Observations of Primary Ship Waves at the Margins of a Confined Tidal River

Data Availability Statement

Acknowledgments

Notation

$A_c$

channel cross-sectional area (m²);

$A_{c,\mathrm{side}}$

channel cross-sectional area on one side of ship (m²);

$a$

wave amplitude (cm);

$B$

ship beam (m);

$C_B$

blockage ratio (–);

$C_{1,2,\dots 6}$

Almström and Larson (2020) depression prediction equation coefficients (–);

$c$

wave celerity (m/s);

$d$

ship draft (m);

$E$

wave energy (J/m²);

$\hat{E}$

estimated wave energy (J/m²);

$Fr$

Froude number;

$f$

frequency (Hz);

$g$

gravitational acceleration (m/s²);

$H$

wave height (cm);

$h$

depth at instrument (m);

$h_c$

mean channel depth (m);

$h_{SC}$

shipping channel depth (m);

$K$

constrainment factor in Hochstein (1967) depression prediction equation (–);

$k$

wave number (m⁻¹);

$L$

ship length (m);

$P$

pressure (kPa);

$S$

absolute ship speed (m/s);

$S^{\prime }$

relative ship speed (m/s);

$T$

wave period (s);

$t$

time (s);

$t^{\prime }$

time relative to depression (s);

$\overrightarrow{\mathbf{V}}$

tidal current (m/s);

$V$

alongshore component of tidal current (m/s);

$\overrightarrow{\mathbf{v}}$

midband velocity (cm/s);

$|\hat{v}|$

estimated wave velocity amplitude (cm/s);

$w_c$

channel top width (m);

$w_{c,\mathrm{side}}$

channel top width from ship to shore (m);

$x_{e,n}$

east and north coordinates of ship position (m);

$y$

cross-shore distance between the ship and the sensor (m);

$\alpha$

primary wave driver parameter (–);

$\beta$

Hochstein (1967) depression prediction equation intermediate (–);

$\eta$

midband water surface fluctuations (cm);

$|{\eta }_d|$

depression magnitude (cm);

$\widehat{|{\eta }_d|}$

predicted depression magnitude (cm);

$|{\eta }_d{|}_{\mathrm{side}}$

maximum depression magnitude on side of ship with top width $w_{c,\mathrm{side}}$ (cm);

$|{\eta }_d{|}_0$

depression magnitude computed from the Schijf equation [Eq. (13)] (cm);

${\eta }_s$

primary wave surge (cm);

$\kappa$

Maynord (1996) depression prediction equation intermediate (–);

$\xi$

tidal stage (m); and

$\rho$

water density (kg/m²).

References