The potential for sea ice-albedo feedback to give rise to nonlinear climate change in the Arctic Ocean – defined as a nonlinear relationship between polar and global temperature change or, equivalently, a time-varying polar amplification – is explored in IPCC AR4 climate models. Five models supplying SRES A1B ensembles for the 21 st century are examined and very linear relationships are found between polar and global temperatures (indicating linear Arctic Ocean climate change), and between polar temperature and albedo (the potential source of nonlinearity). Two of the climate models have Arctic Ocean simulations that become annually sea ice-free under the stronger CO 2 increase to quadrupling forcing. Both of these runs show increases in polar amplification at polar temperatures above-5 o C and one exhibits heat budget changes that are consistent with the small ice cap instability of simple energy balance models. Both models show linear warming up to a polar temperature of-5 o C, well above the disappearance of their September ice covers at about-9 o C. Below-5 o C, surface albedo decreases smoothly as reductions move, progressively, to earlier parts of the sunlit period. Atmospheric heat transport exerts a strong cooling effect during the transition to annually ice-free conditions. Specialized experiments with atmosphere and coupled models show that the main damping mechanism for sea ice region surface temperature is reduced upward heat flux through the adjacent ice-free oceans resulting in reduced atmospheric heat transport into the region.

Geophysical fluid dynamics.

Hydrodynamic and hydromagnetic stability

Современное состояние, проблемы и направления развития деятельности Технопарка национального исследовательского Иркутского государственного технического университета

Abstract Plane Poiseuille flow of two immiscible fluids in a non-isothermal “capillary” channel under the combined action of pressure gradients, gravitational fields and surface tension gradients is studied. Conditions for attaining a Poiseuille-type regime are derived. Closed form solutions are obtained and discussed.

Plane Marangoni-Poiseille flow of two immiscible fluids

Введение в макроэкономику. 6-е изд.

A new class of exact solutions has been obtained for three-dimensional equations of themal diffusion in a viscous incompressible liquid. This class enables the description of the temperature and concentration distribution at the boundaries of a liquid layer by a quadratic law. It has been shown that the solutions of the linearized set of thermal diffusion equations can describe the motion of a liquid at extreme points of hydrodynamic fields. A generalization of the classic Couette flow with a quadratic temperature and concentration distribution at the lower boundary has been considered as an example. The application of the presented class of solutions enables the modeling of liquid counterflows and the construction of exact solutions describing the flows of dissipative media.

A new class of exact solutions for three-dimensional thermal diffusion equations

A new class of exact solutions of nonlinear and linearized Navier–Stokes equations has been proposed, which generalize the well-known family of exact solutions in which the velocity is linear in some coordinates. The case of the quadratic dependence of the velocities on two horizontal (longitudinal) coordinates with coefficients that are the functions of the vertical (transverse) coordinate and time was considered in detail. The solutions were generalized for rotating liquids. Equations for constructing exact solutions with an arbitrary dependence of velocities on the horizontal coordinates were derived.

New Class of Exact Solutions of Navier–Stokes Equations with Exponential Dependence of Velocity on Two Spatial Coordinates

An exact time-dependent solution of the system of Navier–Stokes equations governing large-scale viscous vortical incompressible flows is derived The solution generalizes that describing the Couette flow Two ways of preassigning the boundary conditions at the upper boundary of a fluid layer are considered These are the time-dependent variation of the velocity value with the conservation of its direction and the variation of the angle at which the velocities parallel to the coordinate axes are directed It is shown that at certain values of vorticity, viscosity, and the layer thickness the velocities within the layer can be severalfold greater than the given velocity at the boundary

Unsteady layered vortical fluid flows

An exact solution describing the convective flow of a vortical viscous incompressible fluid is derived. The solution of the Oberbeck–Boussinesq equation possesses a characteristic feature in describing a fluid in motion, namely, it holds true when not only viscous but also inertia forces are taken into account. Taking the inertia forces into account leads to the appearance of stagnation points in a fluid layer and counterflows, as well as the existence of layer thicknesses at which the tangent stresses vanish on the lower boundary. It is shown that the vortices in the fluid are generated due to the nonlinear effects leading to the occurrence of counterflows and flow velocity amplification, compared with those given by the boundary conditions. The solution of the spectral problem for the polynomials describing the tangent stress distribution makes it possible to explain the absence of the skin friction on the solid surface and in an arbitrary section of an infinite layer.

Nonuniform convective Couette flow

An exact solution of the Navier - Stokes equations is given that describes the vorticity of a viscous incompressible liquid or gas, dissipative mediums, stationary shear counter-current of continuous vortical medium in the absence of the Coriolis field.

E. Yu. Prosviryakov

Papers

A new class of exact solutions for three-dimensional thermal diffusion equations

New Class of Exact Solutions of Navier–Stokes Equations with Exponential Dependence of Velocity on Two Spatial Coordinates

Unsteady layered vortical fluid flows

Nonuniform convective Couette flow

Large-scale flows of viscous incompressible vortical fluid