In fluid dynamics

Fluid dynamics

In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...

, wave–current interaction is the interaction between surface gravity waves and a mean flow

Mean flow

In fluid dynamics, the fluid flow is often decomposed into a mean flow – and deviations from the mean. The averaging can be done either in space or in time....

. The interaction implies an exchange of energy, so after the start of the interaction both the waves and the mean flow are affected.

For depth-integrated

Integral

Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...

 and phase

Phase (waves)

Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...

-average

Average

In mathematics, an average, or central tendency of a data set is a measure of the "middle" value of the data set. Average is one form of central tendency. Not all central tendencies should be considered definitions of average....

d flows, the quantity of primary importance for the dynamics

Dynamics (mechanics)

In the field of physics, the study of the causes of motion and changes in motion is dynamics. In other words the study of forces and why objects are in motion. Dynamics includes the study of the effect of torques on motion...

 of the interaction is the wave radiation stress tensor

Radiation stress

In fluid dynamics, the radiation stress is the depth-integrated – and thereafter phase-averaged – excess momentum flux caused by the presence of the surface gravity waves, which is exerted on the mean flow...

.

Classification

identifies five major sub-classes within wave–current interaction:

• interaction of waves with a large-scale current field
  Field (physics)
  In physics, a field is a physical quantity associated with each point of spacetime. A field can be classified as a scalar field, a vector field, a spinor field, or a tensor field according to whether the value of the field at each point is a scalar, a vector, a spinor or, more generally, a tensor,...
  
  , with slow – as compared to the wavelength
  Wavelength
  In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
  
   – two-dimensional horizontal variations of the current fields;
• interaction of waves with small-scale current changes (in contrast with the case above), where the horizontal current varies suddenly, over a length scale
  Length scale
  In physics, length scale is a particular length or distance determined with the precision of one order of magnitude. The concept of length scale is particularly important because physical phenomena of different length scales cannot affect each other and are said to decouple...
  
   comparable with the wavelength;
• the combined wave–current motion for currents varying (strongly) with depth below the free surface
  Free surface
  In physics, a free surface is the surface of a fluid that is subject to constant perpendicular normal stress and zero parallel shear stress,such as the boundary between two homogenous fluids,for example liquid water and the air in the Earth's atmosphere...
  
  ;
• interaction of waves with turbulence
  Turbulence
  In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic and stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time...
  
  ; and
• interaction of ship waves and currents, such as in the ship's wake
  Wake
  A wake is the region of recirculating flow immediately behind a moving or stationary solid body, caused by the flow of surrounding fluid around the body.-Fluid dynamics:...
  
  .