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Prepared by

Physical Science Services Branch

Scientific Services Division

Educational Pamphlet #4

April 1981

l

&1.5. DIPARTMENT Of COMMERCE

National Oceanic and Atmolpheric Adminiltration

National Ocean Survey

Office of Program Development and Management
Illustrations

1 - Map showing principal ocean currents or the world.

Fig. 2 - Example of a typical reversing current showing time vs.

velocity ror one day.

3 - Effect of nontidal current on reversing tidal current.

4 - Typical current curves showing daily and mixed types of

reversing currents.

5 - Example or a typical rotary current.

.

6 - Typical computation of reversing currents.

1 - Sample page of daily predictions for the Narrows,

New York Harbor, N.Y.

Pig. 8 - Sample page of Table 2 showing places referred to the

Narrows.

9 - Sample page from a tidal current chart.
,

U. S. DEPARTMENT OF COMMERCE

Natianal Oceanic and Atmospheric Administration

National Ocean Survey

Rockville, Md.

TIDAL CURRmfTS

Man in his never ending search for knowledge and in his travels

on the sea has long known about the ocean's tides and currents.

Although he may not have fully understood the reasons for the

movements of these waters, he was very much aware of their

benefits and dangers to him. Today the study of the tide and

current is still a major problem facing the oceanographer due

to the increased needs of the scientist, engineer, military,

and the general public.

In presenting a study of the ocean's tides and currents, the

usual practice is to consider each separately. In this paper

the primary emphasis is on tidal currents with only a brief

reference to the tide. For a more complete discussion on the

tide, the reader is referred to various C&GS manuals as well as

the paper "Significant Aspects of The Tide."

Basically the current in the seas can be broken down into two

parts, namely tidal and nontidal. Tidal currents are the

horizontal movements of the water that accompany the rising

and falling of the tide. The horizontal movement of the tidal

current and the vertical movement of the tide are intimately

related parts of the same phenomenon brought about by the tideproducing forces of sun and moon. Tidal currents, like the

tides, are therefore periodic.

It ie the periodicity or the tidal current that chierly distinsuishes it rrom other kinds of currents in the sea, which are

known by the general name of nontidal currents. These latter

currents are brought about by causes that are independent or the

tides, such as winds, rreshwater runoff, and dirrerences in

density and temperature. Currents or this class do not eXhibit

the periodicity or tidal currents. The permanent currents in

the ge~eral circulatory system such as the Gulr Stream also raIl

into this grouping.

Tidal and nontidal currents occur together in the open sea and

in ~nahore tidal waters, the actual cur~ent experienced at any

point being the resultant of the two classes of currents. In

some places tid~l currents predominate and in others nontidal

currents are stronger. Tidal currents generally attain considerable velocity in narrow entrances to bays, in constricted

parts of rivers, and in passages from one body of water to

another. Along the coast and farther offshore tidal currents

1

3

are generally of moderate velocity; and in the open sea, calculation based on the theory of wave motion, gives a tidal current

of less than one-tenth of a knot.

The Tide-Producing Forces

The gravitational forces of the various celestial bodies, principally the sun and the moon upon the rotating earth, result in

the periodic changes in the sea. These forces are reflected in

the vertical rise and fall of the sea called the tide and in its

horizontal motion called the tidal current. Due to its nearness

to the earth, the moon is the predominent tide-producing body.

The intensity with which the sun (or moon) attracts a particle

of matter on the earth varies inversely as the square of the distance. For the solid earth as a whole the distance 1s obviously

to be measured from the center of the earth, since that is the

center of mass of the whole body. But the waters of the earth,

which may be considered as lying on the surface of the earth, are

on the one side of the earth nearer to the heavenly bodies and

on the other side farther away than the center of the earth. The

attraction of sun or moon for the waters of the ocean is thus

different in intensity .froM the attraction for the solid earth

as a whole, and these differences of attraction give rise to the

forces that cause the ocean waters to MOVe relative to the solid

earth and bring about the tides and the tidal currents. These

forces are called the tide-producing forces.

The mathematical development of these forces shows that the tideproducing force of a heavenly body varies directly as its mass

and inversely as the cube of its distance from the earth. The

sun has a mass about 21,000,000 times as great as that of the

moon; but it is 389 times as far away from the earth. Its tideproducing force is therefore to that of the moon as 21,000,000

is to (389)3, or somewhat less than one-half.

When the relative motions or the earth, moon, and sun are introduced into the equations or the tide-producing rorces, it is

round that the tide-producing rorces or both sun and moon group

themselves into classes: (a) Those having a period or approximately one haIr a day, known as the semidiurnal rorces; (b) those

having a period or approximately I day, 'known as diurnal rorces;

(c) those having a period or haIr a month or more, known as

long-period rorces.

The distribution of the tidal forces over the earth takes place

in a regular manner, varying with the latitude. But the response

of the various seas to these forces is very profoundly modified

by terrestrial features. As a result we find the tides and the

currents as they actually occur differing at various places but

apparently with no regard to latitude. Other ce1estial bodies
4

CAn be discounted because their size or distance from earth

produces a pull that is almost nonexistent.

Variations in Velocity ot the Tidal Current

The velocity o~ the tidal current at any place varies ~rom day

to day. In part this variation arises ~rom changes in meteorological conditions, but in much larger part it is o~ a periodic

character due to changes in the position o~ the moon relative

to earth and sun. In its movements the tidal current clearly

reveals the presence o~ three variations, each related to a

partIcular movement o~ the moon.

The most noticeable variation, as a rule, is that related to

the moon's phase. At the times of new and full moon, the speed

of the current is stronger than usual and is called "spring

current." Whp~ the moon is in its first and third quarters,

the current flow is less than usual; hence the speed is less

than the average. The current at such times is called "neapcurren t . "

It is to be noted, however, that at most places there is a lag

o~ a day or two between the occurrence o~ spring or neap currents'and the corresponding phases o~ moon; that is, spring

currents do not occur on the days o~ ~ull and new moon, but a

day or two later. Likewise neap currents ~ollow the moon's

~irst and third quarters a~ter an interval o~ a day or two.

This lag in the response o~ the current expressed in hours or

days is known as the "age o~ phase ineq~lity" or "phase age"

and is generally ascribed to the er~ects o~ ~riction.

The second variation in the velocity or the current is related

to the moon's varying distance rrom the earth. In its movement

around the earth the moon describes an ellipse in a period of

approximately 21~ days. The earth is at one of the roci of

this elliptical brbit. Hence, during this period, the moon is

at one time nearest the earth and at another time farthest away.

When it is nearest the earth, or in perigee, the speed or the

current is stronger than on the average, the currents being

known as "perigean currents.ft When the moon is :farthest rrom

the earth, the speed of the current is weaker than usual. These

latter currents are called "apogea[!. currents."

In the response to the moon's change in position from perigee

to apogee, it is found that, like the response in the case of

spring and neap ti-des, .there is a lag in the occurrence of

perigean and apogean currents. The stronger currents do not

occur on the day when the moon is in perigee but a day or two

later. Likewise, weak currents do not occur on the day of the

moon's apogee but a day or two later. This interval varies

somewhat from place to place, and in some regions it may have a
s

negative value. This lag is known as the "age of parallax

inequality" or "parallax age."

The third periodic variation in the speed of the tidal current

is that associated with the moon's changing declination. Since

the moon moves in an orbit inclined to the plane of the equator,

its declination is constantly changing during the month. When

it is on or close to the equator, the daily strengths of current

do not differ much; in other words, at such times morning and

afternoon currents resemble each other. As the declination

increases, differences between morning and afternoon currents

become pronounced and at the times of the moon's maximum semimonthly declination these differences are most marked. But

like the response to changes in the moon'.s phase and parallax,

there is a lag in the response to the change in geclination,

this lag beinf known as the "age of diurnal inequality" or

"diurnal age. Like the phase and parallax ages, the diurnal

age varies from place to place, being generally about 1 day,

but in some places it may have a negative value.

When the moon is on or close to the equator and the difference

between morning and afternoon currents small, the currents are

known as "equa tori al curren ts . " A t the time s ,of the moon's

maximum semimonthly declination, when the differences between

morning and afternoon currents are at a maximum, the currents

are called "tropic currents," since the moon is then near one

of the tropics.

There are other variations in the speed of the currents, but the

three discussed above are the most prominent. These three variations are exhibited by the current the world over but not everywhere to the same degree. In many regions the variation from

neaps to springs is the principal variation; in certain regions

it is the variation from apogee to perigee that is the principal

variation, and in other regions it is the variation from equatorial to tropic currents that is predominant.

The month of the moon's phases the synodic month) is approximately 2~ days in length; the month of the moon's distance

(the anomaJ.istic month) is approximately 27~ days in length;

the month of the moon's d~~lination (the tropic month) is

approximately 27~ days in length. It follows, therefore, that

considerable variation in the speed of the current occurs

during a year due to the changing relations of the three variations to each other.

Reversing Tidal Currents

In the entrance to a bay or in a river and, in general, where a

restricted width occurs, the tidal current is or the reversing

or rectilinear type; that is, the rlood current runs in one

direction ror a period or about 6 hours and the ebb current ror
6

a like period in the opposite direction. The .1'lood current sets

inland or upstream and the ebb current sets seawa~d or downstream.

The change .1'rom .1'lood to ebb gives rise to a period 0.1' slack

water during which the speed of the current is zero. An example

0.1' this type 0.1' current is given in Figure 2 which shows the

speed and direction 0.1' the current on a typical day.

Current speeds are given in knots, which is the unit generally

used in measuring tidal currents, and represents a speed of

1 nautical mile per hour. Since a nautical mile has a length

of 6,080 feet, knots may be converted into statute miles per

hour by multiplying by 1.15, or into feet per second by multiplying by 1.69.

3rStrength of flood

Rood '" ""

,

t#t

20

~

2

~ Strength of ebb

3L I . . . . . I . . . . . I . . , . . I . . . . . I

0 6 12 18 24

Hours

Fl.. 2 - Example of a typical reversl". current showll'. time ¥s. velocity for one day.

The curve depicting a reversing current resembles a tide curve.

The maximum. velocity of the flood current called the strength

of flood corresponds to the time of high water in the tide

curve, while maximum velocity of the ebb called the strength or

ebb corresponds to the low water. Since the moon in its apparent movement around the earth crosses a given meridian on the

earth on the average of 50 minutes later each day, the strength

of current at most places likewise comes 50 minutes later each

day. The current day, ~ike the tidal day and the lunar day,

has an average length or 24 hours and 50 minutes.

The current curve shown in Figure 2 represents the current near

the sur£ace in the axis o£ a channel. From observation and also

£rom theory it is known that the tidal current extenqs £rom the

gur£ace to the bottom. In general it may be said that the
1

velocity of the tidal current decreases from the surface to the

bottom, the velocity near the bottom being about two thirds that

at the surface. However, the effects of wind and fresh-water

flow may bring about considerable variation in the vertical

velocity distribution.

The current in a channel is also characterized by a variation

in the horizontal distribution of velocity. In a rectangular

channel of uniform cross-section, the velocity is greatest in

the center of the channel, and decreases uniformly to both sides

Combining both the vertical and horizontal variations, it may

be said that the average velocity of the current in a section

of a regular channel is about three-quarters that of the central

surface velocity.

Where the current is undisturbed by wind or fresh-water flow,

the flood and ebb velocities, and the durations of flood and

ebb are approximately equal. In this case, too, the characteristics of the current from the surface to the bottom are much

the same. That is, the strengths of the flood and ebb currents,

and also the slacks, occur at about the same time from top to

bottom. 11', however, nontidal currents are present, the characteristics of the tidal flow are modified considerably. The

effect of nontidal currents on tidal currents may be derived

rrom general considerations.

In Figure 3 a purely tidal current is represented by the curve,

referred to the line AB as the line of zero velocity. The

strengths of the flood and ebb are equal, as are also the durations of flood and ebb. In this case slack water occurs regularly 3 hours and 6 minutes (one-quarter of the current cycle

of 12 hours and 25 minutes) after the times of flood-and ebb

strengths. If now a nontidal current is introduced which sets

in the ebb direction with a velocity represented by the line CD,

the strength of ebb will obviously be increased by an amount

equal to CD and the flood strength will be decreased by the same

amount. The current conditions may now be represented by drawing, as the new line of zero velocities, the line EF parallel

to AB, and distant from it the length or CD.

Figure 3 now shows that the nontidal current not only increases

the ebb strength while decreasing the flood strength, but also

changes the times of slack water. Slack before flood now comes

later, while slack before ebb comes earlier. Hence the duration

of ebb is increased while the duration of flood is decreased.

If the velocity of the nontidal current exceeds that of the

tidal current at time of strength, the tidal current in the

opposite direction will be completely masked and the resultant

current will set at all times in the direction of the nontidal

currents. Thus, if in Figure 3 the line OP represents the
8

velocity of the nontidal current, the new axis for measuring the

velocity of the combined current at any time will be the line GH

and the current will be flowing at times in the ebb direction.

There will be no slack waters; but at ~eriod 6 hours 12 minutes

apart. there will occur minimum and maximum velocities represented,

respectively, by the lines RS and TU.

f"1g. 3 . Effect of nootidal current on reversing current.

Insofar as the errect of the nontidal current on the direction

of the tidal current is concerned, it is only necessary to remark

that the resultant current will set in a direction which at any

time is the resultant of the tidal and nontidal currents at that

time. This resultant direction and also the resultant velocity

may be. determined either graphically by the parallelogram of

velocities or by the usual trigonometric computations.

Types o~ Reversing Currents

Since tides and tidal currents are merely different aspects of

the tidal movement of the waters, the former being the vertical

movement and the latter the horizontal movement, it is to be

expected that tidal currents would show different types, corresponding to the different types of tide. Observations prove

this to be the case. Reversing currents may be readily classed

under three types:semidaily, daily, and mixed. The semidaily

type is one in which 2 flood strengths and 2 ebb strengths occur

in a tidal day with but little inequality between morning and

afternoon currents. Figure 2 represents this type of current

which is common alor!g the East Coast of the United States.

The daily type of tidal current is characterized by I flood and

I ebb in a day. The upper diagram ot Figure 4, which represents

the typical current in the entrance to Mobile Bay, Ala., exemplifies .this type ot current. The mixed type of tidal current

exhibits 2 floods and 2 ebbs in a day with considerable 1nequal~

ity in their speed between the torenoon and afternoon cycles.

The lower diagram of Figure 4, which represents the typical current in Rich's Passage, Puget Sound, Washington, illustrates

this type of current.
9

In general, it may be said that with reversing currents a given

type of current accompanies a like type of tide; that is, semidaily currents occur with semidaily tides, mixed currents with

mixed tides, and daily currents with daily tides. But as noted

in considering the variations in strength of current, the variations in the current that involve semidaily components vill

approximate corresponding changes in the range of the tide, while

in those involving daily components the variation in the current

is about half that in the tide. Hence the diurnal inequality in

the current at any place is generally less than in the tide at

that place.

Oh f!~- 12h ISh Oh

~

24h

Knots

2

0

2

2

0

3

Fig. 4 . Typical current curves showing daily and mixed types of reversing currents.

Relation or Time or Current to Time or Tide

In simple wave motion the times of slack water and strength or

current bear a constant and simple relation to the times or high

and low water. The two principal types of tidal motion are

progressive wave and stationary (standing) wave movements. A

progressive wave is one whose crest advances horizontally; the

times of high and low water progress from one end to the other.

The time of slack water comes midway between high and low water
10

and the time of strength of current at time of high and low

water. A stationary wave is one in which the water surface

oscillates vertically between fixed points called nodes without

progression. The points of maximum vertical rise and fall are

called antinodes. At the nodes there is no vertical motion and

maximum horizontal motion (strength of current). At the antinodes the water has no horizontal motion (slack) and maximum

vertical motion (high and low water).

Dura tion of Slack

In the change of direction of flow from flood to ebb, and vice

versa, the reversing tidal current goes through a period of

slack water or zero velocity. Obviously, this period of slack

is but momentary, and graphically it is represented by the

instant when the current curve cuts the zero line o~ velocities.

For a brief period each side o~ slack water, however, the current is very weak, and in ordinary usage "slack water" denotes

not only the instant o~ zero velocity but also the period o~

weak current. The question is there~ore frequently raised, how

long does slack water last?

To give slack water in its ordinary usage a definite meaning, we

may define it to be the period during which the velocity of the

current is less than one-tenth or a knot. Velocities less than

one-tenth of a knot may generally be disregarded for practical

purposes, and such velocities are, moreover, difficult to measure

either with float or with current meter. For any given current

it is now a simple matter to determine the duration of slack

water, the current curve rurnishing a ready means for this

determination.

In general, regarding the current curve as approximately a sine

or cosino curve, the duration o.f slack water is a .function o.f

the strength o.f current--the stronger the current the less ~he

duration o.f slack-~and .from the equation o.f the sine curve we

may easily compute the duration o.f slack water tor currents of

various strengths. For the normal flood or ebb cycle of 6h 12.0-

we may write the equation o.f the current curve y = A sin 0.483lt,

in which A is the velocity of the current in knots at time of

strength, 0.4831 the angular velocity in degrees per minute, and

t is the time in minutes from the instant o.f zero velocity.

Setting y. 0.1 and solving .for t (this value o.f t giving half

the duration o.f slack) we get ror the duration ot slack the following values: Por a current with a strength of 1 knot, slack

water is 24 minutes; tor currents of 2 knots strength, 12 minutes;

3 knots, 8 minutes" '4 knots, 6 minutes; 5 knots, 5 minutes;

6 knots, 4 minutes' 8 knots, 3 minutes 10 knots, 2 1/3 minutes.

For the daily type of current with a given strength, the duration

o.f slack is obviously twice that of a semidaily current with

like strength.
11

Velocity or Current and Progression or Tide

In the tidal movement of the water it is necessary to distinguish

clearly between the speed of the current and the progression or

rate of advance of the tide. In the former case reference is

made to the actual speed of a moving par~icle, while in the

latter case the reference is to the rate of advance of the tide

phase or the velocity of propagation of wave motion, which

generally is many times greater than the velocity of the current.

It is to be noted that there is no necessary relationship between

the velocity or the tidal current at any place and the rate of

advance or the tide at that place. In other words, if the rate

or advance or the tide is known we cannot rrom that alone inter

the speed of the current, nor vice versa. The rate of advance

of the tide in any given body or water depends on the type of

tidal movement. In a progressive wave the tide moves approximately in accordance with the formula r =..[ir , in which r is the

rate of advance or the tide, , the acceleration of gravity, and

1 the depth of the waterway. In stationary wave movement, we

have seen that the time of high water and low water occur at

very nearly the same time over a considerable area. Thus, there

is no progression of the wave present. When a combination of

progressive and stationary wave movements occur, the relation

between tide and current becomes quite complicated.

The velocity of the current, or the actual speed with which the

particles ot water are moving past any fixed point, depends on

the volume ot water that must pass the given point and the cross

section ot the channel at that point. The velocity ot the current is thus independent ot the rate ot advance ot the tide.

Rotary Tidal Currents

Within the channel or a bay or river, the current is compelled

to l~ollow the direction or the channel, upstream on the rlood

and downstream on the ebb. Out in the open sea, however, this

restriction no longer exists, the current having complete rreedom

so far as direction is concerned. Orfshore, therefore, tidal

currents are generally not or the reversing type. Instead or

flowing in the same general direction during the entire period

of the rlood and in the opposite direction during the ebb, the

tidal currents offshore change direction continually. Such currents are therefore called rotary currents. An example of this

type of current is shown in Figure 5, which represents the speed

and direction of the current at the beginning of each hour of

the ~orenoon for a typical day at Nantucket Shoals Lightship,

stationed ofr the coast of Massachusetts.

The current is seen to have changed its direction at each hourl~

observation, the rotation being in the direction of movement of

the hands of a clock, or rrom north to south by way of east, then

to north again by way to west. In a period of a little more
12.

than 12 hours it is seen that the current has shifted in direction completely round the compass.

It will be noted that the tips of the arrows, representing the

speeds and directions of the current at the. beginning of each

hour, define a somewhat irregular ellipse. If a number of observations are averaged, eliminating accidental errors and temporary

meteorological disturbances, the regularity of the curve is considerably increased. The average period of the cycle is found

to be l2h 25M. In other words, the current day for the rotary

current, like the tidal day, is 24h Sam in length.

A characteristic feature of the rotary current is the absence of

slack water. Although the current generally varies from. hour to

hour, this variation from. greatest current to least current and

back again to greatest current does not give rise to a period of

slack water.

1

Scale of Knots I I . . . . . . . . I ., 0.0 0.4 0.8 1.2

Fil. 5 . Example of a typical rotary current.
13

W~en the speed of the rotary tidal current is least, it is known

as the minimum current, and when it is greatest it is known as

the maximum current. The minimum and maximum speeds of the

rotary current are thus related to each other in the same way as

slack and strength of the rectilinear current, a minimum speed

following a maximum speed by an interval of about 3 hours and

being followed in turn by another maximum after a further interval of 3 hours.

With regard to the current curve, or current ellipse as it may

be called, which represents the rotary tidal current at any

place, the basic features are the relation of the major and minor

axis which determine the ellipticity of the curve, the direction

of rotation, and the direction of the major axis. If the major

and minor axis are nearly equal the ellipse will be nearly circular; if they differ greatly the ellipse will be flattened. In

the northern hemisphere the direction of rotation of the rotary

current is, as a rule, with the hands of a clock, while in the

southern hemisphere it is counter clockwise. But local hydrographic features may bring about a reversal of this general rule.

Rotary tidal currents are subject to the periodic variations

found in tides and reversing currents. These variations are

related to the changes in the phase, .parallax, and declination

of the moon. At times of full and new moon the velocity of the

rotary current is greater than the average, while at the times

of the moon's first and third quarters the velocities are less

than the average. Likewise when the moon is in perigee, stronger

currents occur, while when the moon is in apogee the currents

are weaker. In general it may be taken that the percentage of

increase or decrease in the velocity of the current in response

to changes in phase and parallax is the same as tM like increase

or decrease in the local range of the tide.

In response to changes in the declination of the Moon the rotary

current eXhibits diurnal inequality like the tide and reversing

current. This manifests itself as a difference between Morning

and afternoon current ellipses. When the moon is on the equator

the two current ellipses of a day are 1rIUch alike; but when the

moon .is near its maximum semiMonthly declination the two current

ellipses exhibit differences, principally in velocity.

Like tides and reversing currents, rotary tidal currents may be

grouped under the three types of semidaily, daily, and mixed.

The semidaily type of rotary current is one which exhibits two

full cycles within a tidal day, morning and afternoon currents

differing but little. The daily type is one in which but one

cycle occurs in a day, and the mixed type is one Which eXhibits

two cycles within a day but with considerable difrerences

between morning and a.fternoon currents. In addition to the

periodic variations to which rotary tidal currents are subject,

they also eXhibit rluctuations arising from the errects or nontidal currents.
Hydraulic Current

In addition to reversl.ng and rotary currents, there is a third

type called a hydraulic current. The term applies to a current

in a strait or tidal river that is caused by a difference in

head of water at the two entrances. When this difference in

head results from tidal action that causes the water at one end

to be alternately higher or lower than at the other, the tr.ovement

is periodic and may be treated as a reversing type of curr6nt.

The currents through the East River which connects New York Harbor wi th Long I sl and Sound are an example o~ hydraul i c curren ts .

When there is tidal action at each entrance to a strait, dif-

~erence in the head will result partly from any difference in

the range of tide and partly from any differences in the times

of the high and low waters. Theoretically, the current speed

will vary as the square root of the difference in head, will be

a maximum when this di~ference is greatest, and will be zero or

slack water when the difference is zero. Actually there will be

a lag of several minutes in response of the currents to this

difference in head due to inertia and friction in the waterway

itself.

Harmonic Constants

The reversing tidal current, like the tide, may be regarded as

the resultant of a number of simple harmonic movements, each of

the .form ., = A ~(at+e) ; hence, reversing tidal currents may be

analyzed in a manner analogous to that used in tides and the

harmonic current constants derived. These constants permit the

characteristics of the currents to be determined in the same

manner as the tidal harmonic constants, and they may also be

used in the prediction of the times o.f slack and the times and

velocities of the strength of current.

It can easily be shown that in inland tidal waters. like rivers

and bays. the amplitudes of the various current components are

related to each other. not as the amplitudes of the corresponding tidal components. but as these latter multiplied by their

respective speeds; that is. in any given harbor. if we denote

the various components of the current by primes and of the tide

by double primes, we have

... . ~ . ~" .K' .0, . - - "". . ~'. - ~"'. k VI'. 0' ,

m2.';'2.l~2. I' l'-".2m2- 2';'2."2l~2. IAl.O. 1

where the gmall italic letters represent, respectively, the

angular speed or the corresponding components. This shows at

once that the diurnal inequality in the currents should be approximately half that in the tide.

RotQry currents may likewise be analyzed harmonically, but in

this case it is necessary to resolve the hourly velocity and

direction o~ the current into two components, one in the north
15

and south direction and the other in the east and west direction.

Each set of hourly tabulations is then treated independently and

analyzed in the usual manner. When the two sets of harmonic

constants have been derived the like-named constants of the

north and south and east and west directions may be combined into

a single resultant, which will be an ellipse, either graphically

or by means of the formula

H 2. 2 H 2.

tan 26 = ~12~~~ ~~1~ ~22~ ~~z

HI ~ 2~I+H22~ 2~2

which may be derived by writing each harmonic constant in the

.form .=H1 ~(8-~1) .for the north and south component and

v=H2~(8-~2) .for the east and west component.

Reduction Methods and Results

The purpose in studying tidal currents is to determine their

speed and direction through direct observations ot the speed

and direction ot the current in a tidal body ot water and to

MAke such data available to the general public. Two types or

reduction--harmonic and nonharmonic--are used in s.tudying tidal

currents. A harmonic analysis proceeds through several complicated mathematical procedures to determine harmonic constants

which in turn are used in the prediction or the daily current

at that place.

The mathematics involved is beyond the scope of this paper but

is explained in detail in other C&GS manuals. "Harmonic Constants" has been de.fined in a previous section. A nonharmonic

analysis determines the average speed and direction o~ the current and is a relatively simple reduction. A sample computation

is shown in Fig. 6. Here the observed times of slack water and

strengths o.f .flood and ebb are compared to the predicted times

of their respective phases at a nearby reference station. A

reference station is a place for which daily p!gedictions are

given in the annual tidal current tables and the type of current

is similar in times and velocities to the secondary stations

being reduced.

Thus in selecting a reference station to which to refer any

series of tidal current observations, its characteristics must

be studied and compared with the secondary stations tor which

new data arc being reduced. It no suitable station is available

in the survey area, one must be developed in order that the stations can adequately be reduced.

Likewise the observed speeds and directions of the current at a

secondary station are summed and averaged for flood and ebb.

The velocity of the observed tidal current may be reduced to a

mean value by the application of a ractor derived rrom the current velocity at the rererence station. In using such a station,
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the factor is obtained by dividing the best determined average

speed at the reference station by the average speed .for the

period covered by the observations.

Publishing the Results

Two different types of publications are issued by the Coast and

Geodetic Survey to include results of the tidal current surveys.

Tidal Current Tables are published annually for both the Atlantic

and Pacific Coasts of North America. The other is a series of

Tidal Current Charts for various tidal estuaries on both Atlantic

and Pacific Coasts. Each of these publications is based on

observations obtained over Mm1Y years of current surveys.

The Tidal Current Tables have been published annually since 1890.

They first appeared as part of the Tide Tables and consisted of

brief directions ror obtaining the times of the current for a

few locations. Later daily predictions of slack water were

given. By 1923, the tables had so expanded that they were

issued as a separate publication called "Current Tables, Atlantic

Coast" and "Current Tables, Pacific Coast." A few years later,

the daily predictions were extended to include the times and

speeds of maximum current. Toda¥, each Table is divided into

several tables. Table 1 (Fig. 7) giV9S the predicted times of

slack water and the predicted times and velocities of the maximum

current--f10od and ebb--for each day of the year for a number of

places along the Atlantic and Pacific Coasts.

Table 2 (Fig. 8) furnishes data which will enable the user to

determine the approximate time of slack water and the time and

velocity of maximum current at numerous stati~ns on both the

Atlantic and Pacific coasts. Given for each station are time

differences of slack water and maximum current and flood and ebb

velocity ratios with respect to some stations for which daily

predictions are also given. Finally the'direction and average

speed of maximum flood and ebb are also included in this section

The Tidal Cur'rent Tables also contain data on rotary stations,

Gulf Stream, wind driven currents, etc., all of which may be of

interest to the mariner.

Each T~dal Current Chart (Fig. 9) gives a comprehensive view of

the hourly speed and direction of the current throughout each of

the tidal estuaries tor which a chart has been published. Each

chart also provides a means tor determining the speed and direction of the current at various places covered by each chart.

Pig. 7 - Sample page of predictions for the Narrows, New York

Harbor, N.Y.

Fig. 8 - Sample page of Table 2 showing several places referred

to the Narrows.

Fig. 9 Sample page from a Tidal Current Chart.
18

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19

TAIlE 2.-CUlaENT DlffEftNCES AND 0"*- CONSTANTS 161

~I~M CI.8fNTS T\Mf DlF.

FEIfNCES

velOCITY

IATlOS ~

Flood Ebb

~

PlACE

~

- I cwr..." ~- "--IIood -~ ~1""'1 '8C' Iveioc- A_" I Dirwc' (truel

- - ---~--

A_.

-

.-Ioc. i",

~ L~.

.,

2250

2255

2260

2265

la7P

2275

1280

1. M. I.. M. : c..c. i .,.

.. TIE '.i2 ~

fl.. ..rldl_. ?~.. I

-020 -0 40 1.5 / 10 &SO I.' lorD

+0 15 0 00 1.' 1.2! 80 2.4 245

-100 -05& 1.8 1.& &51 &.ll215

-0 10 +0 10 0.& 0.& T& 0.&1 ITS

-1 25 -11& 1.1 1.1 40 I 1.1 811

s..c table &.

s..c table &. I

40 34

40 35

40 38

40 35

403'7

2310

231~

2320

2325

2330

233~

2340

7S 58

7.. Ol

7.01

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7.. 01

7.. 01

7.. OSI

38,

39,

40'

39:

41 ;

42

LOla Ia.AlD, So.th Cout-COfttl..ed ! I. I. I Shlnnecock Inlet - 40 81 72 89!

Fi..e I. Inlet, 0.5 IIIi. S. of ~k Beech1 40 38 '7a 18;

Jones InJet 40 S8i '7a S4

Long Beech, Inside, between b..ldges--- 40 Sf V3 401

Eest Rockewey In let 40 ~5 15 4~ Ambrose Chennel Lightshlp--- - ,--- ~ 271 V3 .9

Sandy ~ App. Lighted Horn aooy M- 40 27 'S 55

~IU lAY

2a&5 Rockaway Inlet--

2290 Be en Island, east of2SOO Beech Channel (b..ldge>'

2305 Grass Hessock Channel.

lEI YOlK HARloa EITRAICE I

I ~ose Chennel ent..ence 40 SO

Mbr-ose Channe/., SE. of West Benk Lt- 40 sa

Coney Is/end Lt., 1.6 .lles SSW. of 40 S~

AmO.-ose Channel, north end 40 ~.

Coney Island, 0.2 .lle west of 40 S5

Ft. Lafayette, channel .-st of 40 S6

THE NARROWS, .Idchennel 40 S7

lEI YOlK HARI~, U"er I.,

2345 Tompki"sville ~===

8.160

I Robbins Reef Light, east of.

23&5 Red 1t)Ok, 1 1111 Iewest of2310 Statue of Liberty, east ofIUDSOI RlfEI, Nidchaftne'-

23'75 The Bei"t...y, northwest of 43'4 ~ I +1 SO +1 S5 O. 1.'- I 15 1. I 195 2.S

238C Desb..osses S~ t 43 1 74 01 +1 S8 +1 40 0.9 1.a 10 1.8!-- a.s

2385 Chelsea Docks 45'4 Ol +130 +1 40 1.0 1.0 aD 1.7 185 2.0

2390 For~y-s8Cond Street 46'4 00 +1 35 +1 4D 1.0 1.1 30 1. 2.3

2395 Nlnety-slJC1'h S'trHt 48 '7a 59 +1 40 +1 50 1.0 1.1 30 1.' -- ! 2.3

2400 Grants Tomb, 123~ S'tr..~ 49 '7a 58 +1.8 +1 85 0.9 1.1 25, 1.4 2.3

2tOS George N8shl~~ton Brldge 51 V3 57 +1.5 +2 00 0.9 1.1 20 1.& 200 2.2

2410 Spuyten Duyvl' 53 73 5& +2 00 +2 10 0.9 1.1 ao 1.& -- 1.1

2.15 Rlv...d8 I e 54 V3 55 +2 05 +2 20 0.8 1.0 111 1.4 200 2.0

2420 Dobbs F y 01 V3 53 +. 25 +2 40 0.8 0.9 10 1.a - 1.'

.425 Ta ytown 05 f3 83 +2 40 I +2 55 0.4 0.8 1.1 -- 1.1

2430 Osslnlng 10 V3 84 +2 58! +a 10 0.5 0.' 0.9 --- 1.S

2435 HBverstrew 12 f3 57 +a 05 I +a 15 0.5 0.7 0.8 -- 1.3

2440 ~sk 111 17 '7a 57 +3 20 I +a a5 0.5 0.1 0.8 ~.2

2445 Bee.. ~nteln Brldge 19 f3 59 +a 25 +a 40 0.5 0.4 0.8 - 1.1

2450 HI9hlend Fells 22 '7a 58 +a 35 +a eo 0.1 0.4 1.0 188 I 1.2

2455 West A)int, off Duck Island-' U '7a 87 +3 401 +3 55 0.5 0.6 101 1.0 - 1.1

ICur..ent is ..ote..y, 1u..ning clockwise. Mini~ cur..ent of 0.9 knot sets SW. abou~ ~ime of "Slack.

flood beglnsw at The Na..rows. Mlnl.um cu ent of 0.5 knot sets ME. about 1 hour before wSlack, ebb

begIns" et The ows.

i_xl- flood, .{Io 500: _xi- ebb, f(1' 5&-.

'Flood begins, -2. ~5.: maxiMum flood, -QA 058: ebb begins, ~ 05-: -'XlnuM ebb, -1. 50-.

-The values for the Hudson River ...e for ~he su..er months, when the f..esh-wat.. discharge is a

. .

III'nl_.

0

aao

aI&

0

0

&

FiC. 8 . Sample pa.e of Table 2 showin. places referred to the Narrows.
~Q-

-

AheM_".

"'-

...OJTIDAL CURRENT CHAI

~~1

\.

"

:.

,.

!

'"\

UPPER CHESAPEAKE BAY

The arrows show the dlT«tlon. and th.

fig- tM s~ s~ In knob o( tM ~t

at time Indicat" at bottom o( chart.

This chart Is design.d (or use with tM

predicted tlma and l1elocitla o(th. CU1'rent

for Baltimore Harbor Approach. Th. doil"

predictions are gi~n In th. Tidal Current

Tabla. Atlantic Coast of North America

published annual/" b" the Envlronm.ntal

Sden" s...111ca Admlnistnrtlon. Cod-ct and

G.od.tIcSUnIeI/.

NOTE: Speeds shown are lor time 01 spring

currents. To tktermine tM sp.-t ror a

particular time. these speeds must be adjusted bll use 01 the table .. FGdors

ror Correcting ~.. '*- on Po.-l. .~

NAtmCAL IOUS

.

5~ 3 2 1 0
2l

References

Following is a partial list of references for additional infor

mati on on tidal currents:

Carson, Rachel. 'iThe Sea Around Us. II New York, Oxford University Press, 1951. A famous best seller and very readable

Coker, Robert E. "This Great and Wide Sea," New York, Harper

1962. Readable college text.

Defant, Albert. "Ebb and Flow; The Tides or Earth, Air and

Water." Ann Arbor, University or Michigan Press, 1960.

Deals mainly with ocean tides; very fine.

MaI'lller, H. A. "The Sea."

Very readable.

New York, D. Appleton and Co., 1930.

Sverdrup, H. U., Johnson, M. W., and Fleming, R. H. "The

Oceans, Their Physics, Chemistry and General Biology.'f

Englewood Clit't's, N.J. Prentice-Hall, 1962. Technical.

Coast and Geodetic Survey, ESSA. "Tidal Current Tables .ft

Washington, U.S. Government Printing Office. Two volumes

published annually and sold by the U.S. Coast and Geodetic

Survey.

u.s. Naval Oceanographic Ot't'ice. "American Practical Navigator."

Part six, Oceanography, R.O. Pub. No.9. Washington,

Government Printing Ot't'ice, 1958.

u.s. Naval Oceanographic Office. "A Suuunary of Tides and Currents," Informal Manuscript Report No. 0-21-65.

Unpublished Washington, Manuscript. u.s. Naval Oceanographic Office, 1965., ..

Arx, William S. "An Introduction to Physical Oceanography.

Reading, Mass., Addison-Wesley, 1962.