Transient wave resistance upon a real shear current

Li, Yan; Smeltzer, Benjamin K.; Ellingsen, Simen Å.

doi:10.1016/j.euromechflu.2017.08.012

Cited by 27 publications

(24 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As one would expect in light of previous studies (e.g., Ellingsen, 2014;Li et al, 2019) the surface shape is changed visibly, yet moderately by the shear flow. The velocity and pressure fields, on the other hand, are strikingly different in qualitative appearance.…”

Section: Velocity Fieldsupporting

confidence: 78%

See 1 more Smart Citation

A Framework for Modeling Linear Surface Waves on Shear Currents in Slowly Varying Waters

Ellingsen

2019

JGR Oceans

Self Cite

View full text Add to dashboard Cite

We present a theoretical and numerical framework—which we dub the direct integration method (DIM)—for simple, efficient, and accurate evaluation of surface wave models allowing presence of a current of arbitrary depth dependence and where bathymetry and ambient currents may vary slowly in horizontal directions. On horizontally constant water depth and shear current the DIM numerically evaluates the dispersion relation of linear surface waves to arbitrary accuracy, and we argue that for this purpose it is superior to two existing numerical procedures: the piecewise‐linear approximation and a method due to Dong and Kirby (2012, https://doi.org/10.9753/icce.v33.waves.2). The DIM moreover yields the full linearized flow field at little extra cost. We implement the DIM numerically with iterations of standard numerical methods. The wide applicability of the DIM in an oceanographic setting in four aspects is shown. First, we show how the DIM allows practical implementation of the wave action conservation equation recently derived by Quinn et al. (2017, https://doi.org/10.1016/j.ocemod.2017.03.003). Second, we demonstrate how the DIM handles with ease cases where existing methods struggle, that is, velocity profiles U(z) changing direction with vertical coordinate z and strongly sheared profiles. Third, we use the DIM to calculate and analyze the full linear flow field beneath a 2‐D ring wave upon a near‐surface wind‐driven exponential shear current, revealing striking qualitative differences compared to no shear. Finally we demonstrate that the DIM can be a real competitor to analytical dispersion relation approximations such as that of Kirby and Chen (1989, https://doi.org/10.1029/JC094iC01p01013) even for wave/ocean modeling.

show abstract

Section: Velocity Fieldsupporting

confidence: 78%

“…In this article we present a new framework for numerical calculation of wave dispersion on arbitrary shear currents, which compliments the analytical framework developed by Ellingsen and Li () and applied to the case of ship waves by Li et al (). We refer to it as the direct integration method (DIM).…”

Section: Introductionmentioning

confidence: 99%

A Framework for Modeling Linear Surface Waves on Shear Currents in Slowly Varying Waters

Ellingsen

2019

JGR Oceans

Self Cite

View full text Add to dashboard Cite

show abstract

“…In Transient wave resistance upon a real shear current [95], Li, Smeltzer, and Ellingsen study the influence of background shear currents on the development of ship waves. In particular, the authors look at real-world data from the Columbia River in the northwestern United States, and model ships with dimensions and Froude numbers typical of three classes of vessels operating in these waters.…”

Section: Contributions In This Issuementioning

confidence: 99%

Introduction to the Special Issue on Breaking Waves

Kalisch¹,

Ricchiuto²,

Bonneton³

et al. 2019

European Journal of Mechanics - B/Fluids

View full text Add to dashboard Cite

“…The third profile is created using a methodology similar to as detailed in Ref. [16]: a suitable exemplar profile is taken from the Columbia River dataset upon which we fit a low-order polynomial. Further detail on this is given in Sect.…”

Section: Exponential Profilementioning

confidence: 99%

“…Zippel and Thomson found wave steepness predictions to be off by up to 20% if not accounting for sub-surface shear [30]. In the same current some of us have predicted that wave resistance on small ships can vary by a factor of 3 or more between upstream and downstream motion at the same velocity relative to the surface [16], an effect solely due to shear. Methods to reconstruct the sub-surface flow profile from measurements of the dispersion relation have recently been developed [4,18] and tested in the Columbia mouth [3].…”

Section: Introductionmentioning

confidence: 95%

The Error in Predicted Phase Velocity of Surface Waves atop a Shear Current with Uncertainty

2019

Self Cite

View full text Add to dashboard Cite

The effect of a depth-dependent shear current U (z) on surface wave dispersion is conventionally calculated by assuming U (z) to be an exactly known function, from which the resulting phase velocity c(k) is determined. This, however, is not the situation in reality. Field measurements of the current profile are performed at a finite number of discrete depths and with nonzero experimental uncertainty. Here we analyse how imperfect knowledge of U (z) affects estimates of c(k). We performed a numerical experiment simulating a large number of "measurements" of three different shear currents: an exponential profile, a 1/7-law profile, and a profile measured in the Columbia River delta. A number of measurement points were specified, the topmost of which at z = −h s (permitting simulation of measurement points which do not fully extend to the surface at z = 0), and measurements taken from a normal distribution with standard deviation ΔU. Four different methods of reconstructing a continuous U (z) from the measurements are compared with respect to mean value and variance of c(k). We find that an ordinary least-squares polynomial fit seems robust against mispredicting mean values at the expense of relatively high variance. Its performance is similar for all profiles, whereas a fit to an exponential form is excellent in one case and poor in another. A clear conclusion is the need for a measurement of the surface velocity U (0) when there is significant shear near the surface. For the exponential and Columbia profiles alike, errors due to extrapolation of U from z = −h s to 0 dominate the resulting error of c, especially for shorter wavelengths. In contrast, the error in c(k) decreases slowly with a higher density of measurement points, indicating that better, not more, velocity measurements should be invested in. A pseudospectral analysis of the linear operator corresponding to the three velocity profiles was performed. In all cases, the pseudospectrum shows strong asymmetry around the eigenvalue for c, indicating that a perturbation in the underlying current is more likely to push c to higher, not lower, values. This is in tentative agreement with our observation that for sufficiently large ΔU , c is found to have predominantly positive skewness, although the direct relationship between the two is not altogether obvious.

show abstract

Transient wave resistance upon a real shear current

Cited by 27 publications

References 26 publications

A Framework for Modeling Linear Surface Waves on Shear Currents in Slowly Varying Waters

A Framework for Modeling Linear Surface Waves on Shear Currents in Slowly Varying Waters

Introduction to the Special Issue on Breaking Waves

The Error in Predicted Phase Velocity of Surface Waves atop a Shear Current with Uncertainty

Contact Info

Product

Resources

About