Navid Tahvildari

Optimized Determination of Viscous Mud Properties Using a Nonlinear Wave–Mud Interaction Model

The complex process of surface wave propagation over areas of cohesive sediments has generally been treated by assuming a particular rheological behavior for the mud layer, thereby fixing the description of the mud characteristics into the specification of parameters relevant to the selected rheology. The capability of inverting data to recover these parameters is investigated here. Representing the mud layer as a thin viscous fluid, a nonlinear wave‐mud interaction model, coupled with a nonlinear optimization technique (Levenberg‐ Marquardt), is used to deduce mud characteristics from estimates of wave energy. A set of numerical tests with a deterministic phase-coherent cnoidal wave are conducted to individually estimate viscosity and mud layer depth (keeping one fixed while estimating the other), and to determine the limits of convergence of the inversionalgorithm.Itisshownthatinstancesofconvergenceornonconvergencecanbetracedtotheshapeof the dissipation rate curve as a function of the parameter under consideration as well as the location of the initial guesses of the target parameter along that curve. It is found that the estimation of viscosity is less problematic than the estimation of mud layer depth. Tests with random waves are also performed, using both root-mean-square wave height (representation of wave energy) and wave skewness (representation of nonlinearwaveproperties)asinput fortheinversion.Theuseofrandomwavesappearstoamelioratemanyofthe convergence difficulties encountered with the cnoidal wave tests, while the use of wave skewness, while promising, is somewhat less successful. Finally, the inversion algorithm is tested against laboratory data and the deduction of both mud layer depth and viscosity proceed well. Implications for general mud property deduction are discussed.

Analytical Cubic Solution to Weakly Nonlinear Interactions Between Surface and Interfacial Waves

Resonant interaction between one surface wave and two oblique interfacial waves is analyzed in a three dimensional system of a finite-depth, two-layer fluid. A third order perturbation analysis is carried out to obtain the evolution equations of the waves amplitudes. Taking the waves amplitudes as the perturbation small parameter, the evolution equations of the waves are solved simultaneously to obtain the short and long term behavior of the interfacial waves. In contrast to the second order analysis, the current analysis shows that after an initial exponential growth period, the interfacial waves stop growing and stabilize. Furthermore, the influences of surface wave frequency, density ratio and viscosity in the resonant interaction are investigated. Finally, the analytical results are compared with previous experimental observations.Copyright

Generation of oblique interfacial waves due to resonant interaction with surface gravity waves in shallow water

Ocean in deep waters and coastal areas is stratified due to vertical gradient of density. Due to nearly distinct interface between the layers of constant density, a two-layer system is a commonly used configuration to model ocean waters. In such models, various mechanisms can lead to generation of surface and interfacial waves. Furthermore, this system admits nonlinear interactions between surface waves and internal waves. As surface waves approach coastal areas, they become long relative to water depth and through nonlinear interactions can induce long interfacial waves over fluidized seabed. This phenomenon will be studied theoretically in the present paper. The fluid is composed of two layers of density stratified, incompressible, inviscid and immiscible fluids. The depth of the top and bottom layers are assumed to be shallow relative to the typical surface wave and interfacial wave length respectively. The waves in this system are weakly nonlinear and weakly dispersive and can be described by Boussinesq-type equations. First, Boussinesqtype equations describing the displacements of the surface and interface and the depth-integrated horizontal velocities in the two layers are derived for mildly varying bathymetry. Secondly, the nonlinear resonant interactions among surface and interfacial modes are analyzed via a second order multiple scales analysis in time. Consequently, coupled transient evolution equations of wave amplitudes are derived. The results of inviscid theory indicates generation of a pair of oblique subharmonic interfacial waves due to energy gain from surface wave. In a parametric study, the influences of the angle of propagation of interfacial waves with respect to surface wave, lower layer viscosity, surface wave frequency, density difference between fluid layers, thickness of the fluid layers, and surface wave amplitude are studied.

A Numerical Code for Waves in a Two-Layer Shallow Fluid

The preliminary results from a two-dimensional two-layer nonlinear shallow water model are presented. The system is composed of two inviscid, incompressible, and immiscible fluids of constant density. The waves are assumed to be nonlinear and non-dispersive and the water depth is assumed to be constant. A high order predictor-corrector algorithm with a high order finite difference discretization, accurate to O(Δx4) is developed. The numerical algorithm and the boundary conditions are outlined and the model is compared with the analytical solution of internal solitary waves.Copyright

Cubic nonlinear analysis of interaction between a surface wave and two interfacial waves in an open two-layer fluid

A third-order asymptotic analysis is conducted to study the three-dimensional resonant interaction between a monochromatic progressive surface wave and two oblique interfacial waves in an open, lightly viscous, two-layer fluid of intermediate depth. By solving the evolution equations of the waves, the short- and long-term behaviors of the interfacial waves are studied. The analysis provides a correction to the second-order theory. The results indicate that the third-order analysis predicts a much lower limit on the growth of the interfacial waves than the second-order theory. Furthermore, in the long term, viscous effects cause the interfacial wave amplitudes to approach a constant value. The effects of viscosity, surface wave frequency, surface wave amplitude, density difference of the layers and relative thickness of the two layers on the dynamics of the waves are examined. The theory is in qualitative agreement with laboratory observations.