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Surface tension
Description 
The wind over the ocean surface is composed of a large number of molecules that periodically collide with water molecules at the surface.
In this way, the kinetic energy of the air molecules is partially transferred to the water molecules, which can be represented as a stress exerted by the air onto the water.
The resulting effect is the creation of surface eddies, which in turn affect deeper layers, transferring the velocity of the wind to a shallow layer of the ocean. This process allows the energy of the wind to be transferred to the near-surface layer of the ocean, increasing the speed of the water in that area.
ID:(12303, 0)
Velocity profile in the superficial layer (MOST)
Equation
The stress exerted by the wind on the surface can be modeled as the transfer of kinetic energy from the air to the upper layer of the ocean.
In this case, the surface fraction is estimated using the density of kinetic energy, which is related to the surface stress.
Furthermore, we need to consider an efficiency factor that is modeled through the drag coefficient $C_D$.
 $ \tau_t = \rho_a C_D ( U_z - U_0 )^2$ |
In the Monin-Obukhov Similarity Theory (MOST) model, the density of air kinetic energy is considered, which depends on the air density ($\rho_a$) and velocity ($u$):
$\rho_a u^2$
The factor of 1/2 has been omitted as constants are introduced at the end to adjust the model.
The generated stress is related to the drag coefficient ($C_D$) and the velocity difference ($U_z - U_0$) between the velocity at height $z$ ($U_z$) and the velocity at the surface ($U_0$):
$u = U_z - U_0$
Therefore, the stress generated at the surface can be modeled as:
| $ \tau_t = \rho_a C_D ( U_z - U_0 )^2$ |
ID:(12222, 0)
Tensión en la superficie (MOST)
Equation
El modelo de Monin-Obukhov Similarity Theory (MOST) modela la tensión superficial proporcional al cuadrado de la velocidad del aire en la superficie.
Por ello con se indica
| $ \tau_t = \rho_a u_a ^2 $ |
ID:(12220, 0)
Surface layer temperature profile (MOST)
Equation
In the case of heat flux, the heat content is estimated using density, specific heat, and temperature, along with the wind velocity and the transmission coefficient. In this way, the heat flux can be expressed as follows:
| $ H_z = C_H \rho_a c_p ( T_z - T_0 ) U_z $ |
In the Monin-Obukhov Similarity Theory (MOST), the surface heat energy, represented by
$\rho_a c_p (T_z - T_0)$
is transferred to the water with the transfer coefficient $C_H$ and the air velocity $U_z$, resulting in the heat flux.
| $ H_z = C_H \rho_a c_p ( T_z - T_0 ) U_z $ |
ID:(12223, 0)
Concentration profile in the surface layer (MOST)
Equation
Using the Monin-Obukhov Similarity Theory (MOST) model, the flux of elements such as gases can be estimated by considering the displacement of the surface and a transfer coefficient, which is expressed as follows:
| $ C = D_C U_z ( C_z - C_0 )$ |
In the Monin-Obukhov Similarity Theory (MOST) model, the flux of elements such as gases is estimated by considering the difference in concentrations between the air and water, represented by
$C_z - C_0$
and the flux is calculated using the transfer coefficient $D_C$ and the surface velocity $U_z$, as follows:
| $ C = D_C U_z ( C_z - C_0 )$ |
This allows for the estimation of the flux of elements between the air and water.
ID:(12224, 0)
Total voltage at the interface
Equation
The total stress of the atmosphere on the ocean includes the wind stress $\tau_t$, wave stress $\tau_w$, and viscosity stress $\tau_{\eta}$. Therefore, it can be expressed as:
| $ \tau = \tau_t + \tau_w + \tau_{\eta} $ |
ID:(12232, 0)
Drag speed
Equation
Since the total stress is the sum of wind stress, wave stress, and viscosity stress,
| $ \tau = \tau_t + \tau_w + \tau_{\eta} $ |
it leads to a generalization of the generated surface velocity,
| $ \tau_t = \rho_a u_a ^2 $ |
thus, the generalization yields the velocity equal to
| $ u = \sqrt{\displaystyle\frac{ \tau }{ \rho }}$ |
ID:(12233, 0)
Speed ratio
Equation
If we assume that there is a continuous transition in the energy density at the air-water interface and that this energy is of kinetic nature, then we would have:
$\rho_a u_a^2=\rho_w u_w^2$
where $\rho$ represents the densities and $u$ represents the velocities of the air (a) and the ocean (w). Thus, we have:
| $ \displaystyle\frac{ u_a ^2 }{ u_w ^2 } = \displaystyle\frac{ \rho_w }{ \rho_a }$ |
Additionally, we can consider that the energy density has the same unit as the surface tension, which explains the equality based on the fact that in an equilibrium system, the tensions must be equal.
ID:(12234, 0)
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Video
Video: Superficie