Energy and momentum correction factors in tidal estuaries
Authors: Panchenko Evgeniya , Alabyan Andrei 
Published: March 2022

&lt;p&gt;Kinetic energy and momentum correction factors also called Coriolis and Boussinesq coefficients are used for accounting heterogeneity of velocity distribution in unsteady flow cross-sections. These coefficients should be taken into account in the inertial terms of the Saint-Venant momentum equation. The values of these coefficients are close to unity in &amp;#8216;the ordinary&amp;#8217; plain rivers, therefore in most commercial and open 1D hydrodynamic models these coefficients are either neglected or assumed to be constant. Many of these models are positioned by the authors as suitable for simulation unsteady and even reversible currents in tidal rivers.&lt;/p&gt;&lt;p&gt;However, contemporary field research in small tidal estuaries of the White Sea and successive numerical experiments demonstrate that Coriolis and Boussinesq coefficients may vary in a wide range both during the tidal cycle and along the tidal river channel. This effect is the most prominent for reversible tidal currents during the slack water when the mean flow velocity is equal zero and both correction factors tend to infinity. Ignoring this effect of the correction factors variation often leads to considerable errors in numerical experiments and simulations of tidal wave propagation upstream the river mouth.&lt;/p&gt;&lt;p&gt;Values of velocity correction coefficients were calculated on the base of the special detailed flow measurements using the ADCP in estuaries of various tidal ranges: the microtidal Laya (0.8 &amp;#8211; 1.2 m), the mesotidal Kyanda (2 &amp;#8211; 2.5 m), and the macrotidal Syomzha (6 &amp;#8211; 8 m). The field campaigns were undertaken in 2016 &amp;#8211; 2020 during summer low-flow periods.&lt;/p&gt;&lt;p&gt;Although the rivers differ in tidal impact, the main features of the correction factors alteration are similar. Both Coriolis and Boussinesq coefficients vary greatly during the tidal cycle: for most duration of the semidiurnal tidal cycle when the flow was of quasi-steady pattern in both directions correction factors were close to the unity (the Coriolis coefficient did not exceed 1.2), but they both increase sharply by several orders in magnitude during slack water (twice or more during a tidal cycle). The recorded maximum of Coriolis coefficient was 10.9 in the Kyanda estuary, and 4.0 in the Syomzha and the Laya as well. These values correspond to Boussinesq coefficients of 4.3 and 2.0 respectively. However, these values only illustrate the tendency, but the exact values of correction factors depend mainly on the time period between the ADCP transect and the reversal of the current.&lt;/p&gt;&lt;p&gt;The significant temporal and spatial variation of the correction factors determine the need to modify the governing momentum equation of 1D models aimed for applications connected with tidal river dynamics. It could be done by means of adding two additional terms reflecting the variations of Boussinesq coefficient in time and Coriolis coefficient along the river channel. &amp;#160;&lt;/p&gt;&lt;p&gt;The research was supported by the Russian Foundation for Basic Research (Project No. 19-35-90032).&lt;/p&gt;