Irrotational Currents Research Articles

Optimum Estimation of Coastal Currents Using Moving Vehicles

Abstract Ocean acoustic tomography (OAT) deploys most moored stations on the periphery of the tomographic region to sense the solenoidal current field. Moving vehicle tomography (MVT), an advancement of OAT, not only samples the region from various angles for improving the resolution of mapped currents but also acquires information about the irrotational flow due to the sampling points inside the region. To reconstruct a complete two-dimensional current field, the spatial modes derived from the open-boundary modal analysis (OMA) are preferable to the conventional truncated Fourier series since the OMA technique describes the solenoidal and irrotational flows efficiently in which all modes satisfy the coastline and open boundary conditions. Comparisons of the reconstructions are presented using three different representations of currents. The first two representations explain only the solenoidal flow: the truncated Fourier series and the OMA Dirichlet modes. The third representation, accounting for the solenoidal and irrotational flows, uses all the OMA modes. For reconstructing the solenoidal flow, the OMA representation with the Dirichlet modes performs better than the Fourier series. A large difference appears near the bay mouth, where the OMA-Dirichlet reconstruction shows a better fit to the uniform currents. However, considerable uncertainty exists outside the bay mouth where the irrotational currents dominate. This can be improved by the third representation with the inclusion of the Neumann and boundary modes. The reconstruction results using field data were validated against the acoustic Doppler current profiler (ADCP) measurements. Additionally, incorporating constraints from ADCP measurements enhances the accuracy of the reconstruction. Significance Statement This study contributes toward improving our understanding of accurately measuring oceanic circulation patterns over large areas without relying solely upon stationary sensors or satellite imagery. The study combines multiple sources, such as shipboard ADCP and tomographic techniques, to obtain a complete picture of what is happening beneath surface waters across entire regions under investigation. It has important implications for fields such as climate science, marine biology, and fisheries management, where accurate knowledge of the movement and distribution of water masses is crucial for predicting future trends and making informed decisions.

On the model formulations for the interaction of nonlinear waves and current

We study the model formulations of wave–current interactions in the framework of Euler equations. This work is intrigued by a recent paper from Wang et al. (2018) (hereafter WMY), which proposes such a model for the evolution of nonlinear broadband surface waves under the influence of a prescribed steady and irrotational current without vertical shear. We show that WMY’s model can be derived from a more general model accounting for an arbitrary steady and irrotational current. Under further assumption of scale separation between waves and current (i.e. horizontally slowly-varying current), WMY’s model is equivalent to an earlier model, in contrast to WMY’s claim that their model includes additional higher-order effects in wave steepness. We demonstrate the usefulness of such models in a numerical study on wave blocking by opposing current, where the nonlinear effect on the caustic location and wave amplitude amplification is elucidated. We further show that the model formulation in the framework of Euler equations form a Hamiltonian system conserving the total energy of waves and current, justifying the theoretical significance of the model equations. Finally, we generalize the formulation to nonlinear wave evolution in the presence of a rotational current with constant vorticity, which overcomes a limitation of such models that has been overlooked in previous work.

Integral Line-of-Sight Guidance for Path Following Control of Underwater Snake Robots: Theory and Experiments

This paper proposes and experimentally validates a straight line path following controller for underwater snake robots in the presence of constant irrotational currents of unknown direction and magnitude. An integral line-of-sight guidance law is presented, which is combined with a sinusoidal gait pattern and a directional controller that steers the robot toward and along the desired path. The stability of the proposed control scheme in the presence of ocean currents is investigated by using Poincare map analysis. Simulation results are presented to illustrate the performance of the proposed path following controller for both lateral undulation and eel-like motion. In addition, the performance of the path following controller is investigated through experiments with a physical underwater snake robot. The experimental results show that the proposed control strategy successfully steers the robot toward and along the desired path in the presence of an unknown constant irrotational current in the inertial frame.

Phase velocity effects of the wave interaction with exponentially sheared current

The nonlinear interaction between the unidirectional bichromatic wave-train and exponentially sheared current in water of an infinite depth is investigated. The model is based on the vorticity transport equation and the exact free surface conditions, without any assumptions for the existence of small physical parameters. Earlier works of the wave–current interaction were mainly restricted to either current acted on the monochromatic wave or irregular waves limited to irrotational current. Different from these previous works, no constraint is made in our model for amplitudes of the primary wave, and the current owns an exponential type profile along the vertical line. To ensure that the effect of vorticity on the phase velocity is consistent with earlier derivation, the case of a small amplitude wave traveling on the exponentially sheared current is examined firstly. Then the effect of nonlinearity on the phase velocity of primary waves in a bichromatic wave-train is considered. Accurate high-order approximations of the phase velocity are obtained under consideration of both the nonlinear wave self–self and mutual interactions. Finally, the combined effect of vorticity and nonlinearity on the phase velocity is investigated through the case of a bichromatic wave-train propagating on an exponentially sheared current. It is found that the characteristic current slope determines the effect of vorticity on the phase velocity caused by nonlinear wave self–self and mutual interactions, and the surface current strength may amplify/reduce this effect.

Reflection of oblique waves by currents: analytical solutions and their application to numerical computations

Surface waves superimposed upon a larger-scale flow are blocked and reflected at the points where the group velocities balance the convection by the larger-scale flow. In this study, we first extended the theory of Shyu & Phillips (1990) to the situation when short deep-water gravity waves propagate obliquely upon a steady unidirectional irrotational current and are reflected by it. In this case, the uniformly valid solution and the WKBJ solution of the short waves were derived from the Laplace equation and the kinematical and dynamical boundary conditions. These solutions in terms of some parameters (the expressions for which have also been deduced in this case) take the same forms as those derived by Shyu & Phillips, which by referring to Smith's (1975) theory can even be proved to be valid for gravity waves in an intermediate-depth region and near a curved moving caustic induced by an unsteady multidirectional irrotational current. In this general case, the expressions for certain parameters in these solutions cannot be obtained so that their values must be estimated in a numerical calculation. The algorithm for estimates of some of these parameters that are responsible for the amplitude of the reflected wave not being equal to that of the incident wave in the vicinity of the caustic and therefore are crucial for the computer calculation of the ray solution to be continued after reflection, was illustrated through numerical tests. This algorithm can avoid the error magnification phenomenon that occurred in the previous estimates of the reflected wave in the vicinity of the caustic using the action conservation principle directly. The forms of the solutions have also been utilized to clarify the wave profiles near caustics in a general situation, which indicate that in storm conditions freak waves characterized by a steeper forward face preceded by a deep trough will probably occur in the caustic regions.

Wave action on currents with vorticity

The interaction of waves on deep water with spatially varying currents may be described by a ray theory, with the wave amplitudes determined by the principle of conservation of wave action (CWA). However, all previous deep water derivations of CWA are restricted to the case of an irrotational current. In this paper, both the ray theory and CWA are derived by a WKB method without the assumption of irrotationality. Also derived is a new equation for a spatially varying phase shift which is not predicted by the usual ray theory, and which, in general, displaces the positions of the wave crests by a distance on the order of a wavelength. This phase shift, which is caused by variations of the current velocity with depth, vanishes in the irrotational case, and so is in accord with the irrotational theory.

ENERGY FLUX AND WAVE ACTION IN GRAVITY WAVES PROPAGATING ON A CURRENT

The total energy flux with the mean energy level as a datum is shown to be proportional to the wave action flux for waves on steady irrotational currents. This leads directly to the wave action conservation principle. The set-down of the mean water surface is calculated in a new and simple way. In addition the mean Eulerian current velocity profile is discussed, and the myth of a non-zero mass transport in a pure wave motion is reconsidered. Dissipative effects are neglected.

The reflection of short gravity waves on a non-uniform current

AbstractA uniform asymptotic solution is obtained which describes the propagation near an isolated caustic of water waves on a slow irrotational current. Unlike earlier work there is no restriction to straight caustics or to steady currents.