RUSSIAN JOURNAL OF EARTH SCIENCES, VOL. 12, ES4002, doi:10.2205/2012ES000517, 2012

*Yu. Yu. Plaksina ^{1}, A. V. Uvarov^{1}, N. A. Vinnichenko^{1}, V. B. Lapshin^{1}^{,2}*

^{1}Faculty of Physics, Lomonosov Moscow State University, Moscow, Russia

^{2}Fedorov Institute for Applied Geophysics, Moscow, Russia

Constructing models of global heat exchange between the ocean and atmosphere requires information on boundary conditions at water–air interface. Experimental and theoretical studies of near-surface structures both in laboratory and in situ have been a part of geophysics for decades. Nowadays usage of modern CFD methods can be complemented by state-of-art experimental techniques providing visualization of small-scale phenomena. Temperature distributions near the liquid–gas interface for various evaporation regimes are measured in laboratory by Background Oriented Schlieren (BOS) and IR thermal imaging of the surface. The results, obtained by these two methods, are shown to coincide with accuracy about 0.1 K. Thanks to simplicity of experimental realization, both methods can be used also in situ. Thermal imaging yields not only the surface temperature field, but also the velocity gradient near the surface. It is shown to be much larger than vorticity of the bulk convective vortices. Possible separate numerical modeling of hydrodynamic processes in liquid and gas making use of thermal imaging data is discussed.

Thin layer of water and air adjacent to the interface has structure, totally different from that of the remaining part of atmosphere or ocean. Fluid velocity, temperature, water vapor concentration vary drastically inside this layer. Hence, all dissipative processes: viscosity, thermal conductivity and diffusion – are important. The thickness of this layer (from 0.1 mm to several millimeters) is incomparable with typical geophysical scales. Nevertheless, describing this layer is essential for constructing the whole model, since it is there where all heat and mass exchange between ocean and atmosphere takes place. Small-scale structures of this layer can play an important role in energy transport and dissipation of large-scale flows.

Liquid temperature measurements near the liquid–gas interface present serious experimental challenge. Average vertical temperature profile can be approximated by simple exponential fit [

where $T_s$ is the surface temperature of liquid, $T_{bulk}$ is liquid temperature far from the surface and $z$ is the depth. This profile is governed by two parameters: temperature difference $T_{bulk}-T_s$ and surface layer thickness $\delta$. Major experimental difficulties arise from the fact that $T_{bulk}-T_s$ is usually of order 0.1 K and $\delta$ is about 1 mm. This suggests temperature gradients of several hundred K/m and thermal fluxes $\sim10^2\mbox{W/m}^2$. There are two groups of experimental techniques. Methods of the first group allow measuring average values for $\delta$ and $T_{bulk}-T_s$. Temperature difference can be found e.g. by simultaneous thermocouple and thermal imaging measurements [

Thus, layer thickness can be found if the total heat flux is known. In laboratory it can be determined from standard thermophysical measurements of liquid sample cooling, or from evaporation rate. In natural conditions small containers are immersed into water reservoir and evaporation rate is measured, or profiler thermoprobes of various types are used [

It is obvious that non-uniformity of the cold skin in horizontal plane, which is not taken into account by one-dimensional models, is of principal importance because it provides torque for the vortices approaching the surface. More information is required both for deeper understanding of hydrodynamical processes under the liquid–gas interface and for verification of state-of-art numerical codes. Consider the second group of methods, which allow obtaining detailed information about the fields of temperature and other quantities. These are: shadowgraphy [

Consider once more profiler thermoprobes [

Temperature field measurements can shed some light on the structure of surface layer. In particular, they can clarify the question whether Marangoni convection takes place near the surface in different liquids, which was widely debated in literature (see e.g. [

Figure 1 |

Knowing the temperature field, one can obtain information about velocity gradients near the surface. They are related to surface tension by common expression

\begin{equation} \tag*{(1)}\label{1} \frac{\partial v_x}{\partial z}= \frac{1}{\mu}\frac{\partial\sigma}{\partial T}\frac{\partial T}{\partial x},\qquad \frac{\partial v_y}{\partial z}= \frac{1}{\mu}\frac{\partial\sigma}{\partial T}\frac{\partial T}{\partial y}, \end{equation}Figure 2 |

Video record shows that in hot water (with temperature about 50° C) cold fluid filaments below the surface move with velocity about 1 mm/s, whereas average velocity of coal particles at the surface is an order of magnitude less (0.1 mm/s). Since IR radiation comes from depths not more than 100 $\mu$m, a conclusion can be derived that velocity gradient below the surface is very large indeed. This velocity gradient prevents bulk convective vortices from reaching the surface, which implies complex structure of surface layer with vortices of several scales located above each other. Same conclusion was made in [

Thermal imaging allows separating the problem of hydrodynamical simulations in liquid and gas. Instead of solving equations for both media and coupling the solutions by setting equal temperatures and heat fluxes at the interface [

Major drawback of thermography is small thickness of the observable layer. Hence, it is worthwhile to complement thermography with some technique providing data on spatial structure of temperature distribution at considerable depths. In present investigation BOS method is implemented, which is relatively new and has not been used for evaporation studies before. Actually, original scheme of observations by

Figure 3 |

where $n$ is refraction index. For $n=const$ first two equations of the set ((2)) yield linear $\vec{R}(S)$ i.e. straight-line propagation of the light. If refraction index variations are present, total deflection angle is

\begin{eqnarray*} \alpha=\frac{1}{n_0}\int\limits_H\frac{\partial n}{\partial x}\,dz, \end{eqnarray*}Figure 4 |

Figure 5 |

where $a$ is one pixel size in background plane, $\vec{\xi}$ is the displacement vector field measured in pixels, $h$ is the tank width and $L$ is the distance from background to tank. Since pressure variations in small water tanks are negligible, refraction index is a function of density and temperature. Hence, temperature field can be obtained by solving two algebraic equations: empirical equation of state and Lorentz-Lorenz relation for refraction index.

Figure 6 |

Accuracy of the measurements can be estimated by cross-correlating two reference images. This estimate takes into account the errors of cross-correlation algorithm, lens aberrations, noise of the camera sensor and possible camera displacement. Also, it accounts for refraction index fluctuations which are present even without evaporation. It does not take into account distorted image blur caused by nonlinear refraction index variations [

Figure 7 |

BOS images were cropped below liquid surface in order to avoid the errors associated with meniscus and multiple reflections of light from the interface. Water tank dimensions are $30\times50\times19$ mm. The agreement is very good. Use of two different methods justifies the validity of obtained experimental results, making evaporation from a small water tank a good test case for numerical models involving evaporation. BOS temperature is slightly higher, indicating that the upper sublayer about 0.1 mm is not well resolved or is possibly lost during the image crop. However, the difference between two distributions is about 0.05 K, less than accuracy of thermocouple providing the reference temperature value for BOS measurements. Good agreement is related to geometry of the considered flow, which is nearly 2D. If cold filaments are observed near the liquid surface, the complete structure of temperature field is not captured by BOS, since it yields temperature values averaged over line-of-sight. Nevertheless, combination of BOS side view and thermal imaging of the surface gives notion about thermal structures in the considered flow.

Figure 8 |

Figure 9 |

Figure 10 |

Figure 11 |

- BOS method is very promising for investigations of thermal structures near gas–liquid interface. Its accuracy is generally better than 0.1 K. Simplicity of experimental realization allows using it for in situ measurements.
- Combination of BOS with IR thermal imaging provides reliable data on the entire structure of thermal field. Also, boundary conditions for velocity and temperature at the interface can be obtained, making separate modeling of problem in liquid and gas feasible.
- Two configurations of the near-surface layer were observed for various liquids and conditions, both associated with Marangoni convection. Velocity gradients near the interface are shown to be much larger than vorticity of Rayleigh convection vortices in bulk liquid. This implies complex multi-layered vortical structure of the upper liquid layer.

This work was partially supported by Russian Foundation for Basic Research (grant 12-08-01077-a).

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Received 28 May 2012; accepted 31 May 2012; published 4 June 2012.

**Citation:** Plaksina Yu. Yu., A. V. Uvarov, N. A. Vinnichenko, V. B. Lapshin (2012), Experimental investigation of near-surface small-scale structures at water--air interface: Background Oriented Schlieren and thermal imaging of water surface, *Russ. J. Earth Sci., 12*, ES4002, doi:10.2205/2012ES000517.

Copyright 2012 by the Geophysical Center RAS.