Abstract
It is well known that, within the linear nonviscous equations of tidal dynamics, the amplitudes of oscillations of the barotropic and baroclinic tidal velocity components unlimitedly increase when approaching the critical latitude. It is also known that the linear equations of tidal dynamics with a constant and specified vertical eddy viscosity indicate the occurrence of significant tidal velocity shears in the near-bottom layer, which are responsible for increasing the baroclinic tidal energy dissipation, the turbulent kinetic energy, and the thickness of the bottom boundary layer. The first circumstance—the growth of the amplitudes of oscillations of the barotropic and baroclinic tidal velocity components—is due to the elimination in the original equations of small terms, which are small everywhere except for the critical latitude zone. The second circumstance—the occurrence of significant tidal velocity shears—is due to the fact that internal tidal waves, which induce the dissipation of the baroclinic tidal energy and the diapycnal diffusion, are either not taken into account or described inadequately. It is suggested that diapycnal diffusion can lead to the degeneration (complete or partial) of tidal velocity shears, with all the ensuing consequences. The aforesaid is confirmed by simulation results obtained using the QUODDY-4 high-resolution three-dimensional finite-element hydrostatic model along the 66.25° E section, which passes in the Kara Sea across the critical latitude.
Similar content being viewed by others
References
V. Vlasenko, N. Stashchuk, K. Hutter, and K. Sabinin, “Nonlinear internal waves forced by tides near the critical latitude,” Deep-Sea Res. I 50 (3), 317–338 (2003).
T. Furevik and A. Foldvik, “Stability of M2 critical latitude in the Barents Sea,” J. Geophys. Res. 101 (C4), 8823–8837 (1996).
C. F. Postlethwaite, M. A. Morales Maqueda, V. le Fouest, et al., “The effect of tides on dense water formation in Arctic shelf seas,” Ocean Sci. 7 (2), 203–217 (2011).
M. V. Luneva, Y. Aksenov, J. D. Harle, et al., “The effects of tides on the water mass mixing and sea ice in the Arctic Ocean,” J. Geophys. Res.: Oceans 120 (10), 6669–6699 (2015).
J. T. C. Ip and D. R. Lynch, QUODDY3 User’s manual: Comprehensive coastal circulation simulation model using finite elements: Nonlinear prognostic time-stepping model, Rep. No. NML95-1, Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire, 1995.
International Bathymetric Chart of the Arctic Ocean (National Geophysical Data Center, Boulder, Colorado, 2008). http://www.ibcao.org/.
J. Smagorinsky, “General circulation experiments with the primitive equations,” Mon. Weather Rev. 91 (3), 99–164 (1963).
G. L. Mellor and T. Yamada, “Development of a turbulence closure model for geophysical fluid problems,” Rev. Geophys. Space Phys. 20 (4), 854–875 (1982).
Joint US–Russian Atlas of the Arctic Ocean, Oceanography Atlas for the Summer Period, Ed. by E. Tanis and L. Timokhov (Environmental Working Group, University of Colorado, Media Digital, 1998).
B. K. Arbic, S. T. Garner, R. W. Hallberg, and H. L. Simmons, “The accuracy of surface elevations in forward global barotropic and baroclinic tide models,” Deep-Sea Res. II 51 (25), 3069–3101 (2004).
H. L. Simmons, R. W. Hallberg, and B. K. Arbic, “Internal wave generation in a global baroclinic tide model,” Deep-Sea Res. II 51 (25), 3043–3068 (2004).
L. Padman and S. Erofeeva, “A barotropic inverse tidal model for the Arctic Ocean,” Geophys. Res. Lett. 31 (2), L02303 (2004). doi 10.1029/2003GL019003
M. A. Janout and Y.-D. Lenn, “Semidiurnal tides on the Laptev Sea shelf with implications for shear and vertical mixing,” J. Phys. Oceanogr. 44 (1), 202–219 (2014).
Y.-D. Lenn, T. P. Rippeth, C. P. Old, et al., “Intermittent intense turbulent mixing under ice in the Laptev Sea continental shelf,” J. Phys. Oceanogr. 41 (3), 531–547 (2011).
A. Sundfjord, I. Fer, Y. Kasajima, and H. Svendsen, “Observations of turbulent mixing and hydrography in the marginal ice zone of the Barents Sea,” J. Geophys. Res. 112, C05008 (2007). doi 10.1029/2006JC003524
A. Sirevaag and I. Fer, “Early spring oceanic heat fluxes and mixing observed from drift stations north of Svalbard,” J. Phys. Oceanogr. 39 (12), 3049–3069 (2009).
J. N. Moum, D. R. Caldwell, J. D. Nash, and G. D. Gunderson, “Observations of boundary mixing over the continental slope,” J. Phys. Oceanogr. 32 (7), 2113–2130 (2002).
T. D. Finnigan, D. S. Luther, and R. Lukas, “Observations of enhanced diapycnal mixing near the Hawaiian Ridge,” J. Phys. Oceanogr. 32 (10), 2988–3002 (2002).
J. M. Klymak and M. C. Gregg, “Tidally generated turbulence over the Knight Inlet sill,” J. Phys. Oceanogr. 5 (10), 1135–1151 (2004).
J. D. Nash, E. Kunze, J. M. Toole, and R. W. Schmitt, “Internal tide reflection and turbulent mixing on the continental slope,” J. Phys. Oceanogr. 34 (5), 1117–1134 (2004).
B. A. Kagan and A. A. Timofeev, “Simulation of surface and internal semidiurnal tides in the Kara Sea,” Izv., Atmos. Ocean. Phys. 53 (2), 233–241 (2017). doi 10.7868/S0002351517020055
I. E. Kozlov, V. N. Kudryavtsev, E. V. Zubkova, A. V. Zimin, and B. Chapron, “Characteristics of short-period internal waves in the Kara Sea inferred from satellite SAR data,” Izv., Atmos. Ocean. Phys. 51 (9), 1073–1087 (2015).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © B.A. Kagan, E.V. Sofina, A.A. Timofeev, 2018, published in Izvestiya Rossiiskoi Akademii Nauk, Fizika Atmosfery i Okeana, 2018, Vol. 54, No. 2.
Rights and permissions
About this article
Cite this article
Kagan, B.A., Sofina, E.V. & Timofeev, A.A. Critical Latitude in Tidal Dynamics Using the Kara Sea as an Example. Izv. Atmos. Ocean. Phys. 54, 206–212 (2018). https://doi.org/10.1134/S000143381802010X
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S000143381802010X