Nonlinear pumping in oscillatory diffusive processes: The impact on the oceanic deep layers and lakes

• An oscillatory boundary problem is considered for the nonlinear diffusive equation.
• A boundary temperature oscillation is shown to result in a heat nonlinear pumping.
• Temperature drop in the abyssal ocean due to surface oscillations is analyzed.

We discuss a significant mathematical property of the nonlinear diffusion equation, so-called, the pumping effect, which of great importance in many natural diffusion processes. An oscillatory boundary value problem is considered for the nonlinear diffusive equation of thermal conductivity. We demonstrate that pure periodical oscillations of temperature at the boundary result in a nonlinear pumping of the heat implying that the heat is pumped out or into the inner regions depending on the change in the temperature oscillation amplitude. As an example, the residual effect in temperature of the World Ocean’s deep layers and lakes due to the oscillatory processes at the surface is presented and analyzed. As is generally known, the sea surface temperature (SST) profiles indicate long-term oscillations, and, therefore, according to the pumping effect when the SST oscillation amplitudes increase, the heat comes up to the surface while the deep layers become rather cooler, otherwise, as the amplitudes decrease, the heat transfers into the deep layers.