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

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  • 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.


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  • 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 $

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