CMS-Wave:Wave-current Interaction: Difference between revisions

From CIRPwiki
Jump to navigation Jump to search
(Created page with 'big Under Construction == Wave-current Interaction == The characteristic velocities mathc_x/math, mathc_y/math, and mathc_{\theta}/math are calculated as …')
mNo edit summary
 
(3 intermediate revisions by the same user not shown)
Line 1: Line 1:
big
Under Construction
== Wave-current Interaction ==
== Wave-current Interaction ==
The characteristic velocities  mathc_x/math,  mathc_y/math, and mathc_{\theta}/math are calculated as
The characteristic velocities  <math>c_x</math>,  <math>c_y</math>, and <math>c_{\theta}</math> are calculated as
 
{{Equation|<math>c_x = c_g \cos \theta + U </math>|1}}
    mathc_x = c_g \cos \theta + U/math
{{Equation|<math>c_y = c_g \sin \theta + V </math>|2}}
    mathc_y = c_g \sin \theta + V/math
{{Equation|<math>
    mathc_{\theta} = \frac{\sigma}{\sinh 2 k h}
c_{\theta} = \frac{\sigma}{\sinh 2 k h}
\biggl( \sin \theta \frac{\partial h}{\partial x}  - \cos \theta \frac{\partial h}{\partial y } \biggr)
\biggl( \sin \theta \frac{\partial h}{\partial x}  - \cos \theta \frac{\partial h}{\partial y } \biggr)
+ \cos \theta \sin \theta \frac{\partial U}{\partial x}
+ \cos \theta \sin \theta \frac{\partial U}{\partial x}
Line 13: Line 10:
+ \sin ^2 \theta \frac{\partial V}{\partial x}  
+ \sin ^2 \theta \frac{\partial V}{\partial x}  
- \cos \theta \sin \theta \frac{\partial V}{\partial y}  
- \cos \theta \sin \theta \frac{\partial V}{\partial y}  
/math
</math>|3}}


The dispersion relationships between the relative angular frequency σ, the absolute angular frequency ω, the wave number vector k, and the current velocity vector U = U2 +V2 are (Jonsson 1990)
The dispersion relationships between the relative angular frequency σ, the absolute angular frequency ω, the wave number vector k, and the current velocity vector U = U2 +V2 are (Jonsson 1990)


 
{| border="1"
{| border=1
! Symbol !! Description
! Symbol !! Description
|-
|-
| math c /math ||  Wave celerity
| <math> c </math> ||  Wave celerity
|-
|-
| math c_g /math || Wave group velocity
| <math> c_g </math> || Wave group velocity
|-
|-
| math \sigma /math || Wave frequency  
| <math> \sigma </math> || Wave frequency  
|-
|-
| math E /math ||  Spectral wave density
| <math> E </math> ||  Spectral wave density
|-
|-
| math k /math ||  Wave number
| <math> k </math> ||  Wave number
|-
|-
| math h /math ||  Total water depth
| <math> h </math> ||  Total water depth
|-
|-
| math U /math ||  Depth-averaged current velocity in x-direction
| <math> U </math> ||  Depth-averaged current velocity in x-direction
|-
|-
| math V /math ||  Depth-averaged current velocity in y-direction
| <math> V </math> ||  Depth-averaged current velocity in y-direction
|}
|}


----
----
/big
[[CMS#Documentation_Portal | Documentation Portal]]
[[CMS#Documentation_Portal | Documentation Portal]]
[[category:CMS-Wave]]

Latest revision as of 16:13, 23 January 2023

Wave-current Interaction

The characteristic velocities , , and are calculated as

  (1)
  (2)
  (3)

The dispersion relationships between the relative angular frequency σ, the absolute angular frequency ω, the wave number vector k, and the current velocity vector U = U2 +V2 are (Jonsson 1990)

Symbol Description
Wave celerity
Wave group velocity
Wave frequency
Spectral wave density
Wave number
Total water depth
Depth-averaged current velocity in x-direction
Depth-averaged current velocity in y-direction

Documentation Portal

Retrieved from "https://cirpwiki.info/index.php?title=CMS-Wave:Wave-current_Interaction&oldid=14012"