\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Stability analysis of the boundary value problem modelling a two-layer ocean

Abstract Full Text(HTML) Figure(7) Related Papers Cited by
  • We study boundedness of solutions to a linear boundary value problem (BVP) modelling a two-layer ocean with a uniform eddy viscosity in the lower layer and variable eddy viscosity in the upper layer. We analyse bounds of solutions to the given problem on the examples of different eddy viscosity profiles in the case of their parameter dependence.

    Mathematics Subject Classification: Primary: 34B05, 34D23, 34C23; Secondary: 37N10.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
  • Figure 1.  Ekman flow and the net water transport in the Northern Hemisphere

    Figure 2.  Piecewise-constant eddy viscosity profile for a two-layer ocean

    Figure 3.  Piecewise-constant eddy viscosity profile for a three-layer ocean

    Figure 4.  Piecewise-constant generalized eddy viscosity profile for a two-layer ocean

    Figure 5.  Linear eddy viscosity profiles for a two-layer ocean at a fixed ocean depth: red line – the increasing regime and blue points – the decreasing regime

    Figure 6.  The polynominal eddy viscosity profile at a fixed ocean depth $ -h $ for a fixed value of parameter $ a $

    Figure 7.  The exponential eddy viscosity profile at a fixed ocean depth $ -h $ for a fixed value of parameter $ \nu $

  • [1] J. P. Boyd, Dynamics of the Equatorial Ocean, Springer, Berlin, 2018.
    [2] A. Bressan and A. Constantin, The deflection angle of surface ocean currents from the wind direction, J. Geophys. Res.: Oceans, 124 (2019), 7412-7420. 
    [3] A. Constantin, Frictional effects in wind-driven ocean currents, Geophys. Astrophys. Fluid Dyn., 115 (2021), 1-14.  doi: 10.1080/03091929.2020.1748614.
    [4] A. Constantin, D. G. Dritschel and N. Paldor, The deflection angle between a wind-forced surface current and the overlying wind in an ocean with vertically varying eddy viscosity, Phys. Fluids, 32 (2020), 5 pp. doi: 10.1063/5.0030473.
    [5] A. Constantin and R. I. Ivanov, Equatorial wave-current interactions, Commun. Math. Phys., 370 (2019), 1-48.  doi: 10.1007/s00220-019-03483-8.
    [6] A. Constantin and R. S. Johnson, Atmospheric Ekman flows with variable eddy viscosity, Bound. Lay. Meteorol., 170 (2019), 395-414. 
    [7] A. Constantin and R. S. Johnson, On the modelling of large-scale atmospheric flow, J. Differ. Equ., 285 (2021), 751-798.  doi: 10.1016/j.jde.2021.03.019.
    [8] A. Constantin and R. S. Johnson, Ekman-type solutions for shallow-water flows on a rotating sphere: a new perspective on a classical problem, Phys. Fluids, 31 (2019), 021401. 
    [9] A. Constantin and R. S. Johnson, On the nonlinear, three-dimensional structure of equatorial oceanic flows, J. Phys. Oceanogr., 49 (2019), 2029-2042. 
    [10] W. A. Coppel, Stability and Asymptotic Behavior of Differential Equations, Heath Mathematical Monographs, Heath, Boston, 1965.
    [11] D. G. DritschelN. Paldor and A. Constantin, The Ekman spiral for piecewise uniform viscosity, Ocean Sci., 16 (2020), 1089-1093. 
    [12] V. W. Ekman, On the influence of the Earth's rotation on ocean-currents, Ark. Mat. Astron. Fys., 2 (1905), 1-52. 
    [13] B. Grisogono, A generalized Ekman layer profile with gradually varying eddy diffusivities, Quart. J. Roy. Meteorol. Soc., 121 (1995), 445-453. 
    [14] O. S. Madsen, A realistic model of the wind-induced Ekman boundary layer, J. Phys. Oceanogr., 7 (1977), 248-255. 
    [15] K. Marynets, A Sturm-Liouville problem arising in the atmospheric boundary-layer dynamics, J. Math. Fluid Mech., 22 (2020), 6 pp doi: 10.1007/s00021-020-00507-5.
    [16] L. Roberti, The Ekman spiral for piecewise-constant eddy viscosity, Appl. Anal., (2021), 1–9. doi: 10.1080/00036811.2021.1896709.
    [17] L. Roberti, Perturbation analysis for the surface deflection angle of Ekman-type flows with variable eddy viscosity, J. Math. Fluid Mech., 23 (2021), 1-7.  doi: 10.1007/s00021-021-00586-y.
    [18] J. Röhrs and K.H. Christensen, Drift in the uppermost part of the ocean, Geophys. Res. Lett., 42 (2015), 10349-10356. 
    [19] T. Ström, On logarithmic norms, SIAM J. Numer. Anal., 12 (1975), 741-753.  doi: 10.1137/0712055.
    [20] G. K. VallisAtmospheric and Oceanic Fluid Dynamics, Cambridge University Press, Cambridge, UK, 2017. 
  • 加载中

Figures(7)

SHARE

Article Metrics

HTML views(320) PDF downloads(143) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return