equilibrium region of open channels leads to the definition of a constant, universal value for the normalized vertical flux of turbulent kinetic energy irrespective of wall roughness. Moreover, by additionally assuming a gradient-flux model for the turbulent kinetic energy, its bed-normal distribution is easily estimated by an expression with parameters that rely on a physical basis. Turbulence measurements performed in smooth-, transitionally rough-, and fully rough-bed (sandgrain) open channels confirm this hypothesis, providing at the same time an alternative way of determining the lower and upper limits of the intermediate region. Finally, based upon wall-similarity assumptions, a new methodology is proposed for estimating mean bed-shear velocities (stresses) in free-surface flows at high local and global Reynolds numbers, irrespective of roughness condition at the bed.

Orthonormal wavelets are applied to quantify the level of intermittency of energy-containing scales in the surface layer of the atmospheric boundary layer. These scales contain most of the kinetic energy, arise through instabilities, and usually exhibit nonstationary characteristics. The results show that the energy of each of these scales varies significantly with time. Some of these scales have a significant contribution to the total energy over short periods of time. Moreover, from the wavelet coefficients, several quantities are determined. These include the level of contribution of energy by each scale to the total signal, the percentage of time of high-energy events, and the percentage of energy in these events. These quantities allow us to characterize the level of energetic events and intermittency of the energy-containing scales in the surface layer.

To introduce the intermittency effects of the energy cascade process into turbulence modeling, a new fractal turbulence scale based on k, ε, ν, and the fractal dimension of turbulence dissipation D, with D = 2.7, is introduced, and a fractal scale, low Reynolds number turbulence model is proposed. The proposed turbulence model is first examined in detail by predicting a two-dimensional channel flow, and then applied to predict a backward-facing step flow. Numerical results are compared with the direct numerical simulation budgets, experimental data, and the model results of Chien, and Lam and Bremhorst, respectively. It is found that the fractal scale model indeed predicts better results for both of the flows considered.

This study considers the 3D runup of long waves on a uniform beach of constant or variable downward slope that is connected to an open ocean of uniform depth. An inviscid linear long-wave theory is applied to obtain the fundamental solution for a uniform train of sinusoidal waves obliquely incident upon a uniform beach of variable downward slope without wave breaking. For waves at nearly grazing incidence, runup is significant only for the waves in a set of eigenmodes being trapped within the beach at resonance with the exterior ocean waves. Fourier synthesis is employed to analyze a solitary wave and a train of cnoidal waves obliquely incident upon a sloping beach, with the nonlinear and dispersive effects neglected at this stage. Comparison is made between the present theory and the ray theory to ascertain a criterion of validity. The wave-induced longshore current is evaluated by finding the Stokes drift of the fluid particles carried by the momentum of the waves obliquely incident upon a sloping beach. Currents of significant velocities are produced by waves at incidence angels about 45° and by grazing waves trapped on the beach. Also explored are the effects of the variable downward slope and curvature of a uniform beach on 3D runup and reflection of long waves.

A chimera Reynolds-averaged Navier-Stokes (RANS) method has been developed for time-domain simulation of transient flow induced by a ship approaching a berthing facility. The method solves the mean flow and turbulence quantities on embedded, overlapped, or matched multiblock grids. The unsteady RANS equations were formulated in an earth-fixed reference frame and transformed into general curvilinear, moving coordinate systems. A chimera domain decomposition techniques has been employed to accommodate the relative motions between different grid blocks. Calculations have been performed for a full-scale motor vessel in berthing operations. Comparisons have been made between the computations and measurements to demonstrate the feasibility of the chimera RANS approach for time-domain simulation of the hydrodynamic coupling between the ship and berthing structures. The numerical solutions successfully captured many important features of the transient flow around a berthing ship, including the underkeel flow acceleration, wake flow separation, and water cushioning effects between the ship and harbor quay wall.

Fully nonlinear axisymmetric viscous flow due to heave oscillation of a surface-piercing vertical cylinder is analyzed using a finite-difference method based on curvilinear coordinates. Of significance to numerical modeling is the present finding that the free-slip condition used to model the movement of the contact line affects neither the overall flow nor the hydrodynamic pressure force acting on vertical cylinder. The viscous-flow results are compared with fully nonlinear inviscid-flow results, which are obtained using a mixed Eulerian-Lagrangian formulation, to contrast the effects of viscosity on the flow field, hydrodynamic force, and radiating surface waves. New results are presented for a range of parameters to illustrate physical mechanisms of the inception and evolution of vertical structures due to body motion in a free surface and their effects on the hydrodynamic force.

A secondary flow correction has been added to the depth-averaged computer program, RMA2. The program solves a transport equation for streamwise vorticity and converts it to accelerations due to secondary currents. The inclusion of these additional accelerations results in improved predictions of depth-averaged velocity. In particular, their effect is to reduce depth-averaged velocities on the inside of curves and increase them on the outside of curves. The bendway correction has been tested on experimental data from the Riprap Test Facility at the U.S. Army Engineer Waterways Experiment Station.