## Tidal Characteristic Numbers of Current

### From BAWiki

Graphical representation of characteristic numbers of current velocity (with German text only). This graphical representation is also available in Encapsulated PostScript format.

Graphical representation of characteristic numbers of volume fluxes (with German text only). This graphical representation is also available in Encapsulated PostScript format.

Graphical representation of eulerian residual current and residual path (with German text only). This graphical representation is also available in Encapsulated PostScript format.

## Contents

- 1 Motivation
- 2 Time of slack current determination
- 3 Definition of Tidal Characteristic Numbers of Current and Water Transport
- 3.1 Flood Current
- 3.1.1 Slack Water Time of Flood Current
- 3.1.2 Slack Water Duration around Slack Water Time of Flood Current
- 3.1.3 Slack Water Dislocation of Flood Current
- 3.1.4 Flood Current Duration
- 3.1.5 Maximum Flood Current Velocity
- 3.1.6 Mean Flood Current Velocity
- 3.1.7 Residual Flood Current Velocity
- 3.1.8 Eulerian Flood Path
- 3.1.9 Flood Volume
- 3.1.10 Flood Volume Transport Rate
- 3.1.11 Differences of Time of Maximum Flood Current between Different Locations

- 3.2 Ebb Current
- 3.2.1 Slack Water Time of Ebb Current
- 3.2.2 Slack Water Duration around Slack Water Time of Ebb Current
- 3.2.3 Slack Water Dislocation of Ebb Current
- 3.2.4 Ebb Current Duration
- 3.2.5 Maximum Ebb Current Velocity
- 3.2.6 Mean Ebb Current Velocity
- 3.2.7 Residual Ebb Current Velocity
- 3.2.8 Eulerian Ebb Path
- 3.2.9 Ebb Volume
- 3.2.10 Ebb Volume Transport Rate
- 3.2.11 Differences of Time of Maximum Ebb Current between Different Locations

- 3.3 Tidal Cycle
- 3.3.1 Tide Current Duration
- 3.3.2 Flood Current Duration : Ebb Current Duration
- 3.3.3 Flood Current Duration : Tide Current Duration
- 3.3.4 Ebb Current Duration : Tide Current Duration
- 3.3.5 Mean Tide Current Velocity
- 3.3.6 Max. Flood Current Velocity : Max. Ebb Current Velocity
- 3.3.7 Maximum Flood Current Velocity : Mean Tide Current Velocity
- 3.3.8 Maximum Ebb Current Velocity : Mean Tide Current Velocity
- 3.3.9 Mean Flood Current Velocity : Mean Ebb Current Velocity
- 3.3.10 Mean Flood Current Velocity : Mean Tide Current Velocity
- 3.3.11 Mean Ebb Current Velocity : Mean Tide Current Velocity
- 3.3.12 Residual Current
- 3.3.13 Eulerian Flood Path : Eulerian Ebb Path
- 3.3.14 Residual Path
- 3.3.15 Tide Volume
- 3.3.16 Flood Volume : Ebb Volume
- 3.3.17 Flood Volume : Tide Volume
- 3.3.18 Ebb Volume : Tide Volume
- 3.3.19 Residual Tide Volume
- 3.3.20 Residual Tide Volume Transport Rate

- 3.1 Flood Current

## Motivation

Computation as well as graphical display of several tidal characteristic numbers of current add aditional insight into tidally induced dynamic processes which are reflected in the current velocity and its related derived quantities. This type of tidal analysis should therefore go hand in hand with the calculation of tidal characteristic numbers of water level.

- The computation is carried out separately for the periods of flood and ebb current duration. Therefore it yields information about the asymmetry of the tide-induced currents. An asymmetry can result in different durations of ebb and flood currents on the one hand side and on the other hand side in different maximum flood and ebb current velocities. This imbalance might be a result of different speeds for the fall and rise of the water level which causes a distinguished acceleration of the flow. Different values of the maximum flood and ebb current velocities may be a main cause for residual transport (up- or down-estuary) of bedload material or suspended sediments.
- Unequal slack water times of flood or ebb current are mainly due to the varying significance of the various dynamic driving forces (e.g. batropic and baroclinic pressure gradient as well as bottom friction versus inertia forces). They mainly depend on water depth as well as on the precise location of the water volume in the water column.
- Different times of slack water dislocation are related to the character of the tidal wave. In a purely propagating deep water wave there exists a phase shift of approximately 90 ° between current and water level elevation. Whereas in shallow water, bottom friction and reflexion of the tidal wave causes a much smaller phase shift. Remember: for a purely standing wave the phase shift is zero.
- The periods of slack water are good indicators for the times of mild current climate. During these periods suspended sediments may settle to the bottom and become deposited. Unsymmetrical periods of slack water can result in net up- or down-estuary transport of suspended sediments.
- Tidal characteristic numbers of current which are representative for the whole tidal cycle may give some insight into the residual transport paths for the water masses travelling along an estuary. For example the Eulerian residual current is a first order approximation to the respective Lagrangian one. It should be therefore interpreted with some care.

**Automatic analyses for all of the above mentioned tidal characteristic numbers of current are carried out for 2D- as well as for 3D-data by the programs TDKVF and NCANALYSE.**

## Time of slack current determination

Times of ebb slack as well as flood slack are determined in different ways in TDKVF and NCANALYSE.

### Program TDKVF

TDKVF date and time of slack current is derived from current magnitude:

*Ebb slack*is equivalent to the time of minimum current magnitude (local minimum), which is closest to low water (LW).*Flood slack*is equivalent to the time of minimum current magnitude (local minimum), which is closest to high water (HW).

### Program NCANALYSE

NCANALYSE determines slack current using current vector as follows:

- For each location a
*main current orientation*is determined from all available current vectors; - Orthogonal to
*main current orientation*a*plane of current reversal*is defined; - Date and time of slack current is determined from the passage of the current vector through the
*plane of current reversal*:- in case current slack is closest to low water (LW), it is considered as being an
*ebb slack*, or - in case current slack is closest to high water (HW), it is considered as being a
*flood slack*.

- in case current slack is closest to low water (LW), it is considered as being an
- A slack of current event will not be determined in case at least one of the following conditions is true:
- no current reversal occurs (unidirectional current),
- too few current reversals occur (less than twice within a tidal cycle),
- too many current reversals occur (more than twice within a tidal cycle),
- there is no well-defined main current orientation (e. g. in case of a rotating current), or
- current reversals are short in time, not stable enough.

Please notice that "main current orientation" typically depends on the number of data used from which it is computed at a specific location. Therefore also the "plane of current reversal" as well as the time of slack current may be dependent on the length of the period of data analysis.

## Definition of Tidal Characteristic Numbers of Current and Water Transport

Characteristic numbers of water transport which are derived from exact integral flow volumes are subsequently listed under (sub-) section **Computed from integral (water) volume transport**.

### Flood Current

#### Slack Water Time of Flood Current

Time of occurrence for slack water at the end of the flood relative to a reference position.

Example figures: slack water time of flood current.

Data analysis: TDKVF and NCANALYSE.

#### Slack Water Duration around Slack Water Time of Flood Current

Timespan around slack water time of flood current for which the flow velocity does not exceed a certain value (e.g. 0.2 m/s).

Example figures: slack water duration around slack water time of flood current.

Data analysis: TDKVF and NCANALYSE.

#### Slack Water Dislocation of Flood Current

Timespan between high water occurrence and slack water time of flood current.

Example figures: slack water dislocation of flood current.

Data analysis: TDKVF and NCANALYSE.

#### Flood Current Duration

Timespan between ebb slack and subsequent flood slack.

Example figures: flood current duration.

Data analysis: TDKVF and NCANALYSE.

#### Maximum Flood Current Velocity

Maximum value of current velocity during flood current duration.

Example figures: maximum flood current velocity.

Data analysis: TDKVF and NCANALYSE.

#### Mean Flood Current Velocity

Mean value of flood current velocity (computed from magnitude) during flood current duration.

Example figures: mean flood current velocity.

Data analysis: TDKVF and NCANALYSE.

#### Residual Flood Current Velocity

Residual flood current velocity (computed from addition of vectors) during flood current duration.

Example figures: residual flood current velocity.

Data analysis: NCANALYSE.

#### Eulerian Flood Path

Vectorial sum of the path lengths for a certain location during flood current.

Example figures: eulerian flood path.

Data analysis: TDKVF and NCANALYSE.

#### Flood Volume

##### Computed from synoptic current velocity

Volume of water which flows through a certain cross section during flood current.

Example: Flood Volume for the Inner Außenweser. Figure obsolete.

Data analysis: TDKVF.

##### Computed from integral (water) volume transport

Exact volume of water (with exception of roundoff) which passes a certain cross section during flood current. This quantity makes use of the normal flow of water only, which is orthogonal to the flow face. Reconstruction of the total vector by means of *projection* is left to visualization programs (e. g. NCPLOT).

Data analysis: NCANALYSE.

#### Flood Volume Transport Rate

##### Computed from synoptic current velocity

Not computed by program TDKVF.

##### Computed from integral (water) volume transport

Exact volume transport rate of water (with exception of roundoff) passing a certain cross section during flood current. This quantity makes use of the normal flow of water only, which is orthogonal to the flow face. Reconstruction of the total vector by means of *projection* is left to visualization programs (e. g. NCPLOT). On tidal flats this quantity is computed for the period of inundation only.

Data analysis: NCANALYSE.

#### Differences of Time of Maximum Flood Current between Different Locations

Differences of time of maximum flood current occurrence between different locations within the area of data analysis.

Example: Time of Maximum Flood Current for the Inner Außenweser. Figure obsolete.

Data analysis: TDKVF. No more supported by NCANALYSE.

### Ebb Current

#### Slack Water Time of Ebb Current

Time of occurrence for slack water at the end of the ebb relative to a reference position.

Example figures: slack water time of ebb current.

Data analysis: TDKVF and NCANALYSE.

#### Slack Water Duration around Slack Water Time of Ebb Current

Timespan around slack water time of ebb current for which the flow velocity does not exceed a certain value (e.g. 0.2 m/s).

Example figures: slack water duration around slack water time of ebb current.

Data analysis: TDKVF and NCANALYSE.

#### Slack Water Dislocation of Ebb Current

Timespan between high water occurrence and slack water time of ebb current.

Example figures: slack water dislocation of ebb current.

Data analysis: TDKVF and NCANALYSE.

#### Ebb Current Duration

Timespan between flood slack and subsequent ebb slack.

Example figures: ebb current duration.

Data analysis: TDKVF and NCANALYSE.

#### Maximum Ebb Current Velocity

Maximum value of current velocity during ebb current duration.

Example figures: maximum ebb current velocity.

Data analysis: TDKVF and NCANALYSE.

#### Mean Ebb Current Velocity

Mean value of ebb current velocity (computed from magnitude) during ebb current duration.

Example figures: mean ebb current velocity.

Data analysis: TDKVF and NCANALYSE.

#### Residual Ebb Current Velocity

Residual ebb current velocity (computed from addition of vectors) during ebb current duration.

Example figures: residual ebb current velocity.

Data analysis: NCANALYSE.

#### Eulerian Ebb Path

Vectorial sum of the path lengths for a certain location during ebb current.

Example figures: eulerian ebb path.

Data analysis: TDKVF and NCANALYSE.

#### Ebb Volume

##### Computed from synoptic current velocity

Volume of water which flows through a certain cross section during ebb current.

Example: Ebb Volume for the Inner Außenweser. Figure obsolete.

Data analysis: TDKVF.

##### Computed from integral (water) volume transport

Exact volume of water (with exception of roundoff) which passes a certain cross section during ebb current. This quantity makes use of the normal flow of water only, which is orthogonal to the flow face. Reconstruction of the total vector by means of *projection* is left to visualization programs (e. g. NCPLOT).

Data analysis: NCANALYSE.

#### Ebb Volume Transport Rate

##### Computed from synoptic current velocity

Not computed by program TDKVF.

##### Computed from integral (water) volume transport

Exact volume transport rate of water (with exception of roundoff) passing a certain cross section during ebb current. This quantity makes use of the normal flow of water only, which is orthogonal to the flow face. Reconstruction of the total vector by means of *projection* is left to visualization programs (e. g. NCPLOT). On tidal flats this quantity is computed for the period of inundation only.

Data analysis: NCANALYSE.

#### Differences of Time of Maximum Ebb Current between Different Locations

Differences of time of maximum ebb current occurrence between different locations within the area of data analysis.

Example: Time of Maximum Ebb Current for the Inner Außenweser. Figure obsolete.

Data analysis: TDKVF. No more supported by NCANALYSE.

### Tidal Cycle

#### Tide Current Duration

Tide current duration. Period of time between an ebb slack and the subsequent ebb slack.

Example figures: tide current duration.

Data analysis: NCANALYSE.

#### Flood Current Duration : Ebb Current Duration

Ratio of flood current duration to ebb current duration.

Example figures: flood current duration : ebb current duration.

Data analysis: TDKVF and NCANALYSE.

#### Flood Current Duration : Tide Current Duration

Ratio of flood current duration to tide current duration.

Example figures: flood current duration : tide current duration.

Data analysis: NCANALYSE.

#### Ebb Current Duration : Tide Current Duration

Ratio of ebb current duration to tide current duration.

Example figures: ebb current duration : tide current duration.

Data analysis: NCANALYSE.

#### Mean Tide Current Velocity

Mean value of the current velocity during a tidal cycle (from ebb slack to ebb slack).

The computation is based on the local period of flooding (wet duration).

Example figures: mean tide current velocity.

Data analysis: NCANALYSE.

#### Max. Flood Current Velocity : Max. Ebb Current Velocity

Ratio of maximum flood current velocity to maximum ebb current velocity.

Example figures: maximum flood current : maximum ebb current.

Data analysis: TDKVF and NCANALYSE.

#### Maximum Flood Current Velocity : Mean Tide Current Velocity

Ratio of maximum flood current velocity to mean tide current velocity.

Example figures: maximum flood current : mean tide current.

Data analysis: NCANALYSE.

#### Maximum Ebb Current Velocity : Mean Tide Current Velocity

Ratio of maximum ebb current velocity to mean tide current velocity.

Example figures: maximum ebb current : mean tide current.

Data analysis: NCANALYSE.

#### Mean Flood Current Velocity : Mean Ebb Current Velocity

Ratio of mean flood current velocity to mean ebb current velocity.

Example figures: mean flood current : mean ebb current.

Data analysis: TDKVF and NCANALYSE.

#### Mean Flood Current Velocity : Mean Tide Current Velocity

Ratio of mean flood current velocity to mean tide current velocity.

Example figures: mean flood current : mean tide current.

Data analysis: NCANALYSE.

#### Mean Ebb Current Velocity : Mean Tide Current Velocity

Ratio of mean ebb current velocity to mean tide current velocity.

Example figures: mean ebb current : mean tide current.

Data analysis: NCANALYSE.

#### Residual Current

Vectorial sum of all flow velocities for a certain location and a full tidal cycle.

The computation is based on the local period of flooding (wet duration).

Example figures: residual current.

Data analysis: TDKVF and NCANALYSE.

#### Eulerian Flood Path : Eulerian Ebb Path

Ratio of flood path to ebb path.

Example figures: eulerian flood path : eulerian ebb path.

Data analysis: TDKVF and NCANALYSE.

#### Residual Path

Vectorial sum of all transport paths for a certain location and a full tidal cycle.

The computation is based on the local period of flooding (wet duration).

Example figures: residual path.

Data analysis: TDKVF and NCANALYSE.

#### Tide Volume

##### Computed from synoptic current velocity

Sum of ebb volume and flood volume.

Example: Tide Volume for the Inner Außenweser. Figure obsolete.

Data analysis: TDKVF.

##### Computed from integral (water) volume transport

Exact sum for the volume of water (with exception of roundoff) which passes a certain cross section during a full tidal cycle (flood volume plus ebb volume). This quantity makes use of the normal flow of water only, which is orthogonal to the flow face. Data anlysis: NCANALYSE.

#### Flood Volume : Ebb Volume

##### Computed from synoptic current velocity

Ratio between flood volume and ebb volume.

Example: Ratio Flood Volume : Ebb Volume for the Inner Außenweser. Figure obsolete.

Data analysis: TDKVF.

##### Computed from integral (water) volume transport

Ratio between exact flood volume and ebb volume (with exception of roundoff) which passes a certain cross section. This quantity makes use of the normal flow of water only, which is orthogonal to the flow face.

Data analysis: NCANALYSE.

#### Flood Volume : Tide Volume

##### Computed from synoptic current velocity

Not computed by program TDKVF.

##### Computed from integral (water) volume transport

Ratio between exact flood volume and tide volume (with exception of roundoff) which passes a certain cross section. This quantity makes use of the normal flow of water only, which is orthogonal to the flow face.

Data analysis: NCANALYSE.

#### Ebb Volume : Tide Volume

##### Computed from synoptic current velocity

Not computed by program TDKVF.

##### Computed from integral (water) volume transport

Ratio between exact ebb volume and tide volume (with exception of roundoff) which passes a certain cross section. This quantity makes use of the normal flow of water only, which is orthogonal to the flow face.

Data analysis: NCANALYSE.

#### Residual Tide Volume

##### Computed from synoptic current velocity

Residual volume of water, which flows through a certain cross section within a full tidal cycle.

Example: Residual Flow for the Inner Außenweser. Figure obsolete.

Data analysis: TDKVF.

##### Computed from integral (water) volume transport

Exact residual volume of water (with exception of roundoff) which passes a certain cross section during a full tidal cycle (flood current and ebb current). This quantity makes use of the normal flow of water only, which is orthogonal to the flow face. Reconstruction of the total vector by means of *projection* is left to visualization programs (e. g. NCPLOT).

Data analysis: NCANALYSE.

#### Residual Tide Volume Transport Rate

##### Computed from synoptic current velocity

Not computed by program TDKVF.

##### Computed from integral (water) volume transport

Exact residual volume transport rate of water (with exception of roundoff) which passes a certain cross section during a full tidal cycle (flood current and ebb current). This quantity makes use of the normal flow of water only, which is orthogonal to the flow face. Reconstruction of the total vector by means of *projection* is left to visualization programs (e. g. NCPLOT). On tidal flats the transport rate is computed for the period of inundation only.

Data analysis: NCANALYSE.

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